CA2302242C - Method for optimizing spectral re-use - Google Patents
Method for optimizing spectral re-use Download PDFInfo
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- CA2302242C CA2302242C CA002302242A CA2302242A CA2302242C CA 2302242 C CA2302242 C CA 2302242C CA 002302242 A CA002302242 A CA 002302242A CA 2302242 A CA2302242 A CA 2302242A CA 2302242 C CA2302242 C CA 2302242C
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
- H04W16/14—Spectrum sharing arrangements between different networks
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/005—Control of transmission; Equalising
Abstract
A method for optimizing spectral re-use between an interferer cellular system and a desirable cellular system is disclosed wherein an acceptable baseband signal to interference ratio (SIR) is determined, and an interference reduction factor (IRF) is determined. The ratio of the SIR to the IRF is determined, and the fourth root of the determined ratio is determined, which fourth root represents the optimal minimum ratio of the distance of a mobile unit from an interferer cellular system to the distance of the mobile unit from a desirable cellular system.
Description
METHOD FOR OPTIMI~:CNC2 SPEC;'.TRAL RE-USE
TECHNICAL FIELD OF THE TNVENTION
The invention relates generally to radio communications and, more particularly, to a method for optimizing spectral. re-use f,:~x- xTad.ic;~ c.~ommunications.
BACKGROUND OF THE IN17EN"f TON
The advent of Personal. Commm.nication Services (PCS) has resulted in a tremendous increase in the demand for spectrum. To meet this demand, cii f ferent servic:;e providers might rzave to share the scarce spectrum allocated, necessitating several diff:erez~t.: acccss> schemes ernplc~ying different modulation techniques to co-exist. Since optimum spectral re-use i.s of pra.mary cc7z~zc~errz, estimation of both co-channel and adjacent channel (i.e., "interchannel") interference from irzterfer~ers ire the same system (due to frequency re-use) as well as from other systems and services sharing the same band is ver~,r i.mpc>rtar :. ~lhile the effects of adjacent channel interference can be mitigated by good filter design and good frequez~.cy p~.aziz~,ing techrzique:~, co-channel interference remains as a l.i.ma.ti.n.g factor_ for systems sharing the same band. Additionally, the interference between WO 99/12371 PC'f/IB98/01355 co-existing networks is a source of regulatory problems.
One particular type of interference which is becoming more prevalent is interference of systems which use analog (e. g., phase modulated (PM)) signals by systems which use digital (e. g., QPSK or MSK) signals. This type of interference is becoming more prevalent because, while the majority of present systems are analog, users are switching to digital systems because they are less prone to noise, they provide greater security against eavesdropping and theft of services, they permit cell phones to be smaller, lighter, and require less battery power than analog cell phones, and they provide services such as e-mail and headline news which are not available with analog systems. It can be appreciated, therefore, that techniques for optimizing spectrum efficiency with respect to digital signals are becoming increasingly important due to the expected scarcity in the bandwidth available for wireless communication systems. Spectrum-sharing enhances both the spectral utilization and the flexibility of that utilization and, as a result, provides additional capacity to networks. However, to obtain optimal spectral re-use, channel allocation and channel spacing of co-existing systems must be coordinated.
The effects of interchannel interference on analog signals by digital signals are, however, different from the effects on analog signals by analog signals and are not well known in the prior art.
Because the precise interference effects of digital signals on analog signals is not well known, the SUBSTITUTE SHEET (RULE 26) spectral re-use with respect to digital signals can not be optimized using conventional techniques.
Therefore, what is needed is a method for analyzing the interchannel interference effects of digital signals on analog signals and, furthermore, for utilizing such analysis to coordinate channel allocation and channel spacing of co-existing systems so that spectral re-use may be optimized when digital signals interfere with analog signals, and so that network capacity may be enhanced.
TECHNICAL FIELD OF THE TNVENTION
The invention relates generally to radio communications and, more particularly, to a method for optimizing spectral. re-use f,:~x- xTad.ic;~ c.~ommunications.
BACKGROUND OF THE IN17EN"f TON
The advent of Personal. Commm.nication Services (PCS) has resulted in a tremendous increase in the demand for spectrum. To meet this demand, cii f ferent servic:;e providers might rzave to share the scarce spectrum allocated, necessitating several diff:erez~t.: acccss> schemes ernplc~ying different modulation techniques to co-exist. Since optimum spectral re-use i.s of pra.mary cc7z~zc~errz, estimation of both co-channel and adjacent channel (i.e., "interchannel") interference from irzterfer~ers ire the same system (due to frequency re-use) as well as from other systems and services sharing the same band is ver~,r i.mpc>rtar :. ~lhile the effects of adjacent channel interference can be mitigated by good filter design and good frequez~.cy p~.aziz~,ing techrzique:~, co-channel interference remains as a l.i.ma.ti.n.g factor_ for systems sharing the same band. Additionally, the interference between WO 99/12371 PC'f/IB98/01355 co-existing networks is a source of regulatory problems.
One particular type of interference which is becoming more prevalent is interference of systems which use analog (e. g., phase modulated (PM)) signals by systems which use digital (e. g., QPSK or MSK) signals. This type of interference is becoming more prevalent because, while the majority of present systems are analog, users are switching to digital systems because they are less prone to noise, they provide greater security against eavesdropping and theft of services, they permit cell phones to be smaller, lighter, and require less battery power than analog cell phones, and they provide services such as e-mail and headline news which are not available with analog systems. It can be appreciated, therefore, that techniques for optimizing spectrum efficiency with respect to digital signals are becoming increasingly important due to the expected scarcity in the bandwidth available for wireless communication systems. Spectrum-sharing enhances both the spectral utilization and the flexibility of that utilization and, as a result, provides additional capacity to networks. However, to obtain optimal spectral re-use, channel allocation and channel spacing of co-existing systems must be coordinated.
The effects of interchannel interference on analog signals by digital signals are, however, different from the effects on analog signals by analog signals and are not well known in the prior art.
Because the precise interference effects of digital signals on analog signals is not well known, the SUBSTITUTE SHEET (RULE 26) spectral re-use with respect to digital signals can not be optimized using conventional techniques.
Therefore, what is needed is a method for analyzing the interchannel interference effects of digital signals on analog signals and, furthermore, for utilizing such analysis to coordinate channel allocation and channel spacing of co-existing systems so that spectral re-use may be optimized when digital signals interfere with analog signals, and so that network capacity may be enhanced.
SUBSTITUTE SHEET (RULE 26) SUMMARY OF THE INVENTION
According to the present invention, spectral re-use is optimized by determining an apt::irnal guard band to use with adjacent channel interference, o~:~ b~~ determining an optimal guard zone to use with c:o-channel interference.
This is achieved by determining the e~:'fec:t of digital interference on the baseband. :~:i.gna:~ of an analog system. By the use of this invention, the c:apac~.t::y crf a system and/or the quality of a service pro°sri.de~c~ lay ~u system may be enhanced.
The invention may be swmmax°i. zed. as a methcad for optimizing spectral re-use between an i.nterferer digital phase modulated cellular system (220) utilizing a first transmitter/receiver (704) configurable to operate substantially at a first frequer~cyY Grid a desirable analog phase modulated cellular system ( a.1() ) utilizing a second transmitter/recei.ver (702) c~:z~f~.gwrc~ble to aperat:e substantially at a second frequency, the first and second transmitter/receivers being separated by a re-use distance, the method being characterized by true steps of: determining a carrier-to-interference .rat~ia (oIF~) with reference to the re~-use distance; setting an acceptable baseband signal-to~-interference ratio (SIR); determinincs an interference reduction factor (IRF) as the ratio of the SIR to the CIR;
determining an optimum frequency separation fd with reference to the power spectral density of the randc:~m phase angle, an interference-to-signal-carriex pawex° ratira, and autocorrelation functions of the baseband phase modulated processes; configuring the fa.rst transmitter (704) to operate substantially at the first frequency; and configuring the second transmitter (7~.')2) to operate substantially at t:he second frequency, wYuerein the second frequency is substantially separated ~.n bandwidth from the first frequency by at least the determined frequency separation fd.
According to another aspect the invention provides a method for optimizing spectral re-use between an interferer digital phase rnodulatec~ ceJ..lular system (120) utilizing a first: base station antenrua ( 70~) ope.rat~ve substantially at a. first frequency, and a desirable analog phase modulated cellular system (110) utilizing a second base station antenna (702') operative substantially at a second frequency, tree first frequency arid second frequency being substantially separated ir:~t~andwidth by a frequency separation of fd, the method being further characterized by the steps of: determining the power spectral density of the random phase angle at the separatzor~ frequency fa, with reference to the interference--t.c:~--sigr~a.l carr:i.er power ratio, the separation frequency fd, and autocorrelation functions of the baseband phase modulated processes; determining an interference reduction factor (IRF) with reference to the baseband power spectral density of the desired signal, the power spectral density o~~ a :ranciorri phase angle at f~~, .and an interference carrier--to-signal c;arrz.ex power ratio; setting an acceptable baseband sigx~al~-to--i.nt.erference ratio (SIR) ;
determining a carrier-to-interference ratio (CIR) as a ratio of the SIR to the IRF; determining the re-use distarxce with reference to the CIR; and spacing apaz°t the first: base station antenna (704) and the second base station antenna (702) to obtain at least the determined re-use distance therebetween.
~a BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:
FIGURE 1 is a schematic diagram of two systems which coexist in one area.
FIGURE 2 is a schematic diagram of two systems which coexist in adjacent areas.
FIGURE 3 is a chart showing, in the frequency domain, adjacent channel interference which is in-band.
FIGURE 4 is a chart showing, in the frequency domain, adjacent channel interference which is out-of-band.
FIGURE 5 is a chart showing, in the frequency domain, co-channel interference.
FIGURE 6 is a block diagram showing an analog phase modulated system.
FIGURE 7 is a schematic diagram showing a link between two systems.
FIGURE 8 is a chart illustrating a normalized MSK
spectrum.
FIGURE 9 is a chart illustrating a normalized QPSK spectrum.
FIGURE 10 is a chart illustrating a spectrum of an FM signal having a bandwidth of 30 kHz and an RMS
mod index of 1.19.
FIGURE 11 is a chart illustrating an interference spectrum of two identical FM signals having an RMS mod index of 1.19 and B/2W = 3.75.
FIGURE 12 is a chart illustrating an interference spectrum of an FM desired signal and an MSK interferer across a 30kHz bandwidth.
SUBSTITUTE SHEET (RULE 26) WO 99/12371 PC'T/IB98/01355 FIGURE 13 is a chart illustrating an interference spectrum of an FM desired signal and an QPSK
interferer across a 30kHz bandwidth.
FIGURE 14 is a chart summarizing FIGS. 11-13 without normalization.
SUBSTITUTE SHEET (RULE 26) DETAILED DESCRIPTION OF THE INVENTION
Referring to FIGURES 1 and 2, the reference numerals 100 and 102, respectively, generally designate first and second areas, each of which have two coexisting cellular systems 110 and 120, such as cellular base stations or any fixed stations. The systems 110 and 120 may use different modulation schemes, occupy different bandwidths, have different propagation characteristics, and/or have different access schemes.
The systems 110 and 120 are shown in FIG. 1 as coexisting in one area (i.e., have coverage overlay) resulting primarily in adjacent channel interference (ACI). Also shown in FIG. 1 is a frequency spectrum overlay 130 which depicts, in a frequency domain, a band 132 of frequency channels used by the system 110 and a band 134 of frequency channels used by the system 120. A guard band 136 comprising a band of unused frequencies separating the bands 132 and 139, is provided to minimize interference between the two systems 110 and 120.
ACI may be classified as either "in-band" or "out-of-band". In-band ACI is illustrated in FIGURE
3, wherein a center 300 of an interfering signal bandwidth 302 falls within a bandwidth 304 of a desired signal. Out-of-band ACI is illustrated in FIGURE 4, wherein a center 400 of an interfering signal bandwidth 402 falls outside of a bandwidth 404 of a desired signal.
Referring back to FIG. 2, the systems 110 and 120 are shown there as coexisting in adjacent overlays SUBSTITUTE SHEET (RULE 26) (i.e..; have coverage non-overlay) resulting primarily in co-channel interference (CCI). Also shown in FIG.
2 is a frequency spectrum overlay 140 which depicts, in a frequency domain, a band 192 of frequency channels used by the system 110, and a band 144 of frequency channels used by the system 120. The bands 142 and 144 overlap each other in a CCI band 146 in which some frequency channels are re-used by both of the systems 110 and 120. As a result of the CCI band 146, a guard zone 148 defining a geographical distance between the systems 110 and 120 is established to minimize interference between the two systems 110 and 120 in the CCI band 146.
FIGURE 5 graphically depicts CCI, which is the dominant interference in frequency re-use systems arranged as the system 110 and 120 are in FIG. 2. As shown in FIG. 5, with CCI, a desired signal 500 and an interfering signal 502 make use of the same carrier frequency 504.
FIGURE 6 illustrates a conventional analog phase modulated (PM) system 600 which is often "victimized"
by ACI and CCI from digital systems. The PM system 600 comprises a PM transmitter 602, such as a cellular base station, and a PM receiver 604, such as a cell phone within the coverage of the PM transmitter 602.
The PM transmitter 602 includes an amplifier 606 configured for receiving and amplifying an input baseband signal m(t) and passing an amplified signal ~g(t) to an angle modulator 608. The modulator 608 is configured for outputting a modulated carrier signal s(t) to an antenna (not shown) for transmission to the PM receiver 604. The signal s(t) is degraded into a SUBSTITUTE SHEET (RULE 26) WO 99/11371 PC'T/IB98/01355 signal r(t) by interference i(t) and noise n(t) received symbolically at a summer 609. The PM
receiver 604 includes an intermediate frequency (IF) filter 610 configured for receiving and filtering the degraded signal r(t), and is connected for passing a filtered signal to a limiter 612. The limiter 612 is configured to pass an amplitude limited signal to an ideal angle demodulator 614 which demodulates the signal. The demodulator 614 is connected for passing the demodulated signal to a low pass filter 616 configured to filter out noise and undesirable frequencies and to output the baseband signal m(t) (with added interference and noise) for use, such as by a telephone receiver (not shown). Because analog phase modulated systems such as the system 600, and the operation of such systems, are well known to those skilled in the art, they will not be described in further detail herein.
For the purpose of illustration, it will be assumed that the system 110 (FIGS. 1-2) is an analog phase modulated system such as the system 600 (FIG.
6), and that the system 120 (FIGS. 1-2) is a digital system that generates ACI (FIG. 1) or CCI (FIG. 2) which interferes with the system 110. Then, to determine the optimal guard band 136 (FIG. 1), the optimal guard zone 148 (FIG. 2), or the optimal capacity of the systems 110 and 120, the effect of digital interference i(t) (ACI or CCI, respectively), on the baseband signal m(t) output by the PM receiver 609 of the system 110 must be determined. Noise n(t) may be neglected in determining the optimal guard band and optimal guard zone because the signal is limited much more by interference than by noise.
SUBSTITUTE SHEET (RULE 26) in accordance with a method of the present invention, closed form expressions for the baseband interference. spectra are determined as a function of the RF carrier-to-interference (CIR) ratio, which can be translated into the co-channel re-use ratio.
System performance is determined by the baseband signal-to-interference (SIR) ratio. From the interference spectral density, the baseband SIR at a spot frequency, where the interference is a maximum or the SIR is minimum, is determined.
The method the present invention may be more clearly understood with reference to FIGURE 7, which illustrates the cellular systems 110 and 120 as coexistent in adjacent areas (i.e., coverage non-overlay), as was shown in FIG. 2. As shown in FIG. 7, two distances dl and d2 are depicted. The distance dl represents a worst case distance from a mobile unit 700 to a transmitter 702 centrally located within the system 110, depicted herein as a desired system. The distance d2 represents a distance from the mobile unit 700 to a transmitter 704 centrally located within the system 120, depicted herein as an interferer system.
For the sake of example, the interference reduction factors -IRF = Signal Spectral Density __ ~_z /2W
Maximumlnterference Spectral Density S~ {0) / R 2 are calculated for different modulation techniques which may be used, as discussed below with respect to Equations 19-21 and Tables 2-4, for a bandwidth of 30 kHz, and for an interference to signal carrier power ratio of RZ - 0.01 (corresponding to a carrier to interference ratio (CIR) of 20 dB), when both signal SUBSTITUTE SHEET {RULE 26) and interference are non-fading. The IRF values for CCI are summarily tabulated as follows:
Modulation IRF
Phase Modulation 6.g3 dB
(PM) Quadrature Phase Shift Keying 9.31 dB
(QPSK) Minimum Shift 10.14 dB
Keying (MSK) In accordance with the present invention, the signal to interference ratio, SIR, at the baseband may be computed as the sum of CIR and IRF. Accordingly, if an SIR of 30 dB is acceptable, then to achieve such SIR, the required CIR resulting from CCI for each type of modulation would be calculated as follows:
SIR - IRF = CIR
For PM: 30 dB - 6.83 dB = 23.17 dB
For QPSK: 30 dB - 9.31 dB = 20.69 dB
For MSK: 30 dB - 10.14 dB = 19.86 dB
It is well known that:
CIR =_ C d., r I d, The value for 7(' is generally between 2 and 6, and will be considered to be 4 for this example.
Accordingly, for the different modulation techniques:
According to the present invention, spectral re-use is optimized by determining an apt::irnal guard band to use with adjacent channel interference, o~:~ b~~ determining an optimal guard zone to use with c:o-channel interference.
This is achieved by determining the e~:'fec:t of digital interference on the baseband. :~:i.gna:~ of an analog system. By the use of this invention, the c:apac~.t::y crf a system and/or the quality of a service pro°sri.de~c~ lay ~u system may be enhanced.
The invention may be swmmax°i. zed. as a methcad for optimizing spectral re-use between an i.nterferer digital phase modulated cellular system (220) utilizing a first transmitter/receiver (704) configurable to operate substantially at a first frequer~cyY Grid a desirable analog phase modulated cellular system ( a.1() ) utilizing a second transmitter/recei.ver (702) c~:z~f~.gwrc~ble to aperat:e substantially at a second frequency, the first and second transmitter/receivers being separated by a re-use distance, the method being characterized by true steps of: determining a carrier-to-interference .rat~ia (oIF~) with reference to the re~-use distance; setting an acceptable baseband signal-to~-interference ratio (SIR); determinincs an interference reduction factor (IRF) as the ratio of the SIR to the CIR;
determining an optimum frequency separation fd with reference to the power spectral density of the randc:~m phase angle, an interference-to-signal-carriex pawex° ratira, and autocorrelation functions of the baseband phase modulated processes; configuring the fa.rst transmitter (704) to operate substantially at the first frequency; and configuring the second transmitter (7~.')2) to operate substantially at t:he second frequency, wYuerein the second frequency is substantially separated ~.n bandwidth from the first frequency by at least the determined frequency separation fd.
According to another aspect the invention provides a method for optimizing spectral re-use between an interferer digital phase rnodulatec~ ceJ..lular system (120) utilizing a first: base station antenrua ( 70~) ope.rat~ve substantially at a. first frequency, and a desirable analog phase modulated cellular system (110) utilizing a second base station antenna (702') operative substantially at a second frequency, tree first frequency arid second frequency being substantially separated ir:~t~andwidth by a frequency separation of fd, the method being further characterized by the steps of: determining the power spectral density of the random phase angle at the separatzor~ frequency fa, with reference to the interference--t.c:~--sigr~a.l carr:i.er power ratio, the separation frequency fd, and autocorrelation functions of the baseband phase modulated processes; determining an interference reduction factor (IRF) with reference to the baseband power spectral density of the desired signal, the power spectral density o~~ a :ranciorri phase angle at f~~, .and an interference carrier--to-signal c;arrz.ex power ratio; setting an acceptable baseband sigx~al~-to--i.nt.erference ratio (SIR) ;
determining a carrier-to-interference ratio (CIR) as a ratio of the SIR to the IRF; determining the re-use distarxce with reference to the CIR; and spacing apaz°t the first: base station antenna (704) and the second base station antenna (702) to obtain at least the determined re-use distance therebetween.
~a BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:
FIGURE 1 is a schematic diagram of two systems which coexist in one area.
FIGURE 2 is a schematic diagram of two systems which coexist in adjacent areas.
FIGURE 3 is a chart showing, in the frequency domain, adjacent channel interference which is in-band.
FIGURE 4 is a chart showing, in the frequency domain, adjacent channel interference which is out-of-band.
FIGURE 5 is a chart showing, in the frequency domain, co-channel interference.
FIGURE 6 is a block diagram showing an analog phase modulated system.
FIGURE 7 is a schematic diagram showing a link between two systems.
FIGURE 8 is a chart illustrating a normalized MSK
spectrum.
FIGURE 9 is a chart illustrating a normalized QPSK spectrum.
FIGURE 10 is a chart illustrating a spectrum of an FM signal having a bandwidth of 30 kHz and an RMS
mod index of 1.19.
FIGURE 11 is a chart illustrating an interference spectrum of two identical FM signals having an RMS mod index of 1.19 and B/2W = 3.75.
FIGURE 12 is a chart illustrating an interference spectrum of an FM desired signal and an MSK interferer across a 30kHz bandwidth.
SUBSTITUTE SHEET (RULE 26) WO 99/12371 PC'T/IB98/01355 FIGURE 13 is a chart illustrating an interference spectrum of an FM desired signal and an QPSK
interferer across a 30kHz bandwidth.
FIGURE 14 is a chart summarizing FIGS. 11-13 without normalization.
SUBSTITUTE SHEET (RULE 26) DETAILED DESCRIPTION OF THE INVENTION
Referring to FIGURES 1 and 2, the reference numerals 100 and 102, respectively, generally designate first and second areas, each of which have two coexisting cellular systems 110 and 120, such as cellular base stations or any fixed stations. The systems 110 and 120 may use different modulation schemes, occupy different bandwidths, have different propagation characteristics, and/or have different access schemes.
The systems 110 and 120 are shown in FIG. 1 as coexisting in one area (i.e., have coverage overlay) resulting primarily in adjacent channel interference (ACI). Also shown in FIG. 1 is a frequency spectrum overlay 130 which depicts, in a frequency domain, a band 132 of frequency channels used by the system 110 and a band 134 of frequency channels used by the system 120. A guard band 136 comprising a band of unused frequencies separating the bands 132 and 139, is provided to minimize interference between the two systems 110 and 120.
ACI may be classified as either "in-band" or "out-of-band". In-band ACI is illustrated in FIGURE
3, wherein a center 300 of an interfering signal bandwidth 302 falls within a bandwidth 304 of a desired signal. Out-of-band ACI is illustrated in FIGURE 4, wherein a center 400 of an interfering signal bandwidth 402 falls outside of a bandwidth 404 of a desired signal.
Referring back to FIG. 2, the systems 110 and 120 are shown there as coexisting in adjacent overlays SUBSTITUTE SHEET (RULE 26) (i.e..; have coverage non-overlay) resulting primarily in co-channel interference (CCI). Also shown in FIG.
2 is a frequency spectrum overlay 140 which depicts, in a frequency domain, a band 192 of frequency channels used by the system 110, and a band 144 of frequency channels used by the system 120. The bands 142 and 144 overlap each other in a CCI band 146 in which some frequency channels are re-used by both of the systems 110 and 120. As a result of the CCI band 146, a guard zone 148 defining a geographical distance between the systems 110 and 120 is established to minimize interference between the two systems 110 and 120 in the CCI band 146.
FIGURE 5 graphically depicts CCI, which is the dominant interference in frequency re-use systems arranged as the system 110 and 120 are in FIG. 2. As shown in FIG. 5, with CCI, a desired signal 500 and an interfering signal 502 make use of the same carrier frequency 504.
FIGURE 6 illustrates a conventional analog phase modulated (PM) system 600 which is often "victimized"
by ACI and CCI from digital systems. The PM system 600 comprises a PM transmitter 602, such as a cellular base station, and a PM receiver 604, such as a cell phone within the coverage of the PM transmitter 602.
The PM transmitter 602 includes an amplifier 606 configured for receiving and amplifying an input baseband signal m(t) and passing an amplified signal ~g(t) to an angle modulator 608. The modulator 608 is configured for outputting a modulated carrier signal s(t) to an antenna (not shown) for transmission to the PM receiver 604. The signal s(t) is degraded into a SUBSTITUTE SHEET (RULE 26) WO 99/11371 PC'T/IB98/01355 signal r(t) by interference i(t) and noise n(t) received symbolically at a summer 609. The PM
receiver 604 includes an intermediate frequency (IF) filter 610 configured for receiving and filtering the degraded signal r(t), and is connected for passing a filtered signal to a limiter 612. The limiter 612 is configured to pass an amplitude limited signal to an ideal angle demodulator 614 which demodulates the signal. The demodulator 614 is connected for passing the demodulated signal to a low pass filter 616 configured to filter out noise and undesirable frequencies and to output the baseband signal m(t) (with added interference and noise) for use, such as by a telephone receiver (not shown). Because analog phase modulated systems such as the system 600, and the operation of such systems, are well known to those skilled in the art, they will not be described in further detail herein.
For the purpose of illustration, it will be assumed that the system 110 (FIGS. 1-2) is an analog phase modulated system such as the system 600 (FIG.
6), and that the system 120 (FIGS. 1-2) is a digital system that generates ACI (FIG. 1) or CCI (FIG. 2) which interferes with the system 110. Then, to determine the optimal guard band 136 (FIG. 1), the optimal guard zone 148 (FIG. 2), or the optimal capacity of the systems 110 and 120, the effect of digital interference i(t) (ACI or CCI, respectively), on the baseband signal m(t) output by the PM receiver 609 of the system 110 must be determined. Noise n(t) may be neglected in determining the optimal guard band and optimal guard zone because the signal is limited much more by interference than by noise.
SUBSTITUTE SHEET (RULE 26) in accordance with a method of the present invention, closed form expressions for the baseband interference. spectra are determined as a function of the RF carrier-to-interference (CIR) ratio, which can be translated into the co-channel re-use ratio.
System performance is determined by the baseband signal-to-interference (SIR) ratio. From the interference spectral density, the baseband SIR at a spot frequency, where the interference is a maximum or the SIR is minimum, is determined.
The method the present invention may be more clearly understood with reference to FIGURE 7, which illustrates the cellular systems 110 and 120 as coexistent in adjacent areas (i.e., coverage non-overlay), as was shown in FIG. 2. As shown in FIG. 7, two distances dl and d2 are depicted. The distance dl represents a worst case distance from a mobile unit 700 to a transmitter 702 centrally located within the system 110, depicted herein as a desired system. The distance d2 represents a distance from the mobile unit 700 to a transmitter 704 centrally located within the system 120, depicted herein as an interferer system.
For the sake of example, the interference reduction factors -IRF = Signal Spectral Density __ ~_z /2W
Maximumlnterference Spectral Density S~ {0) / R 2 are calculated for different modulation techniques which may be used, as discussed below with respect to Equations 19-21 and Tables 2-4, for a bandwidth of 30 kHz, and for an interference to signal carrier power ratio of RZ - 0.01 (corresponding to a carrier to interference ratio (CIR) of 20 dB), when both signal SUBSTITUTE SHEET {RULE 26) and interference are non-fading. The IRF values for CCI are summarily tabulated as follows:
Modulation IRF
Phase Modulation 6.g3 dB
(PM) Quadrature Phase Shift Keying 9.31 dB
(QPSK) Minimum Shift 10.14 dB
Keying (MSK) In accordance with the present invention, the signal to interference ratio, SIR, at the baseband may be computed as the sum of CIR and IRF. Accordingly, if an SIR of 30 dB is acceptable, then to achieve such SIR, the required CIR resulting from CCI for each type of modulation would be calculated as follows:
SIR - IRF = CIR
For PM: 30 dB - 6.83 dB = 23.17 dB
For QPSK: 30 dB - 9.31 dB = 20.69 dB
For MSK: 30 dB - 10.14 dB = 19.86 dB
It is well known that:
CIR =_ C d., r I d, The value for 7(' is generally between 2 and 6, and will be considered to be 4 for this example.
Accordingly, for the different modulation techniques:
2 0 Fo r PM : CIR = 23. l7dB = 207.5 = d2 , d2 = 3.80 d, d, For QPSK : CIR = 20.69dB =117.2 = d2 , a2 = 3.29 d, d, For MSK: CIR=19.86dB=96.8= d2 , d2 =3.14 d, d, SUBSTITUTE SHEET (RULE 26) Given dl, it is then a straightforward algebraic problem to calculate d2 and the guard zone 148 (FIG.
2), and may be solved in a manner well known to those skilled in the art.
Alternatively, the guard band 136 (FIG. 1) for ACI may be calculated given an SIR of, for example, 50 dB, and by calculating the IRF from Equations 15-18, as discussed below. The carrier to adjacent channel interference ratio may then be calculated as the CIR
was calculated above, i.e., as the difference between the SIR and the calculated IRF. The guard band 136 may then be determined from the carrier to adjacent channel interference ratio using techniques which are well known to those skilled in the art, and will, therefore, not be discussed in further detail.
Alternatively, if dl and d2 are both given, then an improvement in the quality of service, reflected in the SIR, would be gained by switching from PM to QPSK
or MSK modulation techniques. The improvement gained by switching to QPSK would be 2.48 dB (9.31-6.83), and by switching to MSK would be 3.31 dB (10.14-6.83).
Alternatively, for an acceptable baseband performance, a switch from PM to a digital modulation such as QPSK
or MSK would permit frequencies to be used closer together, which would permit the number of subscribers per channel for a given area to be increased. In still another alternative, a smaller re-use distance ratio d2/dl corresponds to a smaller number N of cells per cluster according to the well known equation:
d2 = 3N
d, SUBSTITUTE SHEET (RULE 26) itC~~. ~<)1,~I-:l'.A-~lll:\C:IIt.:.~ 11 i . a-)'=-:1:1 ~ t1._~.1 . - rn..
..,rm~m.,. m ~ ."
wc-u3~;ya ui:~,~a~r rrom- ~-u~u r ~iiir-~ r-na VY4 99/12391 PCTILB98lOI355 Thus, more channels per cell :nay be used by switching from PM to either QPSK or MSK, resulting in a higher capacity for the system since the total number of available channels in the system is generally fixed.
The following describes how the values for the IRFs used in the foregoing equations are determined.
The genexal methodology for evaluating the baseband iaterchannel interfewerce when two angle modulated waves interfere with each other has been considered by V. K. Prabhu and L. Vii. nloe in "Interchannel Interference Considerations in Angle-"
The Bell System :ethnical Journal, Modulated Systems, pp. 2333-57, September 1969. An ideal angle demodulator is assumed in the system. This method is ertended to the case of a digital interferer to ~:::
a:>alag desired signal for calculating the baseband interchan~el interference. The digital interfe=er is an i~SK/QPSF< system modulated by a binary sequence i ak j taking values.tl, and the analog desired signal is phase modulated by band limited white gaussian rar~do:n p:ocess. .It is assuned that there is only one interfering wave corrupting t~:e desired signal. '='he _ 25 effect of linear filters is not considered. Let the analog pi:ase modulatea wave be represented ass(t)=~Icns(?rrf~t+4~,(t)), where ft is the carrier frequency and ~,(r) is the phase modulation of. the deaired s=gnat.
MSK znrerferer The interfering MSK signal is rEpresented as ar.
angle modulated signal by CA 02302242 2000-02-28 p~l~'~r'~'ry ;~~~;.~.
', ., ..
'1O.\ . \ ():\ : Lf'r\-~1l'l:.W.lli..v m:~ . .>- m-:r,~ . m . _w . - , . .. ,.
r;ec-ua-try uz;z;~m frcm- i-uju '~~.ueiz~ ~ 'h=iuj' WO 991'371 PCT/189l1l01335 i(t)=:~Rco 2n (,f~+fo)t+h~ar ~rarc y1 ~~~dt +~ i1;
where tP, (t) = 2~de~ a;, ~ rect l t T ~ 'd1 ( 2 ) is the phase modulation of the ilnterfJering signal.
MSK is a special form of binary Continuous Phase Frer~uency Shift Keying (CPFSK) in cahicr~ h=1/4T and is detected as a phase modulated signal. AR is the amplitude of the MSK signal, R being the relativa aL-npli~ude of the in~ex~ering wave witri respect to the :.U tleslred wave. Tr.e CIR at RF is trerefvre given by 1IR''.f~, is zhs difierer.ce betwean the carrier freguency of the inter;ering signal ar_d that of the desired signal. For co-channel int2rferen~e, fd is usually very shall. ~ is the random phase offset between the des~zed and interfering signals. The probability density fur_ct~.on of ~ is uriforrn and given by _1 0 _ 2~r f" (~) ' ~~ otherwise t 3 ) is t:>e ainary sequence taking values ~1. T is r the baud interval and recta.] is the rectangular pulse given by (4>
rect(x) = 1 0 <_ N < ?~ .
0 other~:ise v~hen de;ected as a phase modulated signal, at odd multiples of ~~, the phase that is neasured l:nod~:lo 2n) will take va:.ues ~/2 and at even trultiples oz T it can take values 0 and n.
~iviEV~a~rC! ~ y-_.
hC'\. \~)~:l;le1-ill t:~.Cllt.:~, no, . :s- W-O;, : rs:_'m : -x'1:1 ():l _. ).lJt'flh)~h .1 Ue:-tJ!-dH UZ:Z9~n rr~r~- i-um r uslcr r-!ua WO 99112371 PCTl189&01355 _ MSK may re rppresen=ed as a farm of four phase PSK. The equivalent low pass digitally modulated signal may be re~rresented ~n t?se form y(t) =~a~tg(t -2nT')- j~a,"_~g(t _?~r _T) t 5 ) w where g(t)= sin~~~ 0<t~2T [6) 0 otherwise Thus, this t~.-Fe of signal is viewed as a faun p.~3Se PSK signal in which the pulss shape is one-half of 3 sinusoid. The even numbered binary valued t1 symbols ~azp~ of the information sequence fa"~ are transmu ted via the cosine of the carrier wh-le the odd numbered symbols ta~"~1~ are transmitted via t:~e sine of the carrier. Thz transmission on the two ~ orthogonal ca=tier compare.~.ts is 1/2T bi~~s per second so .hat the combined transmission rate is 1/T bits per second. The bit transitions on the sine and cosine carrier components arG staggered or offset in time by T seconds. Therefore, MSK can be represented as RR~ ~ ~ a~~(t _ ~n~~ 'yes[2x(f~ + f~)t+Xj- ~ n a~~gtt _.?nT_T) ~ Sia[?~(f~
+Id)tTlr]~
(7) eq~,~;valent to two staggered quadrature modulated binary PSK signals so that the corresponding sum of the t;ao quadxature sig:.als is a constant envelope frequency modulated signal.
b:l'. \~)'~.:~:I'~\ \1I 1~..'~.111U..', m:, . .~-~_-.i.~ . ,. _~ . . . . .. ,.
".
uec-c~-ay u~.:zaa~ ~rorr- i-uaa ' a iuiit ~r-i'u~ .
W O 99/L'.371 PGT~1898~OI355 QPSx L~ L erfe tar The interfering QP3K signal is given by i(t)=ARca- 2.~(f.;-fa)t+~u"g{t-n?")+~c , where w ~p,(t)= ~a"g{t-rrT~ is trm phase modulation of the n interfering signal. This is rapresented as two quadratu=a anodulated binary PSK signals by the equivalent~amplitude modulation representatior_ r 1l ( 1 ~t ~~a~»recr~r ~T fycos[2rt(fct f~)rr~:J-~~a~rrrlrecc~l ~T~~sinj2R(fc+f~N+,~]
/J
E_ (s) The shapi~g pu?se in the amplitude modulation representation is rect[.] as in Equation 4.
rvaluaricn of the 5ase band Interference Spectra The composite voltage into the ideal angle demodulator is r(t)=s(t)+i(t) given by Rej{e~.u > ~. Re'~=~."m, u~.w )e~:~r t~ = Re[e'm.a~ {1 + Re'c~.~-m, m-~,c~ ~r )e..:~ ~~
whera the amplitude A _~s normalised to unity and Re[.]
denotes t!:e real part. The phases of this eompositE
signal into =?~e phase demodulator relative to the . carrier frequency f~ is given by Im[ln(s(t) + i{t))j = GPs (t) t Im[lu(I + Rz'c='~~'=~~c~rm,cra-,~~)] ( 10 ) where rrr[.'] is the imaginary part.
Equyvalently, ~.(I)T~R~(-1)"''~sia[k(?nfdt+~,(r)-~,(t)+y~J is i~i the composito phas= when R ~1. ~,(t) is the ideal desired prose anc tre sum,.~nation term,, denoted as ~~(t), corresponds to thN phase noise appearing at the CA_ 02302242 2000-02-28 ~~:,~,'~,1,~.-,~ J~I''j Kl.~. 1W\~l:l'~1-Eli 1.~.l.~ll:~ m.~ . .. ._ ,.,. . .. ~~ ~ .. . . .
uec-ua-~e uz:zazr ~ron~- i-uau ' a i ii~r-~ '~~'-iua ' WO 99I1Z371 PCT~LB98~I01355 detector due .o the in=erference. To determine the effect of this phase no=se, its spectrum nEeds to be determined. The autocorrelation function of ~(r) is given by Rx (z) = E[~1(t)~(t * z)] ( 11 ) where E[.] denotes expectation. The random phase angle a makes the complex random process Wide sense stationary, and Raft) can be shown to be p 1 ° R''' Rz (z) = E ' ~ k~ cos[k(2rrfaT t ~, (t t T) - ~. (t)-4>. (t t T) t ~, (t))]~ ( 12 ) .~ l w',~er. R<1. The above may be expanded as 1 ,~ Rzx R~(r)=E~2~ k~ eos[2az~Efdz].Re[e-.Irm,vro.u,.soe~cs~m,c~r-~.n.:m~ (13) x-~
Here, ~,(t) and ~;(T) are statistically independent and hence, zhe complex processes e'w'e a:.d e~s~'~ are also statistically independent. The autoccr_elation function of a complex base bend phases modulated process v(t)=e'~''j is given by the Wiener-Khi ntchine theorem as R, (z) = E[v(t)v ~ (t * t)] _ .E~e'coc'~..~u",n ~.
(1~) Hence the k~' term of R.z(t) is given by R,~ (z) - ~k, COS[~7G~Cf~T~RYr T ~~ T ( 1 S ) where R~~(z) and R,~(r) are the autocorrelation functions of t::e processes v,~(t)=e''w'~ and ve(t)=e'"w'~ .
For high CIR, Rccl. In this case, only the first term of Ra(i) gives significant contribution. Therefore, Rx(z;=R,,1(z) for (k=1) . Therefore, R,~(z) is given by R~ (T) = 2' C0~~271f,~Y~Rr (T)R,,~ (Z) ( 16 ) /:.1.v.14J.-u. v..w 1 hC\.\t)\:i:l'~\-Vlll:.'vCill\ ~)5 . :)-L'.:-:1;1 : ti:y1 . ~ ro:i c~,~
_,S:l:Iywll,~~.m_ Uec-U3-srB UZ:Y.3~a Frcm- 1-U9U Y.ILIIi F-IU3 The power spectral density S~(f) of the random phase angle ~ is giver. by the Fourie= Transform of R;, (r) sz~f~=~~ kix~~'~.~~ (17) _ x_i where S,~(,f~ is given by 'e-l~sl~,N?-mr(rts~~e,!(t(~D,(rYm.(i~sule-~'-~4~Tew'-~9:t.~1 ~ ( 1~ ) For R ~c 1, S,~(f) is given by (Rzl2}S,,(f) . For ca-channel interference, f~, =0 . Hence z R~ (r} ._ Z R~. (T)R~, (r) ( 19 ) which is RZl2 times the product of the a,.:tocorrelatian functions of the base bang phase madulaticn processes e~'°'.~r? and e'~~~') . Therzfore, S,~(f} is given by Sx (f ) = R l~R,.. ('')R., (: )e '2'~=~' . : t 2 4 ) Equi~Jal=nrly, S,~(f) rnay be crrirten as Sx(f)= R fs~ ( f)~5.,(I)~ c21) where, S,, (f) and S,,,r,f) are the spectra? densities of the base band processes e'~'~'~ and e'~'~" respectively and ~ denotes the convolution operation. Hence tc determine the spectral dens~.ty of the co-channel interzerence at base ba~~d, the convolut~or, of the base band spectral de:~sit~es cf the desired and interfering signals must be eva~uazecl.
Power spec=raZ Density cf a PM Analog Signal A sinusoi3al wave of constant amplitude phase modulated by a signal m(t) may be written as s(tf~Atos(w;-tkpm(t)+A), where A is thz ampl:.tude of is CA 02302242 2000-02-28 ; '.~:~-,'--. , .-h(:\~.1U1:E:1'A-lil l:''.tfll:\ Ir; . :S-1'=-:J:I : tS:_1 . - rn:s rsa _.s:rne~m~:~.Hi.s UoC-UWBw OZ:i4an hro!e- I-U3U f 13/Lf r-IU3 WO 99/113'I1 PCTI1898~OI355 the wave, f~ = w~ I2tr is the carrier frequency of the ways, 6 is the random phase associated with the wave which has a probability der_sity _ ~ OSB52~r fa (B) - 2sr otherwise ( 22 ) a and ko is the modulation indEx. ~,(t)=kpnt(t) is the phase modulation of s(t). Here, m(t) is a random voice signal having bandwidth W approxi.~nately 4 kH?.
m(t) is~modnled by a stGtionary band limited Gaussian random process with mean 0 and variance cry. The fir. 10 average spectral density of m(t), S~,(f) is given by the Fouriez transform of the autocorrelatior. fu>zcticn R,~ (r) = E(nt(t)m(t * r)] = oz ~~ T a s S.~ (.f ) = W ~~ ~ ~ ( 2' ) 0 otherwise ' ' R~,(0) is given by Fjmz(t)]=crZ which is the power in the ~5 voice s-final. The phase mod',:lated signal s(t) can be show.~. to be w~.de senss stationary and can be written as s(t) = AReje~~=~'~r~,~~:rey .
iT Tlrie complex basE band phase mcdulat=d process of 20 s (t) is given by v, (t)=e~'"~'~ and the autocorrelation function of v, (r) is given by R. (r) _ ~y~ (J~V~ ~ (t tT)~ _ ~B ~~~~Sr~°nr.s~Jl~. ( ~q ) Since m (t) is Gaussian, Ry,(r)=a ~tR'1°~rR'~li~ . 'The spectral der_sity of v, (t) is he:.ce given by 2 5 5,. ~ _ ~e-'':«r,,c°?-R.,c.»e-~z~rr dz. ( 2 5 ) kC'\ . W)\ : [~.!'r1- \1l EiVC~lit~~ U:, . :i- I '=-:I.f : Z4 : y I . - r.i .~
cva _.s:~:us~~m ~:, . n , ,(, Uec-03-aU UZ:Z4~m f~.~am- I-U~ti P It/1l h-~U~
V4'O 9~lIIZ371 PCT~I~9$/01355 Now the autocorrelation function o° the angle modulated signal s(t) can be written zs R. (~? _ ~= e-~~.t°)- :fr)) CC'sS(2~rI} t 2 ~ ) and the spectral density is given by S S,(f)= ~R,(r)e''~rdr. Sg(f) can be expressed in terria of the spectral density o~f the base bard process S,,{f) as (A~I4)[S~.{j-f~)+S.(ftf~)~. Therefore, to evaluate the spectral density of the modulated signal s~t),~ S,,(f) must be date=-mined. For :ow index modulation ti. e.
:.0 for kr,~>1 ? . the approximation for R, (r) :aay be made as Ry. (r) =e-';roc°'e';R,c~~ ! e-t:~.~°l~l t kpR"(r)~
The spectral density S,.(f} is there=ore given by r S,. (f) = e-''~'<oyd(f ) ~ e-x'R°E°~kp ~Rm(T~-'2'~'dT (? ~ 7 ..
for this case. The first part corresponds to the 15 carrier cor.Epor7ent of the spectrum a:~d the second part corresnor_ds to the first order side band component.
mho r~~cdulation index kp .s considered low, if kP <0.1 radian. If kP <I.5 radian, it is ,:~nsiderEd high-index and i f O.I < kP < 1.5 , it i s cons idered medi um index . Wi:en 20 kP is madium or high indexed, the saries expansion IlluSL be used as Rr. (T) = e'~Fw(°?ek~wlel ~ e~~;$E°)~~ ~kPR~(z}~
This series expansicn is called Lewart's expaas_or..
If zhe spectral density of m(t) is ~-~.own, the spectra!
25 density of kP"R;;(t) can, in principle, be calculated as vcv. wv:ct~A-au t:v.c~tt~:.v ~;;~ . a-i~~_;~:~ : ~~:_~_~ : , +.~:~ cs:~
_~a:~;~.~a~;:::m:~
Uac-G3-6Y UC:X4aP h~o;n- f-USJ h lS/Li r-IU3 WO 99112371 PG'T/189&OI355 the n fold convolution of the sp~cLral density of kPR~(T} with itself. For a mean square mGdulation index ~; yor the phase modulation ~s(t) ~ kpm(t) , kpR,~(z)=~Pf~~T' such that the spectral density of m, (t) denoted by Sm,(f"j is g=ven by (3~) ~hus the spe:tral density of medium, index phase medula ted signal can be dete rc2ined using Lsvrart' s far:rula and the n-.ol d convolut:.o~ theorem.
c If tze rms madulation _ndex ~P, exceeds 2 rad;ans (gyp= > 2.0 radians; the number ef convolutions required will ba ve=y farce. ucwever, for small ~rodulation index, as well as fcr large index, far down on the tails, the number or terms to be included; in tY'e series is very large. In such cases, the spectrum may be calculated using the sadd::e point :nezhod disc'_osed by 'J. K. Prabhu and H. F. Ro,ae, "$peci.al r'Jensity Bounds of a P~" Wave," The Bell System TecY~.nical 2C Jourr~a'_, op. 769-511, March X969. As long as she mod~~I4tion index is even moderately high (~2 > 10) tha spectrum can be estimated by the saddle point method fo; all values of : in a simple manner with a fzactional arror of less trap 10%.
~5 Powsr Spectral Density of MSK/~PSK signals For a digital signal, the spectral density is a :unction of the spectral characteristics of the shaping pulse and the bGud rate T. The base band rate of MSK and QPSK signals can be determined =rom the 2.
CA 02302242 2000-o2-ZS P,"~:;~'r'~~~ ~''~~~T
KC\.\(~iv:If':1-1111:\C_IIf.::\ 1)~r ~ d-1::-:i:l : ~:_~y : -~ r.r,~ tr:~
_.r:r.nr~nt.:,.nre.
gee-u~-srsf uz:eaam rrem- r-ueu N.ibizt r-.us WO 99I3Z371 PCT/I898~01355 ampl~.tucle modulated representation of these signa'_s '?, Eq. 8) .
MSK Signal The spectral density of base bank MSK s~.gnal y'(t)=e'~~~'~ can be estimated from the amplitude rnodu:.ation representation of Via. 'l. The spectral density is given by z S., CI ) = ~ ~G(.f )~Z ( 31 ) where G!f) i' the Fourier transform of the signaling pulse g(t)=sin T (Eq. 6) . There: ore S,'{f) is given by 16T (co~(2nfl ))' !32) S.,(f)= ~Z(1_16 fzTi):
QPSK Signal 1~ The spectral der.3ity of base band QPSK sig~:al v, (t)=e'mr'~ can bz estimated frog' the amplitude modularion representation. of Eq. 8. The spectral densely is given by S,,(f)T T jP(~~~ ('~3) '~ 20 where P(f) is the Fourier trarsrorm or the rectangular signaling pulse. S~,(f) therefore is given by 5,., (f ) = T (s~~))2 ! 34 y )' In MSIC, the base band wa~eform that multiples the guadxature Carrier is much smoother than the abrupt 25 rectangular Waveform of QPSK. The waveform of MSK
exhibits phase continuity whereas that of QPSK is disccntir_uous. MSK has a main center lobe which is ._ hC~.~()\:f~t'~\-111'f:\C.HL;\ 1)i . B-f!_:):i : ti:y_ ~ -. Tn:r «:~
.~;rrn~r~.:~.m, N
Uac-U~~88 UZ:Zbae~ rrom- 1~U3U f If/Zf h~iUi WD 99/123~I PCUlB98/01355 1.5 times as wide as the main lobe cf Q?SK: but the side lobes fall off much faster. Hence the fractional out of band power for MSK is less compared to QPSK, accounting for the higher bandwidth efficiency of MSK.
The convolution of the base band spectrum of the desired signal S,,(f) with that of the interfering signal S,,(f) gives the base band inter'erence spectrum S~,(f) as given by Eq. 21 for high CIR (R2 ~ 1) . The ?0 baseband output due to interference ca:. therefore be corlputed as a function of the interference to carrier ration R2, the mean square modulation index tp; of the y- Ptd signal, and the baud rate T of the digital interferer, assuming fd~ 0. It is seen that the ratio of interference pawer density to signal power density is maximum at the lowest base band frequency.
However, for narrow bard signals, the basebard ini:erference spectrum is quite flat in the rarg~
~f!< W . Hence the =atio of total signal t4 t~Lal ?G interference in the baseband width W is approximately eaual to that at the lowest base band frequency.
Co-c~:annal Irterferencs Spectral Densisy under Non -fad_n~ Condw Lions Under non-fading conditions, the RF interference-to-signal ;aria R~ is a fixed quantity. For high average CIR, trerefore R'<1. The minimum bese band SIR relative to CIR is computed as SIR,, = ~~ ~ 2W= t 35 ~
S~ (D)~ R
~~rhere Sz(D) is the interference power spectral density at the lowest base band freqe~ency. This gives the . y.,,r IiC\. \is~\:ia'~\-lil i:'.C'fll:\ (1:: ~ :.s- J'.S-a:l : tt:__ ~ ~ Tw;ma ~.sa:rr-uu~ ~ n ~ a Uoc-U5-'i9 OL:Zb~n From- I-U3J N.IdIZI F-I03 imprevement in base band SIR relative to R'. Hence the total SIR at the lowest base band frequency is given by CIR t SIR,~;~ .
Tables 2, 3 and 4 give the results for the ratio of signal to interference power density SIR", for R'=.01 (ccrresponding to CIR of 20 d8), when both signal and interference are non fading. The interference spectra are Estimated with both desired signal and interferer occupying the same band~ridth.
The bandw~.dth of the angle modulated signal ~s estiriiated usin g Carson's rule, while the bandwiQth occupied by the digital signal is assumed to be 1.3/T.
The minimum signal to interference power density when the systems under ca~sideration occupy ciitferent bandwidths have beer, evaluated. The spectra of the MSK and QPSK modulated interferers for a bandwidth occupancy of 30 kHz are shown in FIGtTRES'8 and 9 respectively. Tre spectrum of the phase modulated signal with root mean scuarz (RMS) r~od~:lation ir_dex of 1.?9 (corrESponding to 30 kH? bandwidth; is given in rIGURE 10. The interfere~:ce spectra for analog to analog and digital to analog are evaluated and given in E'IGURES 11-13 when the desired signal 'as will as the interfering signs' are occupying an equivalen;.
bandwidth ef 3D kEiz. FIGURES 11-13 are summarized without normalization in F1'Gll~c~ 14. The SIRo,," ofered en the t~hase mfldu:.ated signal by MSK interference is seen tQ be better by about 3.3 dB and that offered by PSK interference by about 2.5 d8 compared to an equivalent analog phase modulated interferer_ce. The effect of increasing the modulation index or. the base bard SIR is observed from the tables. It is seen teat CA 02302242 2000-02-28 '''~~C~~
RC~.W)l:fl'A-All~h:'vCllf:': U:; . a-1v-a:! : t3::!:3 : ~ +.;~i t3:~ '_:3;Ja-1-lti;~Nl;i UoC-U3-NY UL:T9~IA I~ror~- 1-U3U f IY/Lf r-IU3 WO 9J113371 PCTlI~i9$/Q1355 if high CIR ar RF is maintained, the base band SrR
improves as the modulation index of the desired signal is ~.ncreased. This can be used to advantaqe in improving the output S:R by~zrad:ng bandwidth.
TABLE 2 ?M - PM
Bandwidth M ~2~iW
(KHz ) dulation (0)IR= dB
S
Index m, = 4~, ,~
25 0.9 4.6 3d 1.19 6.93 4p 1.732 10.58 MSK Interferer ~qnal SIR imin) ~
Bandwidth Baud Pate Modalarioz 3 Flllo dB
(Krizy ~, l Inter .5,~(O)~B' ~ ~, baud) 25 19.23 0.9 7.03 30 23.08 1.19 10.14 40 30.77 1.732 14.68 f:l~. W v:fa'A-V11 f:'W III:', W ~ _1-J_'-;l:l : ti:_:i : - +.t:i ~:;t ~.i'.Ja~f l~c;:, : y~ ~
Uoc-03-dt~ OZ:Zb~~ hr~~l- 1-030 f' l0/Zl F-143 WO 99112371 PCT~lB98J0i355 Te~BLE 4 PM - QPSK
QPSK Interferes $iq al SIR (min) 8au3 Rate Bandwidth Modulati 1 '~2 ~?W
1 (Kilo an ~ d8 ~ ~~2? ~, Index 5~~0)~R
baudl cp, 25 -I~.23 0.9 6.18 30 23.08 1.19 9.31 40 30.77 1.732 13.86 In light of the foregoing, it can be appreciated t:-:az the base. band SIR in Oho case of an MSK
,- interferes is bEtter than an equivalent QPSK
interferes, and that both of the digital interferers under consideration provide higher base band SIR than that p=ovided by an eauivalent analog phase modulated 1G interferes.
By thz use of ~he present irven-ions performance tray be ecaluazed for co-existing digital and analog systems, such as, for exar~pie, mob~.ie radio systems whore analog AMPS and digital TDMA systems share tt~.e same band. S4ch evaluation permits the capacity and/or the Quality oservice of such systems to be - optimized.
It is understood than the present invention can take many forms an~ embodiments. Accordingly, several variations may be made ~.z the fcregeing without departing from the spirit or the scope of the invention. For example, the method of the present invent;:on tray be employed to analyze the interference im.-nunity offered by different modulation schemes a:~d can be extended to estimate the effects of botn ACI
i:i'\. ~'()~'~:f:f'A-Vt( 1:'W.'Ilf:.\ (n ~ :i-1'=-;1!1 : H:_~;; : ~ ~.I:r rs:a _'s;rf~1~1t;:.,:,y.~
Uec-Ui-5Y UL:'ctiim prom- I-09fi N.Z:IZI h-BUY
WO 99/I23~I PGT/IB98/OI355 and CCI under fading and also the effect of diversity in coi2~sting interference in high capacity mobile radio systems.
Having thus described. the present invention by reference to certain of its preferred embodiments, a is noted that the embodiments disclosed are ill:»strative rather tY,an limiting in nature and that a wide range of variations, modifications, charges, and 1C substitutions are conte_mplGtQd in the foregoing disclosure and, in some instances, some feaz:;res of the Present invention may be employed without a corresponding use of the ctrer features. Accord=ugly, it is appropriate that t,'~e appended claims be construed broadly and :.n a manner consistent with the scooe oz the in~renzion.
L
2), and may be solved in a manner well known to those skilled in the art.
Alternatively, the guard band 136 (FIG. 1) for ACI may be calculated given an SIR of, for example, 50 dB, and by calculating the IRF from Equations 15-18, as discussed below. The carrier to adjacent channel interference ratio may then be calculated as the CIR
was calculated above, i.e., as the difference between the SIR and the calculated IRF. The guard band 136 may then be determined from the carrier to adjacent channel interference ratio using techniques which are well known to those skilled in the art, and will, therefore, not be discussed in further detail.
Alternatively, if dl and d2 are both given, then an improvement in the quality of service, reflected in the SIR, would be gained by switching from PM to QPSK
or MSK modulation techniques. The improvement gained by switching to QPSK would be 2.48 dB (9.31-6.83), and by switching to MSK would be 3.31 dB (10.14-6.83).
Alternatively, for an acceptable baseband performance, a switch from PM to a digital modulation such as QPSK
or MSK would permit frequencies to be used closer together, which would permit the number of subscribers per channel for a given area to be increased. In still another alternative, a smaller re-use distance ratio d2/dl corresponds to a smaller number N of cells per cluster according to the well known equation:
d2 = 3N
d, SUBSTITUTE SHEET (RULE 26) itC~~. ~<)1,~I-:l'.A-~lll:\C:IIt.:.~ 11 i . a-)'=-:1:1 ~ t1._~.1 . - rn..
..,rm~m.,. m ~ ."
wc-u3~;ya ui:~,~a~r rrom- ~-u~u r ~iiir-~ r-na VY4 99/12391 PCTILB98lOI355 Thus, more channels per cell :nay be used by switching from PM to either QPSK or MSK, resulting in a higher capacity for the system since the total number of available channels in the system is generally fixed.
The following describes how the values for the IRFs used in the foregoing equations are determined.
The genexal methodology for evaluating the baseband iaterchannel interfewerce when two angle modulated waves interfere with each other has been considered by V. K. Prabhu and L. Vii. nloe in "Interchannel Interference Considerations in Angle-"
The Bell System :ethnical Journal, Modulated Systems, pp. 2333-57, September 1969. An ideal angle demodulator is assumed in the system. This method is ertended to the case of a digital interferer to ~:::
a:>alag desired signal for calculating the baseband interchan~el interference. The digital interfe=er is an i~SK/QPSF< system modulated by a binary sequence i ak j taking values.tl, and the analog desired signal is phase modulated by band limited white gaussian rar~do:n p:ocess. .It is assuned that there is only one interfering wave corrupting t~:e desired signal. '='he _ 25 effect of linear filters is not considered. Let the analog pi:ase modulatea wave be represented ass(t)=~Icns(?rrf~t+4~,(t)), where ft is the carrier frequency and ~,(r) is the phase modulation of. the deaired s=gnat.
MSK znrerferer The interfering MSK signal is rEpresented as ar.
angle modulated signal by CA 02302242 2000-02-28 p~l~'~r'~'ry ;~~~;.~.
', ., ..
'1O.\ . \ ():\ : Lf'r\-~1l'l:.W.lli..v m:~ . .>- m-:r,~ . m . _w . - , . .. ,.
r;ec-ua-try uz;z;~m frcm- i-uju '~~.ueiz~ ~ 'h=iuj' WO 991'371 PCT/189l1l01335 i(t)=:~Rco 2n (,f~+fo)t+h~ar ~rarc y1 ~~~dt +~ i1;
where tP, (t) = 2~de~ a;, ~ rect l t T ~ 'd1 ( 2 ) is the phase modulation of the ilnterfJering signal.
MSK is a special form of binary Continuous Phase Frer~uency Shift Keying (CPFSK) in cahicr~ h=1/4T and is detected as a phase modulated signal. AR is the amplitude of the MSK signal, R being the relativa aL-npli~ude of the in~ex~ering wave witri respect to the :.U tleslred wave. Tr.e CIR at RF is trerefvre given by 1IR''.f~, is zhs difierer.ce betwean the carrier freguency of the inter;ering signal ar_d that of the desired signal. For co-channel int2rferen~e, fd is usually very shall. ~ is the random phase offset between the des~zed and interfering signals. The probability density fur_ct~.on of ~ is uriforrn and given by _1 0 _ 2~r f" (~) ' ~~ otherwise t 3 ) is t:>e ainary sequence taking values ~1. T is r the baud interval and recta.] is the rectangular pulse given by (4>
rect(x) = 1 0 <_ N < ?~ .
0 other~:ise v~hen de;ected as a phase modulated signal, at odd multiples of ~~, the phase that is neasured l:nod~:lo 2n) will take va:.ues ~/2 and at even trultiples oz T it can take values 0 and n.
~iviEV~a~rC! ~ y-_.
hC'\. \~)~:l;le1-ill t:~.Cllt.:~, no, . :s- W-O;, : rs:_'m : -x'1:1 ():l _. ).lJt'flh)~h .1 Ue:-tJ!-dH UZ:Z9~n rr~r~- i-um r uslcr r-!ua WO 99112371 PCTl189&01355 _ MSK may re rppresen=ed as a farm of four phase PSK. The equivalent low pass digitally modulated signal may be re~rresented ~n t?se form y(t) =~a~tg(t -2nT')- j~a,"_~g(t _?~r _T) t 5 ) w where g(t)= sin~~~ 0<t~2T [6) 0 otherwise Thus, this t~.-Fe of signal is viewed as a faun p.~3Se PSK signal in which the pulss shape is one-half of 3 sinusoid. The even numbered binary valued t1 symbols ~azp~ of the information sequence fa"~ are transmu ted via the cosine of the carrier wh-le the odd numbered symbols ta~"~1~ are transmitted via t:~e sine of the carrier. Thz transmission on the two ~ orthogonal ca=tier compare.~.ts is 1/2T bi~~s per second so .hat the combined transmission rate is 1/T bits per second. The bit transitions on the sine and cosine carrier components arG staggered or offset in time by T seconds. Therefore, MSK can be represented as RR~ ~ ~ a~~(t _ ~n~~ 'yes[2x(f~ + f~)t+Xj- ~ n a~~gtt _.?nT_T) ~ Sia[?~(f~
+Id)tTlr]~
(7) eq~,~;valent to two staggered quadrature modulated binary PSK signals so that the corresponding sum of the t;ao quadxature sig:.als is a constant envelope frequency modulated signal.
b:l'. \~)'~.:~:I'~\ \1I 1~..'~.111U..', m:, . .~-~_-.i.~ . ,. _~ . . . . .. ,.
".
uec-c~-ay u~.:zaa~ ~rorr- i-uaa ' a iuiit ~r-i'u~ .
W O 99/L'.371 PGT~1898~OI355 QPSx L~ L erfe tar The interfering QP3K signal is given by i(t)=ARca- 2.~(f.;-fa)t+~u"g{t-n?")+~c , where w ~p,(t)= ~a"g{t-rrT~ is trm phase modulation of the n interfering signal. This is rapresented as two quadratu=a anodulated binary PSK signals by the equivalent~amplitude modulation representatior_ r 1l ( 1 ~t ~~a~»recr~r ~T fycos[2rt(fct f~)rr~:J-~~a~rrrlrecc~l ~T~~sinj2R(fc+f~N+,~]
/J
E_ (s) The shapi~g pu?se in the amplitude modulation representation is rect[.] as in Equation 4.
rvaluaricn of the 5ase band Interference Spectra The composite voltage into the ideal angle demodulator is r(t)=s(t)+i(t) given by Rej{e~.u > ~. Re'~=~."m, u~.w )e~:~r t~ = Re[e'm.a~ {1 + Re'c~.~-m, m-~,c~ ~r )e..:~ ~~
whera the amplitude A _~s normalised to unity and Re[.]
denotes t!:e real part. The phases of this eompositE
signal into =?~e phase demodulator relative to the . carrier frequency f~ is given by Im[ln(s(t) + i{t))j = GPs (t) t Im[lu(I + Rz'c='~~'=~~c~rm,cra-,~~)] ( 10 ) where rrr[.'] is the imaginary part.
Equyvalently, ~.(I)T~R~(-1)"''~sia[k(?nfdt+~,(r)-~,(t)+y~J is i~i the composito phas= when R ~1. ~,(t) is the ideal desired prose anc tre sum,.~nation term,, denoted as ~~(t), corresponds to thN phase noise appearing at the CA_ 02302242 2000-02-28 ~~:,~,'~,1,~.-,~ J~I''j Kl.~. 1W\~l:l'~1-Eli 1.~.l.~ll:~ m.~ . .. ._ ,.,. . .. ~~ ~ .. . . .
uec-ua-~e uz:zazr ~ron~- i-uau ' a i ii~r-~ '~~'-iua ' WO 99I1Z371 PCT~LB98~I01355 detector due .o the in=erference. To determine the effect of this phase no=se, its spectrum nEeds to be determined. The autocorrelation function of ~(r) is given by Rx (z) = E[~1(t)~(t * z)] ( 11 ) where E[.] denotes expectation. The random phase angle a makes the complex random process Wide sense stationary, and Raft) can be shown to be p 1 ° R''' Rz (z) = E ' ~ k~ cos[k(2rrfaT t ~, (t t T) - ~. (t)-4>. (t t T) t ~, (t))]~ ( 12 ) .~ l w',~er. R<1. The above may be expanded as 1 ,~ Rzx R~(r)=E~2~ k~ eos[2az~Efdz].Re[e-.Irm,vro.u,.soe~cs~m,c~r-~.n.:m~ (13) x-~
Here, ~,(t) and ~;(T) are statistically independent and hence, zhe complex processes e'w'e a:.d e~s~'~ are also statistically independent. The autoccr_elation function of a complex base bend phases modulated process v(t)=e'~''j is given by the Wiener-Khi ntchine theorem as R, (z) = E[v(t)v ~ (t * t)] _ .E~e'coc'~..~u",n ~.
(1~) Hence the k~' term of R.z(t) is given by R,~ (z) - ~k, COS[~7G~Cf~T~RYr T ~~ T ( 1 S ) where R~~(z) and R,~(r) are the autocorrelation functions of t::e processes v,~(t)=e''w'~ and ve(t)=e'"w'~ .
For high CIR, Rccl. In this case, only the first term of Ra(i) gives significant contribution. Therefore, Rx(z;=R,,1(z) for (k=1) . Therefore, R,~(z) is given by R~ (T) = 2' C0~~271f,~Y~Rr (T)R,,~ (Z) ( 16 ) /:.1.v.14J.-u. v..w 1 hC\.\t)\:i:l'~\-Vlll:.'vCill\ ~)5 . :)-L'.:-:1;1 : ti:y1 . ~ ro:i c~,~
_,S:l:Iywll,~~.m_ Uec-U3-srB UZ:Y.3~a Frcm- 1-U9U Y.ILIIi F-IU3 The power spectral density S~(f) of the random phase angle ~ is giver. by the Fourie= Transform of R;, (r) sz~f~=~~ kix~~'~.~~ (17) _ x_i where S,~(,f~ is given by 'e-l~sl~,N?-mr(rts~~e,!(t(~D,(rYm.(i~sule-~'-~4~Tew'-~9:t.~1 ~ ( 1~ ) For R ~c 1, S,~(f) is given by (Rzl2}S,,(f) . For ca-channel interference, f~, =0 . Hence z R~ (r} ._ Z R~. (T)R~, (r) ( 19 ) which is RZl2 times the product of the a,.:tocorrelatian functions of the base bang phase madulaticn processes e~'°'.~r? and e'~~~') . Therzfore, S,~(f} is given by Sx (f ) = R l~R,.. ('')R., (: )e '2'~=~' . : t 2 4 ) Equi~Jal=nrly, S,~(f) rnay be crrirten as Sx(f)= R fs~ ( f)~5.,(I)~ c21) where, S,, (f) and S,,,r,f) are the spectra? densities of the base band processes e'~'~'~ and e'~'~" respectively and ~ denotes the convolution operation. Hence tc determine the spectral dens~.ty of the co-channel interzerence at base ba~~d, the convolut~or, of the base band spectral de:~sit~es cf the desired and interfering signals must be eva~uazecl.
Power spec=raZ Density cf a PM Analog Signal A sinusoi3al wave of constant amplitude phase modulated by a signal m(t) may be written as s(tf~Atos(w;-tkpm(t)+A), where A is thz ampl:.tude of is CA 02302242 2000-02-28 ; '.~:~-,'--. , .-h(:\~.1U1:E:1'A-lil l:''.tfll:\ Ir; . :S-1'=-:J:I : tS:_1 . - rn:s rsa _.s:rne~m~:~.Hi.s UoC-UWBw OZ:i4an hro!e- I-U3U f 13/Lf r-IU3 WO 99/113'I1 PCTI1898~OI355 the wave, f~ = w~ I2tr is the carrier frequency of the ways, 6 is the random phase associated with the wave which has a probability der_sity _ ~ OSB52~r fa (B) - 2sr otherwise ( 22 ) a and ko is the modulation indEx. ~,(t)=kpnt(t) is the phase modulation of s(t). Here, m(t) is a random voice signal having bandwidth W approxi.~nately 4 kH?.
m(t) is~modnled by a stGtionary band limited Gaussian random process with mean 0 and variance cry. The fir. 10 average spectral density of m(t), S~,(f) is given by the Fouriez transform of the autocorrelatior. fu>zcticn R,~ (r) = E(nt(t)m(t * r)] = oz ~~ T a s S.~ (.f ) = W ~~ ~ ~ ( 2' ) 0 otherwise ' ' R~,(0) is given by Fjmz(t)]=crZ which is the power in the ~5 voice s-final. The phase mod',:lated signal s(t) can be show.~. to be w~.de senss stationary and can be written as s(t) = AReje~~=~'~r~,~~:rey .
iT Tlrie complex basE band phase mcdulat=d process of 20 s (t) is given by v, (t)=e~'"~'~ and the autocorrelation function of v, (r) is given by R. (r) _ ~y~ (J~V~ ~ (t tT)~ _ ~B ~~~~Sr~°nr.s~Jl~. ( ~q ) Since m (t) is Gaussian, Ry,(r)=a ~tR'1°~rR'~li~ . 'The spectral der_sity of v, (t) is he:.ce given by 2 5 5,. ~ _ ~e-'':«r,,c°?-R.,c.»e-~z~rr dz. ( 2 5 ) kC'\ . W)\ : [~.!'r1- \1l EiVC~lit~~ U:, . :i- I '=-:I.f : Z4 : y I . - r.i .~
cva _.s:~:us~~m ~:, . n , ,(, Uec-03-aU UZ:Z4~m f~.~am- I-U~ti P It/1l h-~U~
V4'O 9~lIIZ371 PCT~I~9$/01355 Now the autocorrelation function o° the angle modulated signal s(t) can be written zs R. (~? _ ~= e-~~.t°)- :fr)) CC'sS(2~rI} t 2 ~ ) and the spectral density is given by S S,(f)= ~R,(r)e''~rdr. Sg(f) can be expressed in terria of the spectral density o~f the base bard process S,,{f) as (A~I4)[S~.{j-f~)+S.(ftf~)~. Therefore, to evaluate the spectral density of the modulated signal s~t),~ S,,(f) must be date=-mined. For :ow index modulation ti. e.
:.0 for kr,~>1 ? . the approximation for R, (r) :aay be made as Ry. (r) =e-';roc°'e';R,c~~ ! e-t:~.~°l~l t kpR"(r)~
The spectral density S,.(f} is there=ore given by r S,. (f) = e-''~'<oyd(f ) ~ e-x'R°E°~kp ~Rm(T~-'2'~'dT (? ~ 7 ..
for this case. The first part corresponds to the 15 carrier cor.Epor7ent of the spectrum a:~d the second part corresnor_ds to the first order side band component.
mho r~~cdulation index kp .s considered low, if kP <0.1 radian. If kP <I.5 radian, it is ,:~nsiderEd high-index and i f O.I < kP < 1.5 , it i s cons idered medi um index . Wi:en 20 kP is madium or high indexed, the saries expansion IlluSL be used as Rr. (T) = e'~Fw(°?ek~wlel ~ e~~;$E°)~~ ~kPR~(z}~
This series expansicn is called Lewart's expaas_or..
If zhe spectral density of m(t) is ~-~.own, the spectra!
25 density of kP"R;;(t) can, in principle, be calculated as vcv. wv:ct~A-au t:v.c~tt~:.v ~;;~ . a-i~~_;~:~ : ~~:_~_~ : , +.~:~ cs:~
_~a:~;~.~a~;:::m:~
Uac-G3-6Y UC:X4aP h~o;n- f-USJ h lS/Li r-IU3 WO 99112371 PG'T/189&OI355 the n fold convolution of the sp~cLral density of kPR~(T} with itself. For a mean square mGdulation index ~; yor the phase modulation ~s(t) ~ kpm(t) , kpR,~(z)=~Pf~~T' such that the spectral density of m, (t) denoted by Sm,(f"j is g=ven by (3~) ~hus the spe:tral density of medium, index phase medula ted signal can be dete rc2ined using Lsvrart' s far:rula and the n-.ol d convolut:.o~ theorem.
c If tze rms madulation _ndex ~P, exceeds 2 rad;ans (gyp= > 2.0 radians; the number ef convolutions required will ba ve=y farce. ucwever, for small ~rodulation index, as well as fcr large index, far down on the tails, the number or terms to be included; in tY'e series is very large. In such cases, the spectrum may be calculated using the sadd::e point :nezhod disc'_osed by 'J. K. Prabhu and H. F. Ro,ae, "$peci.al r'Jensity Bounds of a P~" Wave," The Bell System TecY~.nical 2C Jourr~a'_, op. 769-511, March X969. As long as she mod~~I4tion index is even moderately high (~2 > 10) tha spectrum can be estimated by the saddle point method fo; all values of : in a simple manner with a fzactional arror of less trap 10%.
~5 Powsr Spectral Density of MSK/~PSK signals For a digital signal, the spectral density is a :unction of the spectral characteristics of the shaping pulse and the bGud rate T. The base band rate of MSK and QPSK signals can be determined =rom the 2.
CA 02302242 2000-o2-ZS P,"~:;~'r'~~~ ~''~~~T
KC\.\(~iv:If':1-1111:\C_IIf.::\ 1)~r ~ d-1::-:i:l : ~:_~y : -~ r.r,~ tr:~
_.r:r.nr~nt.:,.nre.
gee-u~-srsf uz:eaam rrem- r-ueu N.ibizt r-.us WO 99I3Z371 PCT/I898~01355 ampl~.tucle modulated representation of these signa'_s '?, Eq. 8) .
MSK Signal The spectral density of base bank MSK s~.gnal y'(t)=e'~~~'~ can be estimated from the amplitude rnodu:.ation representation of Via. 'l. The spectral density is given by z S., CI ) = ~ ~G(.f )~Z ( 31 ) where G!f) i' the Fourier transform of the signaling pulse g(t)=sin T (Eq. 6) . There: ore S,'{f) is given by 16T (co~(2nfl ))' !32) S.,(f)= ~Z(1_16 fzTi):
QPSK Signal 1~ The spectral der.3ity of base band QPSK sig~:al v, (t)=e'mr'~ can bz estimated frog' the amplitude modularion representation. of Eq. 8. The spectral densely is given by S,,(f)T T jP(~~~ ('~3) '~ 20 where P(f) is the Fourier trarsrorm or the rectangular signaling pulse. S~,(f) therefore is given by 5,., (f ) = T (s~~))2 ! 34 y )' In MSIC, the base band wa~eform that multiples the guadxature Carrier is much smoother than the abrupt 25 rectangular Waveform of QPSK. The waveform of MSK
exhibits phase continuity whereas that of QPSK is disccntir_uous. MSK has a main center lobe which is ._ hC~.~()\:f~t'~\-111'f:\C.HL;\ 1)i . B-f!_:):i : ti:y_ ~ -. Tn:r «:~
.~;rrn~r~.:~.m, N
Uac-U~~88 UZ:Zbae~ rrom- 1~U3U f If/Zf h~iUi WD 99/123~I PCUlB98/01355 1.5 times as wide as the main lobe cf Q?SK: but the side lobes fall off much faster. Hence the fractional out of band power for MSK is less compared to QPSK, accounting for the higher bandwidth efficiency of MSK.
The convolution of the base band spectrum of the desired signal S,,(f) with that of the interfering signal S,,(f) gives the base band inter'erence spectrum S~,(f) as given by Eq. 21 for high CIR (R2 ~ 1) . The ?0 baseband output due to interference ca:. therefore be corlputed as a function of the interference to carrier ration R2, the mean square modulation index tp; of the y- Ptd signal, and the baud rate T of the digital interferer, assuming fd~ 0. It is seen that the ratio of interference pawer density to signal power density is maximum at the lowest base band frequency.
However, for narrow bard signals, the basebard ini:erference spectrum is quite flat in the rarg~
~f!< W . Hence the =atio of total signal t4 t~Lal ?G interference in the baseband width W is approximately eaual to that at the lowest base band frequency.
Co-c~:annal Irterferencs Spectral Densisy under Non -fad_n~ Condw Lions Under non-fading conditions, the RF interference-to-signal ;aria R~ is a fixed quantity. For high average CIR, trerefore R'<1. The minimum bese band SIR relative to CIR is computed as SIR,, = ~~ ~ 2W= t 35 ~
S~ (D)~ R
~~rhere Sz(D) is the interference power spectral density at the lowest base band freqe~ency. This gives the . y.,,r IiC\. \is~\:ia'~\-lil i:'.C'fll:\ (1:: ~ :.s- J'.S-a:l : tt:__ ~ ~ Tw;ma ~.sa:rr-uu~ ~ n ~ a Uoc-U5-'i9 OL:Zb~n From- I-U3J N.IdIZI F-I03 imprevement in base band SIR relative to R'. Hence the total SIR at the lowest base band frequency is given by CIR t SIR,~;~ .
Tables 2, 3 and 4 give the results for the ratio of signal to interference power density SIR", for R'=.01 (ccrresponding to CIR of 20 d8), when both signal and interference are non fading. The interference spectra are Estimated with both desired signal and interferer occupying the same band~ridth.
The bandw~.dth of the angle modulated signal ~s estiriiated usin g Carson's rule, while the bandwiQth occupied by the digital signal is assumed to be 1.3/T.
The minimum signal to interference power density when the systems under ca~sideration occupy ciitferent bandwidths have beer, evaluated. The spectra of the MSK and QPSK modulated interferers for a bandwidth occupancy of 30 kHz are shown in FIGtTRES'8 and 9 respectively. Tre spectrum of the phase modulated signal with root mean scuarz (RMS) r~od~:lation ir_dex of 1.?9 (corrESponding to 30 kH? bandwidth; is given in rIGURE 10. The interfere~:ce spectra for analog to analog and digital to analog are evaluated and given in E'IGURES 11-13 when the desired signal 'as will as the interfering signs' are occupying an equivalen;.
bandwidth ef 3D kEiz. FIGURES 11-13 are summarized without normalization in F1'Gll~c~ 14. The SIRo,," ofered en the t~hase mfldu:.ated signal by MSK interference is seen tQ be better by about 3.3 dB and that offered by PSK interference by about 2.5 d8 compared to an equivalent analog phase modulated interferer_ce. The effect of increasing the modulation index or. the base bard SIR is observed from the tables. It is seen teat CA 02302242 2000-02-28 '''~~C~~
RC~.W)l:fl'A-All~h:'vCllf:': U:; . a-1v-a:! : t3::!:3 : ~ +.;~i t3:~ '_:3;Ja-1-lti;~Nl;i UoC-U3-NY UL:T9~IA I~ror~- 1-U3U f IY/Lf r-IU3 WO 9J113371 PCTlI~i9$/Q1355 if high CIR ar RF is maintained, the base band SrR
improves as the modulation index of the desired signal is ~.ncreased. This can be used to advantaqe in improving the output S:R by~zrad:ng bandwidth.
TABLE 2 ?M - PM
Bandwidth M ~2~iW
(KHz ) dulation (0)IR= dB
S
Index m, = 4~, ,~
25 0.9 4.6 3d 1.19 6.93 4p 1.732 10.58 MSK Interferer ~qnal SIR imin) ~
Bandwidth Baud Pate Modalarioz 3 Flllo dB
(Krizy ~, l Inter .5,~(O)~B' ~ ~, baud) 25 19.23 0.9 7.03 30 23.08 1.19 10.14 40 30.77 1.732 14.68 f:l~. W v:fa'A-V11 f:'W III:', W ~ _1-J_'-;l:l : ti:_:i : - +.t:i ~:;t ~.i'.Ja~f l~c;:, : y~ ~
Uoc-03-dt~ OZ:Zb~~ hr~~l- 1-030 f' l0/Zl F-143 WO 99112371 PCT~lB98J0i355 Te~BLE 4 PM - QPSK
QPSK Interferes $iq al SIR (min) 8au3 Rate Bandwidth Modulati 1 '~2 ~?W
1 (Kilo an ~ d8 ~ ~~2? ~, Index 5~~0)~R
baudl cp, 25 -I~.23 0.9 6.18 30 23.08 1.19 9.31 40 30.77 1.732 13.86 In light of the foregoing, it can be appreciated t:-:az the base. band SIR in Oho case of an MSK
,- interferes is bEtter than an equivalent QPSK
interferes, and that both of the digital interferers under consideration provide higher base band SIR than that p=ovided by an eauivalent analog phase modulated 1G interferes.
By thz use of ~he present irven-ions performance tray be ecaluazed for co-existing digital and analog systems, such as, for exar~pie, mob~.ie radio systems whore analog AMPS and digital TDMA systems share tt~.e same band. S4ch evaluation permits the capacity and/or the Quality oservice of such systems to be - optimized.
It is understood than the present invention can take many forms an~ embodiments. Accordingly, several variations may be made ~.z the fcregeing without departing from the spirit or the scope of the invention. For example, the method of the present invent;:on tray be employed to analyze the interference im.-nunity offered by different modulation schemes a:~d can be extended to estimate the effects of botn ACI
i:i'\. ~'()~'~:f:f'A-Vt( 1:'W.'Ilf:.\ (n ~ :i-1'=-;1!1 : H:_~;; : ~ ~.I:r rs:a _'s;rf~1~1t;:.,:,y.~
Uec-Ui-5Y UL:'ctiim prom- I-09fi N.Z:IZI h-BUY
WO 99/I23~I PGT/IB98/OI355 and CCI under fading and also the effect of diversity in coi2~sting interference in high capacity mobile radio systems.
Having thus described. the present invention by reference to certain of its preferred embodiments, a is noted that the embodiments disclosed are ill:»strative rather tY,an limiting in nature and that a wide range of variations, modifications, charges, and 1C substitutions are conte_mplGtQd in the foregoing disclosure and, in some instances, some feaz:;res of the Present invention may be employed without a corresponding use of the ctrer features. Accord=ugly, it is appropriate that t,'~e appended claims be construed broadly and :.n a manner consistent with the scooe oz the in~renzion.
L
Claims (12)
1. A method for optimizing spectral re-use between an interferer digital phase modulated cellular system (120) utilizing a first transmitter/receiver (704) configurable to operate substantially at a first frequency, and a desirable analog phase modulated cellular system (110) utilizing a second transmitter/receiver (702) configurable to operate substantially at a second frequency, the first and second transmitter/receivers being separated by a re-use distance, the method being characterized by the steps of:
determining a carrier-to-interference ratio (CIR) with reference to the re-use distance;
setting an acceptable baseband signal-to-interference ratio (SIR);
determining an optimum frequency reduction factor (IRF) as the ratio of the SIR to the CIR:
determining an optimum frequency separation f d with reference to the power spectral density of the random phase angle, are interference-to-signal-carrier power ratio, and autocorrelation functions of the baseband phase modulated processes;
configuring the first transmitter (704) to operate substantially at the first frequency; and configuring the second transmitter (702) to operate substantially at the second frequency, wherein the second frequency is substantially separated in bandwidth from the first frequency by at least the determined frequency separation f d.
determining a carrier-to-interference ratio (CIR) with reference to the re-use distance;
setting an acceptable baseband signal-to-interference ratio (SIR);
determining an optimum frequency reduction factor (IRF) as the ratio of the SIR to the CIR:
determining an optimum frequency separation f d with reference to the power spectral density of the random phase angle, are interference-to-signal-carrier power ratio, and autocorrelation functions of the baseband phase modulated processes;
configuring the first transmitter (704) to operate substantially at the first frequency; and configuring the second transmitter (702) to operate substantially at the second frequency, wherein the second frequency is substantially separated in bandwidth from the first frequency by at least the determined frequency separation f d.
2. The method of Claim 1, wherein the step of determining are optimal frequency separation f d is further characterized by numerically determining an optimal frequency separation f d with reference to the equation given by:
as .function. .fwdarw. .function. d, wherein S .lambda.(.function.) is the power spectral density of the random phase angle .lambda., R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, .tau. is time variable of integration, and R v i, and R v s, are autocorrelation functions of the baseband phase modulated processes; and wherein the IRF is determined with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, S .lambda.(.function. d) is the value of the power spectral density of a random phase angle .lambda. at f d.
as .function. .fwdarw. .function. d, wherein S .lambda.(.function.) is the power spectral density of the random phase angle .lambda., R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, .tau. is time variable of integration, and R v i, and R v s, are autocorrelation functions of the baseband phase modulated processes; and wherein the IRF is determined with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, S .lambda.(.function. d) is the value of the power spectral density of a random phase angle .lambda. at f d.
3. The method of Claim 1 wherein the step of setting an acceptable baseband SIR is further characterized by setting the SIR to about 50 dB.
4. A method for optimizing spectral re-use between an interferer digital phase modulated cellular system (120) utilizing a first base station antenna (704) operative substantially at a first frequency, and a desirable analog phase modulated cellular system (110) utilizing a second base station antenna (702) operative substantially at a second frequency, the first frequency and second frequency being substantially separated in bandwidth by a frequency separation of f d, the method being further characterized by the steps of:
determining the power spectral density of the random phase angle at the separation frequency f d, with reference to the interference-to-signal carrier power ratio, the separation frequency f d, and autocorrelation functions of the baseband phase modulated processes;
determining an interference reduction factor (IRF) with reference to the baseband power spectral density of the desired signal, the power spectral density of a random phase angle at f d, and an interference carrier-to-signal carrier power ratio;
setting an acceptable baseband signal-to-interference ratio (SIR);
determining a carrier-to-interference ratio (CIR) as a ratio of the SIR to the IRF;
determining the re-use distance with reference to the CIR; and spacing apart the first base station antenna (704) and the second base station antenna (702) to obtain at least the determined re-use distance therebetween.
determining the power spectral density of the random phase angle at the separation frequency f d, with reference to the interference-to-signal carrier power ratio, the separation frequency f d, and autocorrelation functions of the baseband phase modulated processes;
determining an interference reduction factor (IRF) with reference to the baseband power spectral density of the desired signal, the power spectral density of a random phase angle at f d, and an interference carrier-to-signal carrier power ratio;
setting an acceptable baseband signal-to-interference ratio (SIR);
determining a carrier-to-interference ratio (CIR) as a ratio of the SIR to the IRF;
determining the re-use distance with reference to the CIR; and spacing apart the first base station antenna (704) and the second base station antenna (702) to obtain at least the determined re-use distance therebetween.
5. The method of Claim 4 wherein the step of determining an IRF is further characterized by determining an IRF with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, S.lambda.(.function. d) is the value of the power spectral density of a random phase angle .lambda., at f d, and R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave.
wherein .PHI.~/2W is baseband power spectral density of the desired signal, S.lambda.(.function. d) is the value of the power spectral density of a random phase angle .lambda., at f d, and R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave.
6. The method of Claim 4 wherein the step of determining an IRF is further characterized by determining an IRF with reference to the equation given by:
wherein .PHI.~/2W is the baseband power spectral density of the desired signal, S.lambda.(.function. d) is the value of the power spectral density of a random phase angle .lambda. at f d, and R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, wherein S.lambda.(.function. d) is determined numerically with reference to the equation given by, as .function. .fwdarw. .function. d, wherein .lambda. is a random phase angle of a desired wave, f d is the separation frequency, .tau. is a tune variable by which the integral is integrated, and R v i and R v s are autocorrelation functions of the baseband phase modulated processes.
wherein .PHI.~/2W is the baseband power spectral density of the desired signal, S.lambda.(.function. d) is the value of the power spectral density of a random phase angle .lambda. at f d, and R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, wherein S.lambda.(.function. d) is determined numerically with reference to the equation given by, as .function. .fwdarw. .function. d, wherein .lambda. is a random phase angle of a desired wave, f d is the separation frequency, .tau. is a tune variable by which the integral is integrated, and R v i and R v s are autocorrelation functions of the baseband phase modulated processes.
7. The method of Claim 9 wherein the step of determining the optimal rep-use distance is further characterized by determining the optimal re-use distance by determining the ratio of the SIR to the IRF to the power of negative .gamma., where .gamma. is the path loss exponent.
8. The method of Claim 4 wherein the step of determining the optimal re-use distance is further characterized by determining the optimal re-use distance by determining the ratio of the SIR to the IRF to the power of negative .gamma., where .gamma. is the path loss exponent within a range of about 2 to about 6.
9. The method of Claim 4 wherein the step of setting an acceptable baseband SIR is further characterized by setting the SIR to about 30 dB for co-channel interference (CCI).
10. The method of Claim 4 wherein the frequency separation f d is set equal to zero for co-channel interference (CCI), and the step of determining the IRF is further characterized by determining the IRF
with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, S.lambda.(0) is the power spectral density of a random phase angle .lambda. at zero, and R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave.
with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, S.lambda.(0) is the power spectral density of a random phase angle .lambda. at zero, and R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave.
11. The method of Claim 4 wherein the frequency separation f d is set equal to zero for co-channel interference (CCI), and the step of determining the IRF is further characterized by determining the IRF
with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, and S.lambda.(0) is the power spectral density of a random phase angle .lambda. at zero, S.lambda.(0) being determined with reference to the equation given by:
as .function. .fwdarw. 0, wherein .tau. is a time variable by which the integral is integrated, and R v i(.tau.) and R v,(.tau.) are autocorrelation functions of baseband phase modulated processes.
with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, and S.lambda.(0) is the power spectral density of a random phase angle .lambda. at zero, S.lambda.(0) being determined with reference to the equation given by:
as .function. .fwdarw. 0, wherein .tau. is a time variable by which the integral is integrated, and R v i(.tau.) and R v,(.tau.) are autocorrelation functions of baseband phase modulated processes.
12. The method of Claim 4 wherein the frequency separation f d is set equal to zero for co-channel interference (CCI), and the step of determining the IRF is further characterized by determining the IRF
with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, and S.lambda.(0) is the power spectral density of a random phase angle .lambda. at zero, S.lambda.(0) being determined with reference to the equation given by:
as .function. .fwdarw. 0, wherein S v i(.function.) and S v i(.function.) are spectral densities of baseband processes, and ~ denotes the convolution operation.
with reference to the equation given by:
wherein .PHI.~/2W is baseband power spectral density of the desired signal, R is the ratio of the amplitude of the interfering wave to the amplitude of the desired wave, and S.lambda.(0) is the power spectral density of a random phase angle .lambda. at zero, S.lambda.(0) being determined with reference to the equation given by:
as .function. .fwdarw. 0, wherein S v i(.function.) and S v i(.function.) are spectral densities of baseband processes, and ~ denotes the convolution operation.
Applications Claiming Priority (5)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US5759697P | 1997-08-29 | 1997-08-29 | |
| US60/057,596 | 1997-08-29 | ||
| US09/141,477 | 1998-08-27 | ||
| US09/141,477 US6085094A (en) | 1997-08-29 | 1998-08-27 | Method for optimizing spectral re-use |
| PCT/IB1998/001355 WO1999012371A1 (en) | 1997-08-29 | 1998-08-28 | Method for optimizing spectral re-use |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2302242A1 CA2302242A1 (en) | 1999-03-11 |
| CA2302242C true CA2302242C (en) | 2004-03-16 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002302242A Expired - Fee Related CA2302242C (en) | 1997-08-29 | 1998-08-28 | Method for optimizing spectral re-use |
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| Country | Link |
|---|---|
| US (1) | US6085094A (en) |
| EP (1) | EP1008268B1 (en) |
| AU (1) | AU8880498A (en) |
| CA (1) | CA2302242C (en) |
| DE (1) | DE69803991T2 (en) |
| WO (1) | WO1999012371A1 (en) |
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| US8064824B2 (en) * | 2007-07-03 | 2011-11-22 | Atc Technologies, Llc | Systems and methods for reducing power robbing impact of interference to a satellite |
| US7978135B2 (en) | 2008-02-15 | 2011-07-12 | Atc Technologies, Llc | Antenna beam forming systems/methods using unconstrained phase response |
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| US8193975B2 (en) | 2008-11-12 | 2012-06-05 | Atc Technologies | Iterative antenna beam forming systems/methods |
| US8339308B2 (en) | 2009-03-16 | 2012-12-25 | Atc Technologies Llc | Antenna beam forming systems, methods and devices using phase adjusted least squares beam forming |
| US8520561B2 (en) | 2009-06-09 | 2013-08-27 | Atc Technologies, Llc | Systems, methods and network components that provide different satellite spot beam return carrier groupings and reuse patterns |
| EP2484027B1 (en) | 2009-09-28 | 2017-03-29 | ATC Technologies, LLC | Systems and methods for adaptive interference cancellation beamforming |
| US10110288B2 (en) * | 2009-11-04 | 2018-10-23 | Atc Technologies, Llc | Frequency division duplex (FDD) return link transmit diversity systems, methods and devices using forward link side information |
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| US10219182B1 (en) | 2017-09-10 | 2019-02-26 | Hewlett Packard Enterprise Development Lp | Channel bandwidth selection |
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| DE69427404T2 (en) * | 1994-10-26 | 2001-11-08 | Ibm | Allocation method and apparatus for reusing network resources in a wireless communication system |
| US5974323A (en) * | 1996-09-13 | 1999-10-26 | Airnet Communications Corporation | Frequency plan for wireless communication system that accommodates demand growth to high efficiency reuse factors |
| US5946625A (en) * | 1996-10-10 | 1999-08-31 | Ericsson, Inc. | Method for improving co-channel interference in a cellular system |
| US5974324A (en) * | 1997-02-10 | 1999-10-26 | Ericsson Inc. | Adaptive frequency reuse plan |
| US5966657A (en) * | 1997-07-24 | 1999-10-12 | Telefonaktiebolaget L M Ericsson (Publ) | Method and system for radio frequency measurement and automatic frequency planning in a cellular radio system |
| US5970411A (en) * | 1997-08-08 | 1999-10-19 | Nortel Networks Corporation | N=4 directional frequency assignment in a cellular radio system |
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- 1998-08-27 US US09/141,477 patent/US6085094A/en not_active Expired - Lifetime
- 1998-08-28 DE DE69803991T patent/DE69803991T2/en not_active Expired - Fee Related
- 1998-08-28 WO PCT/IB1998/001355 patent/WO1999012371A1/en active IP Right Grant
- 1998-08-28 EP EP98940485A patent/EP1008268B1/en not_active Expired - Lifetime
- 1998-08-28 AU AU88804/98A patent/AU8880498A/en not_active Abandoned
- 1998-08-28 CA CA002302242A patent/CA2302242C/en not_active Expired - Fee Related
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| AU8880498A (en) | 1999-03-22 |
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| DE69803991T2 (en) | 2002-10-17 |
| CA2302242A1 (en) | 1999-03-11 |
| EP1008268A1 (en) | 2000-06-14 |
| WO1999012371A1 (en) | 1999-03-11 |
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