WO2017050930A1

WO2017050930A1 - Method and device for symbol-level multiuser precoding

Info

Publication number: WO2017050930A1
Application number: PCT/EP2016/072600
Authority: WO
Inventors: Maha ALODEH; Symeon CHATZINOTAS; Björn OTTERSTEN
Original assignee: Université Du Luxembourg
Priority date: 2015-09-23
Filing date: 2016-09-22
Publication date: 2017-03-30

Abstract

The invention presents a method and device which constructively exploit the inter-symbol interference caused by the concurrent transmission of data symbols from a single transmitter to multiple receivers using a multiple input data communication channel, wherein each receiver may require a different data goodput rate.

Description

METHOD AND DEVICE FOR SYMBOL-LEVEL MULTIUSER PRECODING

Technical field The present invention lies in the field of digital communications. Background of the invention

A multiple input data communication channel allows sending different data symbols to different receivers at the same time. The data symbols that are transmitted concurrently interfere with each other, so that each receiver receives a combination of all data symbols transmitted to all receivers at a given time. In traditional systems, the goal is therefore to design transmission methods which mitigate such multiuser interference. In digital communication systems, data is encoded into signals using a digital modulation technique before being transmitted using a digital communication channel. A digital modulation scheme is typically defined by a signal constellation in a complex plane, each signal point of the constellation corresponding to a data symbol. Once a receiver demodulates the received signal, it maps the received signal point to the signal constellation, and decodes the signal as the symbol associated with the closest available constellation point.

Precoding may be considered as a form of forward error protection. Precoding may be applied at a transmitting device to data symbols, in order to pre-emptively address known or estimated channel behaviour, which adversely affect the reception of the transmitted data symbols. Precoding may also be applied to pre-emptively address other factors that adversely affect the probability of correct reception of transmitted data symbols, such as for example inter-symbol interference in one-to many transmission schemes. In a known generic one-to many transmission framework, precoding can be loosely defined as the design of a signal that is to be transmitted in order to efficiently deliver the desired information to multiple users exploiting, for example, a multiantenna space. Focusing on multiuser downlink systems, the precoding techniques can be classified as

1 ) Group-level precoding in which multiple codewords are transmitted simultaneously but each codeword (i.e. a sequence of symbols) is addressed to a group of users.

This case is also known as multigroup multicast precoding [1]- [4] and the precoder design is dependent on the channels in each user group. 2) User-level precoding in which multiple codewords are transmitted simultaneously but each codeword (i.e. a sequence of symbols) is addressed to a single user. This case is also known as multiantenna broadcast channel precoding [5]-[16] and the precoder design is dependent on the channels of the individual users.

3) Symbol-level precoding in which multiple symbols are transmitted simultaneously and each symbol is addressed to a single user [17]- [25]. This is also known as a constructive interference precoding and the precoder design is dependent on both the channels and the symbols of the users. It has been shown in various literature that symbol-level precoding shows considerable gains in comparison to the conventional group- or user-level precoding schemes [17]- [25]. The main reason is that in symbol-level precoding the vector of the aggregate multiuser interference can be manipulated, so that it contributes in a constructive manner from the perspective of each individual user. This approach cannot be exploited in conventional precoding schemes, since each codeword includes a sequence of symbols and the phase component of each symbol rotates the interference vector in a different direction. As a result, conventional schemes focus on controlling solely the power of the aggregate multiuser interference, neglecting the vector phase in the signal domain. The paradigm of constructive interference for multiuser multiple-input/single output, MISO, downlink was first proposed in [17], but it was strictly limited to PSK modulations. The main concept relies on the fact that the multiuser interference can be pre-designed at the transmitter, so that it steers the PSK symbol deeper into the correct detection region. Based on an MMSE objective, two techniques were proposed based on partial zero-forcing [17] and correlation rotation [18]. These techniques were based on decorrelating the user channels before designing the constructive interference. However, this step leads to suboptimal performance, as channel correlation can be beneficial while aiming for constructive interference. Based on this observation, an MRT-based solution was proposed in [21], which outperformed previous techniques. All aforementioned techniques have a commonality, namely they are based on the conventional approach of applying a precoding matrix to the user symbol vector for designing the transmitted signal. Authors in [21] [22] have shown that in symbol-level precoding, more efficient solutions can be found while designing the transmitted signal directly. Following this intuition, a novel multicast-based symbol-level precoding technique was initially proposed in [21] and later elaborated in [22] for MPSK modulations. In more detail, the transmitted signal can be designed directly by solving an equivalent PHY multicasting problem with additional phase constraints on the received user signal. Subsequently, the calculated complex coefficients can be utilized to modulate directly the output of each antenna instead of multiplying the desired user symbol vector with a precoding matrix. Based on this approach, authors in [23] have extended the multicast-based symbol-level precoding for imperfect CSI by proposing a robust precoding scheme. Going one step further, the above techniques were generalized in [24] [25] taking into account that the desired MPSK symbol does not have to be constrained by a strict phase constraint for the received signal, as long as it remains in the correct detection region. The flexible phase constraints can obviously introduce a higher symbol error rate, SER, if not properly designed. In this direction, the work in [25] studies the optimal operating point in terms of flexible phase constraints that maximizes the system energy efficiency.

These known systems are limited to the use of m-ary phase shift keying, MPSK, signal constellations and fail to take into account any individual requirements of the receivers.

Technical problem to be solved

It is an objective to present a method and device, which overcome at least some of the disadvantages of the prior art.

Summary of the invention

According to a first aspect of the invention, a method for transmitting precoded data symbols using a data transmission device capable of transmitting data symbols using digitally modulated signals to K receivers over a common multiple input data communication channel is provided. The method comprises the following steps:

- providing a desired data transmission rate, and channel state information, for each receiver j, 1 < j < K;

providing for each receiver j, 1 < j < K an indexed sequence of N data symbols dj[n] to be transmitted, 1 < n < N;

selecting using selection means, for each receiver j, a signal constellation , whose associated data transmission rate is higher than said desired data transmission rate, from a plurality of predetermined signal constellations, wherein each signal constellation is associated with a digital modulation scheme, wherein each signal constellation comprises a plurality of signal constellation points in the signal domain, and wherein each signal constellation point is associated with a data symbol and with a corresponding decoding region; generating, using generating means, for each one of said data symbols dj[n], 1 < j < K, a corresponding precoded symbol X j[n], 1 < j < K, such that, after interfering with each precoded symbol Xi≠j[n],1 < i < K having the same index n, 1 < n < N, during transmission over said multiple input data communication channel, the corresponding data symbol received by receiver j lies in its corresponding decoding region,

wherein the vector of precoded symbols x[n]={xi[n]; X2[n], ... , χκ[η]} is computed so as to have minimum power under a set of at least two signal- domain constraints per receiver j, 1 < j < K, said constraints depending on the selected signal constellation for receiver j, and on the channel state information for receiver j;

transmitting, using transmission means, the precoded symbols to each receiver j, 1 < j < K, over said multiple input data communication channel. Preferably, the selection means may comprise a selector. Advantageously the generating means may comprise a precoded symbol generator. The selection and/or generating means may preferably comprise computing means.

Preferably, during the step of generating the precoded symbols, for at least one data symbol dj[n] , 1 < j < K the corresponding precoded symbol may be generated such that, after interfering with each data symbol having the same index di≠j[n],1 < i < K, during transmission over said multiple input data communication channel, the corresponding data symbol received by receiver j corresponds to the associated signal constellation point. During said step of transmitting the precoded symbols, the precoded symbols may preferably be transmitted using a different input among said data communication channel's multiple inputs for each receiver.

In said step of providing a desired data transmission rate for each receiver, the desired data transmission rates may preferably be received over a data communication channel by the transmission device using data reception means.

The method may further preferably comprise the step of receiving channel state information from at least one receiver at the data transmission device. Further, the step of generating the precoded symbols may preferably take into account the received channel state information. For each index, 1 < n < N, the generated precoded symbols may preferably be associated with said data symbols dj[n], 1 < j < K, and stored in a memory element of said data transmission device. The memory element may preferably be a structured memory element. Even more preferably, the memory element may be a look-up table or database.

At said step of generating the precoded symbols, the method may preferably comprise the further steps of:

- checking, for said data symbols dj[n], 1 < j < K, whether corresponding precoded symbols have been previously stored in said memory element;

retrieving said precoded symbols from said memory element if a match is found; generating said precoded symbols otherwise. Said data communication channel may preferably by a wireless communication channel.

The data transmission device may preferably comprise multiple transmission antennas for transmitting data symbols over said data communication channel. Preferably, at said step of transmitting the precoded symbols, N precoded symbols may preferably be transmitted to receiver j, 1 < j < K, in a data frame comprising a preamble identifying the selected signal constellation.

The preamble may further comprise information facilitating the computation of channel state information at each receiver.

According to a further aspect of the invention, a data transmission device for transmitting precoded data symbols using digitally modulated signals to K receivers over a common multiple input data communication channel is provided. The device comprises:

a first memory element for storing a desired data transmission rate for each receiver j, 1 < j < K;

a second memory element for storing an indexed sequence of N data symbols dj[n] to be transmitted, 1 < n < N;

data transmission means adapted to transmit data to each of said receivers using one of said data communication channel's multiple inputs, and

processing means configured to the steps of the method according to the present invention. The data transmission device may preferably further comprise first data reception means adapted to receive each receiver's desired data rate over a data communication channel. Preferably, the data transmission device may further comprise second data reception means adapted to receive channel state information.

According to another aspect of the invention, there is provided a computer program comprising computer readable code means, which when run on a computer, causes the computer to carry out the method steps of selecting said signal constellations and of generating said precoded symbols.

According to yet another aspect of the invention, there is provided a computer program comprising computer readable code means, which when run on a computer, causes the computer to carry out the method according to the invention.

According to a further aspect of the invention, a computer program product is provided, the computer program product comprising a computer-readable medium on which the computer program according to the invention is stored.

According to a final aspect of the invention, there is provided a computer capable of carrying out the method according to the invention.

The main contributions of the invention may be summarized as follows:

- The extension of symbol-level precoding to any multi-level modulation, including the commonly used MQAM and APSK.

The definition of a system architecture for a symbol-level precoding transmitter. The extension of the connections between symbol-level precoding and phase- constrained PHY multicasting for generic multi-level modulations.

- The derivation of a symbol-level precoding algorithm for the power minimization with signal-to-interference-plus noise ratio, SINR, or goodput constraints under an adaptive modulation scheme.

By using the measure according to the present invention, it becomes possible to use a symbol-level multiuser precoding scheme in scenarios where each receiver in the systems requires potentially different goodput/throughput rates, and may be served using a specific signal constellation. The method therefore adapts the modulation scheme to the requirements of each receiver, while, at the same time, constructively exploiting the inter- symbol interference between each users. This results in overall improved performance of the resulting communication system.

Brief description of the drawings

Several embodiments of the present invention are illustrated by way of figures, which do not limit the scope of the invention, wherein:

Figure 1 is a flow diagram showing the main steps of a preferred embodiment according to the invention;

- Figure 2 is a transmitter block diagram for symbol-level precoding according to a preferred embodiment of the invention, wherein block operations are classified into frame-level and symbol-level;

Figure 3 is a detail of the transmitter block diagram of Figure 2.

Figure 4 illustrates the first quadrant of a generic modulation constellation;

- Figure 5 illustrates a classification of the constellation points for a 16-QAM modulation into inner(1 ), outer (2) and outermost (3);

Figure 6 illustrates a classification of the constellation points for a 16-APSK modulation into inner(1 ) and outer(2);

Figure 7 shows Frame-level transmit power in dBW plotted against target SNR; - Figure 8 shows Frame-level energy efficiency plotted against target SNR;

Figure 9 shows Frame-level transmit power plotted against the number of the system size;

Figure 10 shows the power variance during the frame in the case of QPSK modulation;

- Figure 11 shows transmit power regions plotted against users' target SNR and their corresponding modulation;

Figure 12 shows energy efficiency regions plotted against users' target SNR and their corresponding modulation;

- Figure 13 shows SER curves plotted against SNR for 4-QAM and 16-QAM.

Detailed description of the invention

This section describes the invention in further detail based on preferred embodiments and on the figures.

Figure 1 shows the main steps according to a preferred embodiment of the method according to the present invention. A transmission device is capable of transmitting data to multiple receivers using a common multiple input data communication channel. Such multiuser multiple input/single output channels are known in the art. A non-limiting example of such a channel may be a wireless multi-antenna broadcast channel. The transmission device is adapted to transmit data symbols using digitally modulated signals, as known in the art, to K receivers. In a first step 10, target goodput or data transmission rates are provided at a transmission device. Preferably, the desired target data transmission rates are sent to the transmission device by the users or receivers. Thereby, each user of the system is able to request a desired data rate and/or quality of service. Channel state information, is also provided at the transmission device. At step 20, the transmitter is provided with an indexed sequence of N data symbols dj[n] to be transmitted to each one of the receivers. An individual sequence is provided for each receiver. Here the index j refers to a receiver, 1 < j < K, while the index n refers to a specific symbol in the data symbol sequence. Data symbols are typically transmitted in a symbol transmission period, so that for example during period 1 , the j data symbols dj[1], 1≤ j≤ K, are transmitted at the same time to the K receivers and interfere with each other.

The transmission device has access to plurality of signal constellations, such as m-PSK, m- QAM, etc... Any signal constellation may be used by the transmission device. Based on the provided data transmission rates, the transmission device selects in step 30 for each receiver an individual signal constellation, using which the desired data transmission rate is achievable. It is well known that higher order constellations are capable of achieving higher rates. As is well known, each signal constellation comprises multiple signal constellation points and a decoding region is associated with each constellation point. At step 40, the transmission device generates for each one of said data symbols dj[n], 1 < j < K, a corresponding precoded symbol, such that, after interfering with each data symbol having the same index di≠j[n],1 < i < K, during transmission over said multiple input data communication channel, the corresponding data symbol received by receiver j lies in its corresponding decoding region. Instead of mitigating inter-symbol interference among the K users, the invention suggests to construct the precoded symbols such that the aggregate effect of desired symbol and multi-user interference forces the received signals into their respective decoding regions. In a preferred embodiment, each generated precoded symbol vector of K precoded symbols is stored in a memory element together with the original K data symbols. This allows to speed-up the generation of the precoded symbols through a simple look-up operation in case the required precoded symbols have been generated in a previous iteration of the method. During optional step 42, the transmitter checks whether the required precoded symbols are available in the memory element. If a match is found, the required precoded symbols are retrieved from the memory element at step 44. Otherwise the precoded symbols are generated as further detailed here below.

At step 50, the K precoded symbols are transmitted over the multiple input data communication channel towards the K receivers.

For higher order constellations, stricter bounds may be provided for some constellation points. To that end, for a given data symbol dj[n] , 1 < j < K the corresponding precoded symbol is generated such that, after interfering with each data symbol having the same index di≠j[n], 1 < i < K, during transmission over said multiple input data communication channel, the corresponding data symbol received by receiver j corresponds to the associated signal constellation point.

N precoded symbols are preferably transmitted to a receiver j in a data frame comprising a preamble, which includes signalling information identifying the modulation scheme, i.e. signal constellation that was used to encode the N data symbols. The preamble may further comprise pilots that allow each receiver to compute channel state information, which may be fed back to the transmission device for further refinement of the precoding step. Such CSI- based feedback and precoding techniques are as such known in the art.

A transmission device according to a preferred embodiment of the invention comprises transmission means adapted to transmit digitally modulated signals representing data symbols over a multiple input data communication channel. The device comprises memory elements, such as random access memory, RAM, for storing the desired data transmission rates and data symbols for each receiver. The transmission device further comprises processing means, such as a central processing unit, CPU, configured for executing the method steps according to the method described previously.

A transmission device according to a preferred embodiment of the invention is illustrated using a block diagram in Figures 2 and 3 respectively. Goodput target rates are provided at the processing means in accordance with step 10 of the invention. Further, N data symbols are provided at the processing means for each one of K target receivers, corresponding to step 20 of the invention. The block labelled "Symbol Level" outlines the steps carried out by the processing means based on the information provided in the previous steps. The implementation of this block corresponds to steps 20-40 of the method according to the invention. A serial to parallel converter is placed to enable the symbol-level processing and to jointly process the set of all users' symbols and channel state information. Finally, the device transmits the resulting precoded symbols using transmission means, corresponding to step 50. The calculated precoding weights are applied directly on the transmit antennas by applying the corresponding magnitude and phases. A detail of the "Symbol Level" block in Figure 2, corresponding to optional steps 42-44 described here above, is shown in Figure 3. Here, the computed precoded symbols are stored in a memory element for future retrieval.

Further details of the invention and possible implementations thereof are outlined by way of further preferred embodiments.

/. INTRODUCTION TO FURTHER PREFERRED EMBODIMENTS The remainder of this description is organized as follows: the system model is described in section (II). A multicast characterization to symbol-level precoding is explained in section (III). In section (V), we propose a symbol-level precoding for multi-level modulation. Finally, the numerical results are displayed in section (VI). Notation: We use boldface upper and lower case letters for matrices and column vectors,

#f ( A* II || respectively. ' stand for Hermitian transpose and conjugate of (.) E(.) and I I ^" Ί denote the statistical expectation and the Euclidean norm, and A O is used to indicate the positive semidefinite matrix. ^(^' ) ^» I ^' ! are the angle and magnitude of respectively. Re(.), Im(.) are the real and the imaginary parts of (.)

//. SYSTEM AND SIGNAL MODELS

Let us consider a single-cell multiple-antenna downlink scenario, where a single Base Station, BS, is equipped with M transmit antennas that serves K user terminals, each one of them is equipped with a single receiving antennas. The described system can be extended to a multicell system where the signal design takes place in a centralized manner. The MIMO case will be briefly discussed in section lll-C.

As depicted in Fig. 2, the transmission scheme is based on K frames (one per user) which include a common preamble for the pilot symbols and signaling information, followed by N useful symbols for each user (data payload). It should be noted that the preamble is precoded, while the useful symbols are precoded on a symbol-level.

Similar to conventional multiuser precoding schemes, the pilots are exploited by each user in order to estimate its channel through standard CSI estimation methods and feed it back to the BS, so that it can be used in the design of the precoded signal. In this context, we assume a quasi static block fading channel J ⁵³ ' between the BS antennas and the j^th user. The method according to the invention may also be applied to Very High Speed Digital Subscriber Line, VDSL, where the channel remains constant for a long period [12]. This is assumed to be known at the BS based on the channel state information, CSI, feedback and fixed for each frame, i.e. N symbols.

Regarding the useful symbols, the BS can serve each user with a different modulation to support different levels of user rates. This is enabled through an adaptive modulation scheme, which can be concisely described by the Table 1 . In more detail, the modulation for each user is selected from the set ^ ^— 0 based on the user's requested rate min and max thresholds of Table 1 . The supported SINR range is y

and thus, SINRs lower than lead to unavailability (i.e. zero goodput), while SNRs larger than '^max do not provide a further goodput increase.

It should be noted that although the precoding changes on a symbol-basis, the modulation types are allocated to users on a frame-basis. This is necessary because the user expects to receive the same modulation type for all useful symbols in a frame in order to properly adjust the detection regions. The users are notified about their corresponding modulations through the signaling preamble of the frame.

TABLE I

Abstraction of an adaptive modulation scheme For a single symbol period n = 1 . . . N, the received si nal at jth user can be written as

x|ft.j ( ^'L- js the transmitted symbol sampled signal vector at the nth symbol period from the multiple antennas transmitter and zj denotes the noise at jth receiver, which is assumed as an i.i.d. complex Gaussian distributed variable ^{\ "} *

A compact formulation of the received signal at all users' receivers can be written as

y[n] — Hx[n] + z[n]. (2)

Assuming linear precoding, let X ^{rt L}M"^J b he_P w wrriitttte_Pnn a ps« ^{X " L}W ^J =∑i-i ^{W "} ϊiΓHΊ-djM- where W , p x l ¾r ,

is the precoding vector for user j. The received signal at jth user ^J3 in nth symbol period is given by

A more detailed compact system formulation is obtained by stacking the received signals and the noise components for the set of K selected users as

_with H = . hj_ff e C^{Kx M}, W = [w . . . , w_K] C"** _{as tne} compact channel and precoding matrices. Notice that the transmitted symbol vector

d fc ^{"K x l}jncludes the uncorrelated data symbols ⁽¾ for all users with — 1. From now on, we drop the symbol period index for the sake of notation.

The power constraint can be expressed for each symbol vector transmission as

||_x

///. MULTICAST APPROACH TO SYMBOL-LEVEL PRECODING

A. PHY-layer Multicasting Preliminaries

The PHY-layer multicasting aims at sending a single message to multiple users simultaneously through multiple transmit antennas [27]- [30]. In this context, the power min problem for PHY- layer multicasting can be written as:

x(H, ζ) = arg minljxlj^"2 (⁵)

'

where is the SINR target for the jth user that should be granted by the BS, and

^ ^— ^¹ ' ^{' ' '} ' is the vector that contains all the SINR targets. This problem has been efficiently solved using semidefinite relaxation [33] in [27].

B. Symbol-level Precoding Through Multicasting

Ψ) d, · F I?

Let us define a generic constellation represented by the symbol set ¹ , where ^J represent sy h symbol can have two equivalent representations: 1 ) Magnitud

_;

2) ln-phase

quadrature ^Imi^dj } components.

Let us also denote the received signal at the antenna of the jth user (ignoring the receiver noise) as

. In this context, a generic formulation for power minimization in a single symbol period under symbol-level precoding and SINR constraints can be written using the l-Q representation:

K (6)

W^jfcfi^jfc ll

fc=l

ΑΓ

s.t Ci I X{hj ^wkdk } = Kj y/ &z .fie{<¾}_; Vj £ K

~ 1

K k=i

Using the magnitude-phase representation, an equivalent way of formulating the problem can be expressed as:

K

The set of constraints C1 , C2 guarantees that each user receives its corresponding data

(I- "

symbol ³ with a correct amplitude and phase. C1 and C2 depend on the type of modulation and the constellation point as elaborated further in section IV. The desired amplitude for each user depends on two factors: a long and a short-term one. The long-term factor refers to the target SINR ^ which determines the SER and remains constant across all the symbol vectors of a frame. The short-term factor ^J

- basis and adjusts the long-term SINR based on the amplitude of the desired symbol.

Assuming that the entire symbol set D has unit average power i.e. J t J ^~~ ·^{■ » j} denotes the scaling factor needed for the magnitude of the desired symbol with respect to the average power of the entire symbol set.

In symbol-level precoding, the power minimization problem under SINR constraints (Eq. 7) is

H

equivalent to a PHY-layer multicasting problem with an effective channel and phase constraints (Eq. 10).

An equivalent formulation of the optimization problem (Eq. 7) can be expressed by rewriting the magnitude and phase constraints in the form of in-phase and quadrature constraints:

x(ft, C) = arg rmnilxll² dD

where ^"!"3' ^^J are in-phase and out-of-phase components for the detected signal at jth terminal and can be reformulated as:

The PHY-layer multicasting problem in (Eq. 5) is based on constraints in the power domain (amplitude only), while the symbol-level precoding problems are based on constraints in the signal domain (both amplitude and phase). This lower-level optimization is enabled by the fact that the all components (both symbols and channel) that affect the user received signal are taken into account in symbol-level precoding.

C. Multiple Antennas at the Receivers

Let us assume a multiuser downlink system where each user is equipped with an arbitrary number of antennas. As it can be seen, the signal model in (Eq. 4) can be straightforwardly adopted for the multiantenna receivers, considering that each element of y is the received signal at a single antenna instead of a single user. Assuming that the SINR constraints ^ apply for each user antenna the analysis in the previous section also follows straightforwardly for optimizing the transmit signal vector ^x. More importantly, since each antenna can receive the desired symbol without multi-stream or multi-user interference, there is no need for jointly processing the streams received by the multiple antennas of each user.

IV. SYMBOL— LEVEL PRECODING WITH MULTI— LEVEL MODULATION

For practical constellations, we can rewrite the constraints C1 and C2 to exploit the specific detection regions which depend on the type of modulation and the constellation point. In the following paragraphs, we specify the constrains for a number of typical modulation types, but the same rationale can be applied to other modulation types

A. MQAM

For MQAM (see Fig. 5), detailed expressions for C1 C2 can be written as. For the inner- constellation symbols, the constraints C1 C2 should guarantee that the received signals achieve the exact constellation point. For 16-QAM as depicted in Fig. 5 the symbols marked by 1 should be received with the exact symbols. The constraints can be written as

Outer constellation symbols, the constraints C1 , C2 should guarantee the received signals lie in the correct detection. For 16-QAM as depicted in Fig. 5, the symbols marked by 2 should be received with the exact symbols. The constraints can be written as

C₂ Qj / K_ja_tIm{d_j},

Outermost constellation symbols, the constraints C1 , C2 should guarantee the received signals lie in the correct detection. For 16-QAM as depicted in Fig. 5, the symbols marked by 3 should be received with the exact symbols. The constraints can be written as

>

The sign indicates that the symbols should locate in the correct detection region, for the

>

symbols in the first quadrant "^^" means — .

Following the same rationale, C1 , C2 can be defined for any MQAM constellation.

B. APSK

For APSK, detailed expression for C1 , C2 can be written as follows.

For inner constellation point, C1 , C2 should assure that the received signals should be receive at the exact constellation point. The constraints can be expressed as Outermost constellation symbols, the constraints C1 , C2 and C3 should guarantee the received signals lie in the correct detection. For 16 APSK as depicted in Fig. 6, the symbols marked by 2.

C'2 - taji(— = taii( iil_j)

C₃ : sign(Q_j) = sign{/m{ti_j})

Following the same rationale, C1 , C2 can be defined for any APSK constellation by including one or more levels of inner symbols (i.e. equality constraints) as needed.

I) Special case : Any MPSK modulation can be implemented by a single layer APSK constellation. The constraints can be expressed [22] by setting ¹ as: l_j = / aJie{d_j}_t ¥j € K, ^{(1 3)}

The outermost points of multi-level modulations (e.g. denoted by 3 in Fig.5 and 2 in Fig.6) have more flexible detection regions, since the symbol can be received correctly even it moves deeper into the detection region. This concept has been thoroughly investigated in [21 ] [22] for MPSK, where it was shown that this flexibility can lead to performance gains. In the previous sections, the same has be straightforwardly extended for multi-level modulations by using inequalities for the in-phase and quadrature constraints of the outermost symbols (see sec.lV-A,IV-B). However it should be noted that as we move into higher order constellations the effect of this flexibility is expected to diminish due to the large number of equality constraints. In these cases, the performance gain arises mainly from the multicast view rather than the flexible detection regions.

V. SYMBOL LEVEL POWER MINIMIZATION

The problem of power minimization has been addressed in numerous papers in the literature [5]- [6]. In the vast majority of previous works, the constraints were expressed in terms of

SINR, since there is a straightforward connection between the SINR ^ and throughput rate R when Gaussian coding is assumed: J¾ = log₂ (l + C_j )- (^{1 4}) However, when symbol-level precoding is employed in combination with adaptive multi-level modulation, this simple analytical connection ceases to apply. In this case, the effective through-put rate or goodput ^ depends on:

the assigned modulation m, which sets the upper bound on the supported rate R in number of bits per symbol according to Table I the achieved SINR which determines the operating point on the SER curve and it is expressed by :

Rj = f (m₃ , SER( j } ) = R₃ (nij)(l - 8ΒΕ(ζ₃, π ), ^ ⁵^ Now let us denote the consumed power for each of the N symbol vectors in a frame as

^{L ' "' ' ' ' 1} . The objective is to minimize the total power consumed while transmitting the whole frame, i.e. =Ι ^{1 J} . Assuming symbol-level precoding with adaptive multi-level modulation, the frame power minimization problem with goodput constraints can be expressed

ΛΓ N (16) man P^!n\ = nimPliil

' x[nj

%— 1 t=i

given that the power constraint is applied on a symbol vector basis. Dropping the symbol index n, for each symbol vector the transmitted precoded signal that minimizes the power

P = ^lxf l ²

'' " is calculated as:

„ (17) x = arg min j|xj| s.t. Ci _} C_{2 i} ^j€ K.

where C1 , C2 are the set of constraints defined in previous section.

The above problem is always feasible, as the power can scale freely to ensure that the SINR constraints can be satisfied for all effective channels resulting from different symbol vectors in a frame.

In the following sections, we first address the power minimization problem with SINR constraints C1 , C2 and then we build on it to develop a solution with goodput constraints

^{•■ ■}3 — J , where ^J are the effective rates and target rates (throughput) respectively. A. Power Minimization with SINR Constraints (CIPM)

The power minimization with SINR constraints can be expressed as:

x= min |x||² (¹⁸)

X

s. £!i_sC₂V| Glf

For any practical modulation scheme, the above problem can be solved by constructing appropriate C1, C2 constraints as explained in sec. IV. Subsequently, an equivalent channel can be constructed and X can be straightforwardly calculated as described in section lll-B. The Lagran e function of (Eq.12), (Eq.18) can be expressed as:

+ ∑μ, £ . I x ) - «¾ σ_ζ !m{d, } ) .

3

The derivative of with respect t ^T 'Vand can be expressed:

^ = ¾(x) - y ^ ¾h ⁽²¹⁾ ¾^ = ¾(x)-^ M«. ⁽²²⁾ il _{= (j} «i _{= 0} ¾ _{= 0}

By setting ^* <5¾ and ^ci i , we can formulate the following set of equations:

Using (Eq.23)-(Eq.25), the solution of (Eq.18) can be found by solving the set of equations as follows:

(26)

S. Power Minimization with Goodput Constraints

The power minimization with goodput constraints can be expressed as:

The rationale of the proposed algorithm can be summarized in the following steps:

1 ) The first step in solving this problem is allocating a modulation type m for each user. Based on the adaptive modulation rules of table I, we select the lowest modulation that can achieve the target goodput of each user. flu < r₃ < J¾ iff m₃ = I ⁽²⁹⁾

2) In the second step, the goodput constraints r can be converted into SINR constrains given that the modulation types m have been already fixed. This can be performed by exploiting the analytical connection between the SER and the SINR. In more detail, the required SER for a specific goodput constraint r is given by:

SER(C, m) = \ - rjR{m), ⁽³⁰⁾ and the required SINR for MQAM is expressed as a function of SER as follows [34]:

TABLE II: SUMMARY OF THE PROPOSED, STATE— OF— THE— ART ALGORITHMS AND THE THEORETICAL LOWER BOUND, THEIR RELATED ACRONYMS, AND THEIR

RELATED EQUATIONS AND ALGORITHMS For MPSK, the required SINR for a specific goodput and SER constraints as [34]:

For APSK, various approximations can be used [35] or as an alternative, numerically calculated SER vs. SINR curves can be utilized in practical systems.

3) As a result, the power min under goodput constraints has been transformed into a power min under SINR constraint and this can be efficiently solved by the algorithm in section V-A.

C. Multiple Antennas at the Receivers

Assuming that goodput constraints apply for each antenna instead of each user, the above algorithm can be straightforwardly extended for multiantenna receivers. However, when a goodput constraint apply for each user, there can be multiple combinations of per-antenna goodput constraints to be considered. In this case, the constraint in (Eq. 28) is written as:

A (33)

0=1

R- assuming that the jth user has A antennas, and ^{1 1} , is the effective rate of the jth user's antenna a. VI. NUMERICAL RESULTS

Before discussing the numerical results, let us denote 1 ) the symbol-level power consumption p = II ·, Wfc fc l|² = i|xl|²

by ^{k ~λ} and 2) the frame-level power consumption (average over over a large number of symbols) by P =€A ¹P\ ¹. Let us also define the system energy efficiency as:

which is going to be used as an additional performance metric that combines the system goodput with the required power. For the sake of comparison with an achievable user-level precoding method, we use the power minimization objective for user-level linear beamforming which is defined as: (35)

WJR- = arg mm

s.t.

I² + *2

This problem has been efficiently solved in the literature [5]. It should be noted here that the above user-level precoders are calculated only once per frame and are subsequently applied unaltered to all input symbol vectors. In this direction, the target is to minimize the average power per frame under average SINR constraints. On the contrary, the proposed CIPM algorithm minimizes the instantaneous transmit power per input symbol vector and guarantees that the target SINR is achieved for each input symbol vector. As a result, a higher energy efficiency can be achieved while ensuring the SER across the whole frame. As a theoretical bound (lower- bound for transmission power and upper-bound for energy efficiency), we utilize the PHY-layer multicasting [27] as in (Eq. 5).

For 8-QAM, the constraints C1 , C2 for each symbol can be written in detail as

For the 16-QAM modulation, the constraints C1 , C2 can be expressed as

The presented results in Fig. (7)-(9) have been acquired by averaging over 50 frames of N = 100 symbols each. A quasi-static block fading channel was assumed where each block corresponds to a frame and the fading coefficients were generated as

.

Fig. 7 compares the performance between optimal user-level beamforming, symbol-level precoding, and PHY-layer multicasting from an average transmit power perspective. In all cases, the power minimization under SINR constraints is considered. The PHY-multicasting presents a theoretical lower-bound for CIPM since it does not have the phase constraints required to grant the constructive reception of the multiuser interference, while it can be noted that symbol-level precoding (CIPM) outperforms the optimal user-level precoding at every SINR target. This can be explained by the way we tackle the interference. In OB, the interference is mitigated to grant the SINR target constraints. In CIPM, the interference is exploited at each symbol to reduce the required power to achieve the SINR targets. Furthermore, it can be noted that the throughput of CIPM can be scaled with the SINR target by employing adaptive multi-level modulation (4/8/1 6-QAM).

Fig. 8 compares the performance between optimal user-level beamforming, symbol-level precoding, and PHY-layer multicasting from an energy efficiency perspective. It can be noted that CIPM outperforms OB at all target SINR values. This can be explained by the decreased required power to achieve the SINR target since the energy efficiency takes into the account both goodput and power consumption.

Fig. 9 compares OB and CIPM in terms of frame-level transmit power scaling versus system size. It should be reminded that the energy efficiency metric takes into the account the detection errors at the receiver. It can be noted that the average transmit power for CIPM decreases with the system size, while for OB it increases. This can be explained intuitively by the fact that the power leaving each transmit antenna constructively contributes to achieve the SINR targets for each user. On the contrary, OB has to send a higher number of interfering symbol streams as the system size increases and this leads to poor energy efficiency. Fig. 10 depicts the power variation during the frame for CIPM and OB. We study the transmit power at all possible symbol combinations, which is equal to 16 combinations for 2x2 system size and QPSK for both users. It should be noted that channels between the BS and users' terminal are fixed during the frame, the users' channels have the following value:

0.1787 + 1.9179! 0.9201 + 1.0048i

H

-2.1209 - 1.5455 1.5138 + 0.2250t .

The long term average OB equals average OB equals

¾ II Lt-i

. It can be noted that the average transmit power per frame for OB is 2.2 dB higher than CIPM. The power changes within the frame. It can be noted that the maximum power difference between CIPM and OB equals to 4.1 dB at symbol combination no. 3 and no.14 and the minimum power difference equals to 0.4 dB at symbol combination no. 2 and no.15.

In Fig. 11 -12 we depict the transmit power and the energy efficiency regions for the following 2x2 channel:

1.317H- 5.6483i 1.8960 + 0.6877*

H

-0.6569 + 3..7018Ϊ

In Fig. 11 , we illustrate the transmit power with respect to SINR target constraints (and their mapping to the corresponding modulation). At each SINR constraint set, we find the average power for all possible symbol combinations. It should be noted that symbol-level precoding can satisfy different data rate requirements by assigning different modulations to different users.

Moreover, it can be noted that the transmit power increases with increasing the modulation order since this demands higher target SINR.

In Fig. 12, we plot the energy efficiency with respect to SINR target constraints (and their mapping to the corresponding modulation). At each SINR constraints set, we find the energy efficiency for all possible symbol combinations. For each symbol combination and SINR constraint, we vary the noise to capture the impact of SER on the energy efficiency performance. It can be noted that the energy efficiency decreases with increasing the modulation order since this demands higher target SINR.

SER is depicted in Fig. 13 for 4QAM and 16QAM modulations. If we assume that the target rates for user 1 and user 2 are 3.6 bps/Hz, and 1 .998 bps/Hz respectively, the modulation types that suit the rate requirements imposed by each user are 16 QAM and 4 QAM respectively. Based on (30), the corresponding SER for both users are 10^"1, 10^"3 respectively. Using the SER values, we can find the related SINR target constraints from the curves in Fig. (11 ), which are almost 13 dB and 10 dB respectively.

TABLE III

COMPARISON OF THE DIFFERENT TECHNIQUE FROM SIMULATION RUN TIME

¾ = 2** _t. r>3 XJ _ ..-» 2 „ «j.5

PERSPECTIVE' 20ff«, = 4-712d», QPSK, #

A. Complexity

The source of complexity in the symbol-level precoding is the number of possible precoding calculations within a frame. This depends on the number of users, the modulation order of each user and the frame length N. The number of the possible calculations Λ/' can be mathematically expressed:

For small systems (i.e. lower modulation order and small K), the precoding vector can be evaluated beforehand on a frame-level for all possible symbol vector combinations and employed when required in the form of a lookup table. For large system (i.e. high order modulation order, high number of users), the number of the possible calculations in some cases is less than the frame length, so it is not necessary to find the precoding for all the possible combinations.

At each symbol combination, a convex optimization is solved. The complexity of such operation is evaluated using the simulation run-time metric as a metric. The complexity of the proposed algorithm is studied in Table (III) in terms of simulation run-time. We compared the runtime of optimal beamforming (OB) and different symbol-level precoding. From the table, it can be deduced that the run time for OB is the lower than CIPM as expected. Moreover, the run-time for symbol-level precoding techniques depends on the combinations of the modulation order (possible data symbols) and the number of users, which is explained by the factor ^χ in the table. However, for a single solution of the optimization problem, it can be seen that CIPM is less complex than OB as system size increases. Despite the high complexity of the proposed technique, it can be argued that with the emerging of cloud RAN, this computational complexity can be transferred to the cloud RAN level [36].

VII. CONCLUSIONS

Symbol-level precoding that preferably jointly utilizes the CSI and data symbols to exploit the multiuser interference has been proposed for multi-level modulation. In these cases, the precoding design exploits the overlap in users' subspace instead of mitigating it. We propos precoding techniques that extend the concept of symbol-level precoding to adaptive multi- level constellation. This is a crucial step in order to enable the throughput scaling in symbol- level precoded systems. More specifically, we have generalized the relation between the symbol-level precoding and PHY-layer multicasting with phase constraints for any generic modulation. To assess the gains, we compared the symbol-level precoding to conventional user-level precoding techniques. For 2x2 scenario, a 2.2 dB transmit power reduction has been achieved for example. More importantly, this performance gain increases with the system size. Therefore, it can be conjectured that the symbol-level precoding retains some performance trends which resemble the PHY-layer multicasting.

It should be noted that features described for a specific embodiment described herein may be combined with the feature of other embodiments unless the contrary is explicitly mentioned.

It should be understood that the detailed description of specific preferred embodiments is given by way of illustration only, since various changes and modifications within the scope of the invention will be apparent to the person skilled in the art. The scope of protection is defined by the following set of claims. REFERENCES

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Claims

1 . Method for transmitting precoded data symbols using a data transmission device capable of transmitting data symbols using digitally modulated signals to K receivers over a common multiple input data communication channel, comprising the following steps:

providing a desired data transmission rate, and channel state information, for each receiver j, 1 < j < K; (10)

providing, for each receiver j, 1 < j < K an indexed sequence of N data symbols dj[n] to be transmitted, 1 < n < N; (20)

selecting, using selection means, for each receiver j, a signal constellation, whose associated data transmission rate is higher than said desired data transmission rate, from a plurality of predetermined signal constellations, wherein each signal constellation is associated with a digital modulation scheme, wherein each signal constellation comprises a plurality of signal constellation points in the signal domain, and wherein each signal constellation point is associated with a data symbol and with a corresponding decoding region; (30)

generating, using generating means, for each one of said data symbols dj[n], 1 < j < K, a corresponding precoded symbol X j[n], 1 < j < K, such that, after interfering with each precoded symbol Xi≠j[n],1 < i < K having the same index n, 1 < n < N, during transmission over said multiple input data communication channel, the corresponding data symbol received by receiver j lies in its corresponding decoding region,

wherein the vector of precoded symbols x[n]={xi[n]; X2[n], ... , χκ[η]} is computed so as to have minimum power under a set of at least two signal- domain constraints per receiver j, 1 < j < K, said constraints depending on the selected signal constellation for receiver j, and on the channel state information for receiver j; (40)

- transmitting, using transmission means, the precoded symbols to each receiver j, 1 < j < K, over said multiple input data communication channel (50).

2. The method according to claim 1 , wherein during the step of generating precoded symbols (40), for at least one data symbol dj[n], 1 < j < K the corresponding precoded symbol is generated such that, after interfering with each data symbol having the same index di≠j[n], 1 < i < K, during transmission over said multiple input data communication channel, the corresponding data symbol received by receiver j corresponds to the associated signal constellation point.

3. The method according to any of claims 1 or 2, wherein during step (50) the precoded symbols are transmitted using a different input among said data communication channel's multiple inputs for each receiver.

4. The method according to any of claims 1 to 3, wherein in step (10), the desired data transmission rates are received over a data communication channel by the transmission device using data reception means.

5. The method according to any of claims 1 to 4, wherein, for each index, 1 < n < N, the generated precoded symbols are associated with said data symbols dj[n], 1 < j < K, and stored in a memory element of said data transmission device.

6. The method according to claim 5, wherein at said step (40) of generating the precoded symbols, the method comprises the further steps of:

checking, for said data symbols dj[n], 1 < j < K, whether corresponding precoded symbols have been previously stored in said memory element (42); - retrieving said precoded symbols from said memory element if a match is found (44);

generating said precoded symbols otherwise.

7. The method according to any of claims 1 to 6, wherein said data communication channel is a wireless communication channel.

8. The method according to any of claims 1 to 7, wherein the data transmission device comprises multiple transmission antennas for transmitting data symbols over said data communication channel.

9. The method according to any of claims 1 to 8, wherein at step (50), N precoded symbols are transmitted to receiver j, 1 < j < K, in a data frame comprising a preamble identifying the selected signal constellation.

The method according to claim 9, wherein the preamble further comprises information facilitating the computation of channel state information at each receiver.

11. A data transmission device for transmitting precoded data symbols using digitally modulated signals to K receivers over a common multiple input data communication channel, comprising:

a first memory element for storing a desired data transmission rate for each receiver j, 1≤j≤K;

data transmission means adapted to transmit data to each of said receivers using one of said data communication channel's multiple inputs;

processing means configured to the steps according to the method of any one of claims 1 to 10.

12. The data transmission device according to claim 11 , further comprising first data reception means adapted to receive each receiver's desired data rate over a data communication channel.

13. The data transmission device according to any of claims 11 or 12, further comprising second data reception means adapted to receive channel state information.

14. A computer program comprising computer readable code means, which when run on a computer, causes the computer to carry out the method steps 30-40 according to claim 1 .

15. A computer program comprising computer readable code means, which when run on a computer, causes the computer to carry out the method according to any of claims 1 to 11.

16. A computer program product comprising a computer-readable medium on which the computer program according to any of claims 14 or 15 is stored.

17. A computer configured for carrying out the method according to any of claims 1 to 10.