WO2007033676A1

WO2007033676A1 - A method of non-orthogonal spatial multiplexing in a mlmo communication system

Info

Publication number: WO2007033676A1
Application number: PCT/DK2006/000522
Authority: WO
Inventors: Patrick Claus Friedrich Eggers; Xin Zhou; Persefoni Kyritsi
Original assignee: Aalborg Universitet
Priority date: 2005-09-26
Filing date: 2006-09-26
Publication date: 2007-03-29

Abstract

A method of non-orthogonal spatial multiplexing in a multiple-input multiple-output (MIMO) communication system is proposed. The system has an acting transmitter side comprising a transmitter with a number of transmitter antennas and an acting receiver side comprising a receiver with a number of receiver antennas, a number of non-orthogonal parallel channels for data substream spatial multiplexing being generated between the transmitter and the receiver. The method comprises the following steps: a) data intended for being sent from said transmitter to said receiver is divided into a number of data streams at the transmitter side, b) the data streams are weighted using filter weights, said weighting being applied to the transmitter side of the system only, c) the data streams are sent from the transmitter to the receiver via the non-orthogonal parallel channels, d) and the data streams are received and decoded by the receiver. In multiple user communication systems, each user independently detects the data that were destined for that user. In a single user communication system the data streams are after step d) recombined at the receiver side to recreate the original data stream.

Description

Title: A method of non-orthogonal spatial multiplexing in a MlMO communication system

Technical Field

The present invention relates to a method of non-orthogonal spatial multiplexing in a multiple-input multiple-output (MlMO) communication system.

Background Art

Systems with multiple element transmitter (Tx) and receiver (Rx) arrays have received significant attention since they can achieve very high spectral efficiencies (e.g. [1], [2]). This is particularly significant for wireless applications that are limited with respect to power, bandwidth, weight, size and complexity. The capacity advantage of multiple in- put-multiple output (MIMO) channels lies in the decomposition of the channel into several spatial sub-channels, each one with a different gain.

Several open-loop techniques that require advanced signal processing at the Rx have been developed and demonstrated to achieve a hefty portion of the theoretically achiev- able capacity. An example of such an algorithm is the Bell Labs Layered Space-Time algorithm (BLAST) [3].

It has further been demonstrated that in closed loop systems, Channel State Information (CSI) at the Tx can increase the theoretically achievable channel capacity [4]. When the Tx array knows the channel characteristics, it can perform waterfilling and allocate the transmitted power appropriately in space. In [5], [6], a practical rate and power allocation scheme is proposed based on the post-detection signal to noise ratios (SNRs) resulting from the application of the BLAST algorithm at the receiver. A more intuitive technique relies on the decomposition of the channel into orthogonal subchan- nels and performs waterfilling on the spatial sub-channels, and additionally excites the sub-channels with the higher gains with more power, while keeping the total transmitter power constant (see for example [7], [8] and [9]).

MIMO orthogonal channel transmission has gained much attention with respect to spa- tial multiplexing. However, such a scheme requires not only complete link matrix esti- mation, but also simultaneous application of both transmitter and receiver filter weights. In systems where the complexity of the user equipment is constrained because of cost issues, it is desirable to seek alternative solutions, with potentially higher base station equipment cost. This is the issue that is addressed by the present invention.

Disclosure of Invention

The purpose of the present invention is to provide a new and improved non-orthogonal MIMO transmission scheme.

This is according to the invention achieved by a method of non-orthogonal spatial multiplexing in a multiple-input multiple-output (MIMO) communication system, said system having an acting transmitter side comprising a transmitter with a number of transmitter antennas and an acting receiver side comprising a receiver with a number of receiver antennas, a number of non-orthogonal parallel channels for data substream spatial multiplexing being generated between the transmitter and the receiver, and wherein the method comprises the following steps: a) data intended for being sent from said transmitter to said receiver is divided into a number of data streams at the transmitter side, b) the data streams are weighted using filter weights, said weighting being applied to the transmitter side of the system only, c) the data streams are sent from the transmitter to the receiver via the non-orthogonal parallel channels, and d) the data streams are received and decoded by the receiver.

The weighting, processing and weight optimisation are performed on the acting trans- mitter side of the system only, thereby reducing complexity of the receiver side. This applies both for the uplink and the downlink situation. The term "acting" indicates that the one side of the system at a given moment functions as the transmitter side and the other side as the receiver side, and that the functions at a later time can be reversed.

That is, a user side can be the receiver and for instance a network side be the transmit- ter (for down link) or vice versa (for up link).

Particularly the receive situation (down link) at the user equipment is critical, as it inherently requires processing at the user side (the receive side inherently has a problem of sensor signal spilling over, which needs to be dealt with). The reverse direction (up link) transmitting from the user equipment, can here be dealt with at the network side, which is not constrained with respect to size, power etc. The contribution of the inven- tion is also on the down link case (user equipment receive case) to place all data stream isolation processing solely at the transmitter (typically network side). Consequently, the invention allows for very simple user equipment architectures, supporting multi data stream space multiplexing operations.

According to a preferred embodiment, the method further comprises the step of: e) said data streams are recombined at the receiver side to recreate the original data stream.

The situation described above corresponds to the case where all the data are destined to a single user. If the data are destined to multiple users independently, then steps b-d are followed (the data are already separated into separate streams for each user). At step d), each user independently detects the data that were destined to the particular user. The only operation performed at the receiver side is singular value decomposition.

According to an embodiment of the invention, each of the data streams is associated with a single receiver antenna or antenna group, and wherein the filter weights are applied at the acting transmitter side only. That is, the number of data streams is equal to the number of receiver antenna or antenna groups. Since the channel shaping filters are applied at the transmitter side only, and the data streams are directly associated with individual receiver antennas or groups, no cross branch manipulation to retrieve the different data streams is needed. Thereby, the complexity of the receiver side is greatly reduced, since the need for receiver signal processing to isolate the data streams is avoided. Two or more cooperating antennas indicate a group.

In an embodiment according to the invention, the transmitter antennas are grouped in transmitter antenna groups of two or more individual transmitter antennas, where the weighting is performed on the transmitter antenna groups. This can for instance be performed pairwise or with more antennas. The groupings can also be performed as con- secutive groupings, which is a simple way to implement the groupings. The grouping of transmit antennas can achieve simplified transmit architecture at the expense of sub optimal performance, when not all transmitter antenna weights are involved in the overall optimisation of all data streams. Instead groups of transmitter antennas can independently (sub)optimise single data streams. Also trying to reduce complexity at the transmitter side can be relevant in cases, where two terminals are of similar nature and operate under similar constraints (like in peer to peer communications). According to an alternative embodiment, the groups are constructed as a reduced subset of highest link gain and/or lowest interference and/or lowest noise. This allows for implementation of optimised allocation schemes of antenna groups for particular data streams.

In an embodiment of the invention, the groups are constructed as optimum searched groups. Thereby, a joint search optimisation for all data streams is made, and each data stream is individually optimised for the globally best performance.

In another embodiment according to the invention, the filter weights in step b) are divided into at least a number of power maximising weights and a number of interference reducing weights, where the power maximising weights are used for maximising the power of the transmitted data stream to an intended receiver antenna, and the interference reducing weights are used for reducing the self-interference to the receiver an- tennas that are associated with other substreams. This is performed by use of algorithms. This is a further simplification for the transmitter processing, where the (sub)optimization task for each data stream is split into separate objectives, and where these functionalities are distributed on different antennas within the associated groups of transmitter antennas. The advantage is that the weight establishment for the sepa- rate objectives to different antennas can be made simpler (less numerical complexity) than if a joint objective weighting had to be performed for all the antennas within the assigned transmitter antenna group.

According to a particular embodiment of the invention, one transmitter antenna is used per data stream to reduce the interference on each receiver antenna or antenna group not associated with the particular data stream. So for each data stream the number of antennas required to cancel the interference on all the other receivers equals the total number of data streams minus one. The rest of the transmitter antennas are used to maximize the power of the intended data stream. That is, all the antennas not used for interference reduction are used for power maximization. The two objectives are power maximization and interference elimination. This embodiment gives a priority to the objective of maximizing the power by allocating the minimum amount of resources necessary to achieve the objective of interference elimination.

In an embodiment according to the invention, the signal to noise and interference ratio (SINR) of the data streams are estimated and used for transmitter filter weight optimi- sation. The transmitter has full Channel State Information (CSI). Therefore it can predict the SINR that would result at the receiver for any weighting scheme and power allocation. It selects the weighting scheme/power allocation to fulfil the design objectives.

According to another embodiment of the invention, the SINR of an individual data stream intended for a certain receiver antenna or antenna group is estimated as the ratio between the signal strength of said individual data stream and the signal strength of the interference from the remaining data streams received plus an estimated noise term:

SINR, = ^k-

where S and N denote the signal and noise power, respectively. The subscript and superscript are indices of the actual and intended receiver antenna or antenna group, respectively. The SINR is a quality metric for selecting the interference reducing weights at the transmitter side because it is directly related to the probability of error in the detected data.

According to an alternative embodiment according to the invention, an optimum combining (OC) method is used for improving the signal to noise and interference ratio (SINR) performance on the MIMO system, so that a complete set of transmitter weights provides signal isolation for a desired receiver antenna. Similar schemes have previously been used for the uplink case (interferer signals to a single user, interpreted as a single data stream case). In the present embodiment, these weights are used in the downlink (transmit case) with sub optimum performance. A true OC exists for the downlink case and would give a solution/weight different from the known prior art uplink weights. Downlink OC involves the joint optimisation for all data streams and is complex.

According to a particular embodiment, the filter weights according to an optimum com- bining method for a given data stream is calculated using the inverse of the spatial co- variance matrix R_/v+/ of the noise for said given data stream plus interference from the other data streams multiplied by the conjugate of a channel transfer scalar H for the channel used for transmitting said given data stream: where k denotes the W\\\ receiver antenna or antenna group. The matrix R is the spatial covariance matrix of the noise plus interference from the other data

_> ^and (•)^*,(/ indicate the conjugate, transpose of the argument (^■) respectively. RJS a diagonal matrix with diagonal elements equal to the noise variance N. The above equation shows the weight, which per se is known from prior art. Here, the weights are used in the downlink case instead of the uplink, for which they were originally developed. The penalty is sub-optimal performance.

According to an alternative embodiment, optimum selection (OS) of interference reduc- ing weights and transmitter antennas to be used are used for multiplying SINRs of the individual data streams and maximising the value of this multiplication.

In an embodiment according to the invention, a set of weights developed for uplink transmission is used directly for improving downlink transmission SINR performance. One example for such a weighting method is an optimum combining method known per se. These weights provide good (but sub-optimal) signal isolation for a desired receiver antenna.

According to another embodiment, the selection of interference reducing weights and transmitter antennas to be used is performed jointly for the optimization of the metrics for all data streams. This can be performed via for instance optimum selection (OS). For instance, the product of the SINRs for all data streams can be used (i.e. multiplication of the individual metric for each data stream). This is a close approximation to the sum capacity for all data streams. Alternatively, this can be carried out by multiplying SINRs of the data streams and maximising the value of this multiplication.

According to an embodiment of the invention, the optimum selection (OS) is performed using data stream inversion weights with an additional scale parameter α. The scale parameter can be complex or a scalar.

According to a particular embodiment of the invention, a given transmit antenna q is used to cancel a certain percentage of the interference caused by the transmission of data stream k on a given receiver antenna p, and where the other antennas apply a weight corresponding to the conjugate of the channel transfer scalar H for the channel used for transmitting, so that the filter weight for the KVn data stream from the g'th antenna is given by the following expression:

where NT_X denotes the number of transmit antennas or groups, and or is the scale pa- rameter. The equation above allows a simplified weight calculation. It prioritizes the different objectives (power maximization and interference elimination) by a scaling factor determined by α.

According to another particular embodiment, the scale parameter is divided into dis- crete values, such as in the range from 0 to 1. In general, the actual interval steps are chosen depending on the trade off between search time and return/gain.

In an embodiment according to the invention, the interference reducing weights are selected by finding the minimum of a link vector difference, namely:

where H is a channel transfer function, index k denotes the /c"th data stream, and indices p and k denote the p'th and /c"th receiver antenna, respectively, and q denotes the transmitter antenna. This is an all new scheme, which introduces a simple (sub optimum) direct link selection algorithm to choose the transmit antenna that most likely provides the best trade-off between signal isolation and power maximization. The search parameter α can also be subject to joint search for all data streams (though complex and time consuming).

According to another embodiment of the invention, the interference reducing weights are found using Wiener filters. In particular, the interference reducing weights are found using the following modified Wiener filter function:

l '

where H is a channel transfer function, N is a noise term, SNR_k is a signal to noise ratio for the /c"th data stream, p and k denote the p'th and /c"th receiver antenna, respectively, q denotes the transmitter antenna index, and / = 1 N_7x, where N_1x is the number of transmitter antennas. This is an alternative all new scheme to determine the transmitter weights. It is a direct algebraic expression and does not involve any search phase (as it is for the case of α in the previous weight establishment).

Brief Description of the Drawings

The invention is explained in detail below with reference to the drawings, in which

Fig. 1 shows a diagram for a prior art orthogonal transmission MIMO system with N_7x transmitter antennas and NR_X receiver antennas,

Fig. 2 shows an illustration of a double scattering model, where three paths with double bounce transmission are shown,

Fig. 3 shows narrowband SINR of two data streams in a 2 x 1 and a 2 x 2 antenna system with SNRi_nput = 1OdB,

Fig. 4 shows narrowband SINR of two data streams in a 2 x 1 and a 2 x 2 antenna system with SNRi_np_ut = 2OdB,

Fig. 5 shows a capacity Cumulative Distribution Function (CDF) in a 2 x 1 and a 2 x 2 antenna system with SNR_inpUt = 1OdB,

Fig. 6 shows a capacity CDF in a 2 x 1 and a 2 x 2 antenna system with SNRj_nput = 2OdB,

Fig. 7 shows narrowband capacity at median CDF level in a N_7x x 1 and a Nτx x 2 antenna system with SNR_ιnput = 1OdB,

Fig. 8 shows narrowband capacity at median CDF level in a N_7x x 1 and a N_7x x 2 antenna system with SNR_input = 2OdB,

Fig. 9 shows wideband spectral efficiency CDF in a 2 x 1 and a 2 x 2 antenna system with SNR_lnput = 1OdB, Fig. 10 shows wideband spectral efficiency CDF in a 2 x 1 and a 2 x 2 antenna system with SNRj_nput = 2OdB,

Fig. 11 shows wideband spectral efficiency at media CDF level in a N_7xX 1 and a N_7x x 2 antenna system with SNR_input = 1OdB,

Fig. 12 shows wideband spectral efficiency at media CDF level in a N_7x X 1 and a /V_7X x 2 antenna system with SNR_lnput = 2OdB, and

Fig. 13 shows a non-orthogonal communication system according to the invention.

Best Modes for Carrying out the Invention

The critical direction in a communication link is the downlink direction, if the objective is to avoid heavy processing and thereby obtain simple user terminals. The other direction, i.e. the uplink direction, is less critical, as the reception at the radio network infrastructure commonly has sufficient power, space and processing resources for any sort of reception scheme to be acceptable. Consequently, this invention focuses on downlink techniques with low complexity reception. However, depending on the direc- tion of the communication, the same techniques can be applied for reception at uplink as well. This would be relevant for communication between similar low complexity terminals such as in peer-to-peer communications.

In the following, bold symbols indicate matrices, and underlined symbols signify vectors. 0)^r. O)^{* and} (" )^{H are tne} transpose, the complex conjugate and the Hermitian (complex conjugate transpose) of the argument (^• ), respectively, (- )^'1 is the matrix inversion of the argument (^■ ), (•) denotes the expectation operation and tr(-) indicates the trace of the matrix argument (sum of the diagonal elements).

I. Orthogonal Parallel Channels

A. SISO

A single input-single output (SISO) system refers to the case of a single antenna at both the Tx and Rx sides.

B. Ml MO Orthogonal Parallel Channels 1) Singular Value Decomposition (SVD): Assume a system with N_7x transmitter antennas and N_RX receiver antennas, see Fig. 1. It is assumed that N_RX ≤Njχ. H ere the separability of the data streams at the receiver side is of interest, and therefore the number of data streams to be transmitted, /V_sfreams, is equal to the number of receiver elements ( N_sfregms = NRX) . The data streams to be transmitted are denoted as S_k, and each transmitter p sends a signal x_p. S- = Is₁ s₂ ... s_N ^~\ is the parallel data stream

vector and x = [X₁ x₂ ... x_N J is the transmitted signal vector. The covariance matrix of the transmitted signal xis R_x = (xx^H) . The total transmitted power is set to P_t, i.e. &{Rχ) = Pt.

y₁ y₂ ... y_Nκx J is the received signal vector, where y_k is the signal received on the

/f-th receiver antenna. In the case of a flat-fading channel (no variation with frequency), the channel gain from transmitter p to receiver k is a scalar quantity, denoted H_kp The transmitted and received vectors are related by the equation: y = Hx+ n , (1) where n is the Λ/_RX-dimensional noise vector. The matrix H (channel transfer matrix) has dimensions Λ/_RX ^χΛ/τχ and contains the channel gains from each transmitter to each receiver, and incorporates effects such as antenna gains.

The input signal to noise ratio (SNRi_nput) is defined as:

SNR ',,W,..'t = ^ TW- H₁, (2) where /V is the average noise power, P_t is the transmitted signal power and the expec- tation I]H_1J is taken over both channel realizations and transmitter-receiver antenna pairs.

The singular value decomposition (SVD) of the channel transfer matrix H can be written as

H = V - A - W^H

V^HV = 1_NRX , W^HW = I_Nτx, A = diαg(λ_k) ... The unitary matrices W and V contain the right (input) and left (output) singular vectors of H, respectively, I_/ is the / * / dimensional identity matrix, and Λ is a diagonal matrix that contains the singular values λ_/ of H.

All the signals used in the presented formulation are discrete-time complex base-band, so the elements of x, y, n and H are complex. It is assumed that perfect down- conversion, filtering and sampling have been performed.

In general, if the noise vector has a Gaussian distribution, the channel capacity C (maximum mutual information) is achieved, when the input signal distribution is also Gaussian [4], and depends on the input signal covariance matrices according to the following expression:

C = log₂ (det(l + ≡^H (R J¹ HR J (4)

The matrix R_n - (nn ) is the spatial covariance matrix of the noise vector n. For the purpose of this analysis, the components of n are assumed to be additive white Gaussian noise, independent across the receivers (this is in contrast to the analysis in [4] that assumes that the noise vector also includes interference from other sources), and therefore

R_« = M^ (5) where I^ is again the N_RX x N_RX dimensional identity matrix.

Most of the analysis in the literature refers to situations, where the transmitter has no CSI. If the transmitter has complete CSI, it can be assumed that it knows the channel transfer matrix H, and for the following analysis, the transmitter has instantaneous and perfect CSI. It can then optimize the input covariance matrix R^, so as to maximize the expression in Eq. (4). The transmitter sends data along the eigen vectors of the channel ([8], [9]), i.e. the data streams s_k are transmitted along the right singular vectors of H. Remember that, from Eq. (3), H=V-Λ-W^Hand the transmit signal xcan be written as: X=W s. (6) The receiver decodes the transmitted data streams s_k by projecting the received signal vector yonto the left singular vectors of H. Therefore the signal to noise ratio SNRι_< ^csl of the /f-th data stream is y_ = ttx + n = V • Λ • W ¹Ws + n =>

I = V^H|/ = Λs + V^ffn =>

SNRξ^SI = M^

*^{■ N}H (7)

where λ* is the /c-th singular value of H (/c-th element of the diagonal of Λ), p_k =

is the power of the /c-th data stream, and JV~ is the power of the /c-th component of the projected noise vector n_ = Y^H n . Since V is an orthonormal matrix, the noise compo- nents are assumed to be independent and of equal variance, N_²_ = N .

The channel capacity can then be expressed as the sum of the capacities of the resulting orthogonal sub-channels, i.e.

The maximum link capacity with CSI at the transmitter C_Csι is obtained by adjusting the powers p_k = according to the water filling solution (derived from the analysis in

[4]). Here, advanced power allocation techniques will not be investigated, and it will in¬

stead be assumed that p_k = — — — = -^- and P₁ = 1. Then the channel capacity using

^streams -^ RX orthogonal MIMO transmission is given from Equation (8).

Several algorithms have been developed for the signal transmission and detection and the various approaches vary in the amount of information that is available at the Tx and at the Rx side. Pure BLAST [3] assumes that the Tx has no CSI, whereas additional power and rate allocation schemes assume that the Tx has additional CSI. The schemes that rely on the channel decomposition into orthogonal subchannels assume that both the Tx and the Rx have full CSI.

2) Space-Time Block Coding: Another prior art orthogonal transmission scheme is space-time block coding (STBC) [10]. In the following a simple STBC scheme is used, namely the Alamouti scheme [11] in a 2 x 1 and 2 x 2 antenna system. The output SNR at the Rx in a 2 x 1 Alamouti system can be expressed as: _O Λ_{T D} A lamouti, 2x1 m=\ p /Q\

where m indicates the Rx index. In this case the Alamouti scheme corresponds to a twofold Maximum Ratio Combining (MRC) and the capacity is

2

1 ^{1 ■}> '* - π-* τ-rf AIamoιιti,2xl \ _ 1 ^x 1_Λ _. /i _• Σ m=l I ^1. |2 c^^^ = ^- io_g2 (i + 5Ni?— ■-) = ^- iog₂ (i + ^L_ _{P/ ) (10})

If the Alamouti scheme is used in a 2 x 2 system, then the output SNR at the k-th Rx can be written as:

O TW" D A lam outi, 2x2 _ I (Λ Λ \

where it has been assumed that the transmitter power is shared evenly between the two transmitted data streams. The Alamouti scheme in a 2 * 2 system is equivalent to a four-fold MRC. The total capacity in this case is given by

The Alamouti scheme also requires for the receiver to have CSI.

II. MIMO Non-orthogonal Parallel Channels In section I₁ orthogonal transmission has been described, which results in the complete isolation of the transmitted data streams at the receiver, i.e. the streams do not interfere with each other. In this section communication over non-orthogonal channels is considered, where the signals are allowed to interfere with each other.

Such schemes have previously been considered in the context of multi-user situations for capacity improvement with respect to access. Beam space techniques increase the system capacity, directly or indirectly (higher user density is permissible). For instance SDMA (space division multiple access) directly enhances the signal to the user of interest and introduces sectorization in the cell area, and SFIR (spatial filtering for inter- ference reduction) increases the capacity indirectly by suppressing other user interference, lowering the average interference and thus allowing denser frequency reuse. Recently, advanced techniques such as dirty paper coding (DPC) have been proposed to address the problem of sending data to many users so that their signals do not interfere with each other.

The present invention focuses on a single user communication system, but it is in the following assumed that the user equipment is equipped with multiple antennas. The data that is destined for the intended user is demultiplexed into several data streams, which are simultaneously transmitted after being appropriately weighted at the transmitter. Similarly to the Tx side as in Fig. 1 , the filter weight applied at the p-th transmitter to the /f-th data stream is w_kp.

The situation described above corresponds to the case where all the data are destined to a single user. However, a similar approach can be used for situations, where the data are destined to multiple users independently.

Fig. 13 shows a communication system according to the invention using a non- orthogonal parallel channels (data stream Si to S_NRx) approach by solely applying transmitter weights. There is no need for any receiver branch collaboration for data stream extraction, since the receiver antennas are 'pin pointed' with dedicated data streams S^Λi to S^Λ _NRx.

The advantages of this invention lie in the following two additional design objectives:

• Reduction of receiver complexity:

Without loss of generality, it is assumed that the /f-th data stream is destined for the k-th receiver antenna. At the Rx side, the contributions from the individual an- tennas are on/off according to v_kp = δ (δ_kp = 1 if k = p, δ_kp = 0 if k ≠p), i.e. each of the data sub-streams should be individually decoded without having the receiver antennas collaborate. The additional benefit of this approach is that scalability with respect to number of data streams is straightforward.

• Transmitter filter simplification: In the approach according to the invention, all the processing is done at the transmitter side only. Moreover, the invention differentiates from the dirty paper coding approach by assuming that the transmitter filters are linear, and by investigating simplified techniques for their calculation. As a reference, a 2 x 2 orthogonal MIMO system with two data streams is selected. The number of transmitter antennas is increased in order to try to achieve an equivalent performance with non-orthogonal MIMO transmission.

This invention focuses on the investigation of the Signal to Interference plus Noise Ratio (SINR) and capacity issues in both Narrowband (NB) and Wideband (WB) situations. The SINR at the /c-th Rx defines the ratio between the intended signal at the /c-th Rx antenna and interference from other data streams at the /c-th Rx antenna plus noise at the /c-th Rx antenna.

SINR_k = , ^Sk = ^S* . (13)

where S, / and N denote the signal, interference and noise, respectively. S_k' indicates the signal intended for receiver /, as it is received at receiver k (if i ≠k, it causes interference). The capacity of any such link is approximated as Iog₂(1 + SINR_k) [12].

The performance of non-orthogonal data transmission is first considered in a NB situation, for which classical techniques have been developed.

A. Optimum Combining (OC)

[13], [14] introduce a receiver (uplink (UL)) diversity technique in a multiple user scenario for the suppression of interference from other users. [15] also consideres this ap- proach with respect to the user terminal. The metric has been the maximization of the uplink signal to interference plus noise ratio (SINR_UL)- This Optimum Combining (OC) approach can also be interpreted as a spatial Wiener filter [16]. The notation of [17] is used, assuming equal noise on all the receiver antennas. The filter weights w are selected so as to maximize the SINR_UL for data stream /c, and the optimal solution is given as

where the matrix Rw_+/ is the spatial covariance matrix of the noise plus interference from the other data streams Rw_+/ = Rw + R_/.

The above analysis holds for the uplink. In the present invention, the weights are applied on the downlink (DL). Indeed they constitute the limiting behavior of the optimal downlink weights in the interference limited situation. In the noise limited situation, the optimal downlink weights are -w_k = l£_k , which correspond to simple beam forming.

Beam forming has the property that it maximizes the received signal power. In general, the weights in equation (14) are jointly optimal for all data streams in the UL transmission, which are not the same in the DL case.

B. Cancellation/Inversion (Cl) Filters

The calculation of the optimal weights presented in the previous section reaches a compromise between the maximization of the received signal power and the elimination of the spatial interference. To also reduce algorithmic complexity at the Tx side, approaches where the power maximization and the interference cancellation operation are performed by separate filters at different transmit antennas are discussed below.

Power maximization results in setting the w_/ctoH^ . On the antennas that are not used for cancellation, this relation determines the weights in the simplified approach.

The purpose of the cancellation filters is to eliminate or at least reduce interference on the antennas that are supposed to receive other data streams. For each data stream, there is a need for as many antennas for interference cancellation as there are remaining data streams (or equivalents interfered-on receivers). Therefore, the number of cancellation filters that need to be determined for each data stream is also equal to the number of data streams minus one, i.e. for two data streams only one canceling weight is needed. The algorithms below propose different techniques for the calculation of the cancellation weights, as well as for the selection of the transmit antennas, for which they are applied. The objective is to avoid the matrix inversion necessary for the calculation of the optimal weights.

Optimum Selection (CI-OS):

Again, it is assumed that the /c-th data stream is destined for the /c-th receiver antenna. The Cl Optimum Selection (CI-OS) approach aims at maximizing the received SINR at the intended Rx antenna side by partially cancelling the interference on the other an- tennas. Let us assume that transmitter antenna q is used to cancel a certain percentage of the interference caused by the transmission of data stream k on receiver antenna p. The other transmitter antennas (i ≠q) apply the weights {w_k). = H^* _d . Then

(15) where the scaling factor α describes the percentage of the interference cancelled. For each data stream, a search over the index q of the antenna that is used for the cancellation and for the optimal α e [0.2, 0.4, 0.6, 0.8,1] is performed in order to find the combination that jointly maximizes the SINR at the /c-th and p-th receivers. Although the weight will be sub-optimum to a true OC_0/. weight formulation, a joint search for all the data streams is here performed.

Wiener Filter (CI-WF):

The CI-OS filter weight can achieve the optimum joint SINR at the Rx side, however, the numerical search involved may increase the complexity of the signal processing. Therefore, the invention further proposes the Cl Wiener Filter (CI-WF) weight [18] in order to achieve a sub-optimal SINR, but with lower complexity.

The cancellation Tx antenna q is selected based on the minimum of the magnitude of

the link vector difference, namely where k and p denote the Rx an-

tenna indices, respectively. The other transmitter antennas (/ ≠ q) apply the weights ^w _ki ⁼ H_M* ^tnat maximize the received power. Then the cancellation weight is given by:

TT*

PI w* = -

H PI + N+ H k₁q IZJ*¹*-**⁾ <¹⁶⁾

SNR

The denominator has heuristically been expanded with an interference term to contain the possible self cancellation.

In the case of a WB scenario, the system is treated as a superposition of several frequency bins (Orthogonal Frequency Division Multiplexing (OFDM) or similar subcarrier operation). The NB analysis can be applied to each subcarrier independently. IiI. Channel Model

A. Simulation Environment

The layout of the simulation is shown in Fig. 2. The transmitter and the receiver are equipped with uniform linear antenna arrays that are located parallel to each other and separated by 15m. A double bounce model (with only a single path per scatterer), is implemented through two scatter rings (5m radius), which surround the Tx and the Rx antennas. 1000 scatterers are randomly distributed on each scatter ring. A non line of sight (NLOS) situation is assumed from the Tx to the Rx antennas. This results in a channel that resembles the environment of particular target applications (indoor, rich scattering, close proximity). In order to obtain local signal statistics, various receiver locations on a rectangular grid of dimensions 87cm x 87cm with A/2 (3cm) grid size, by using antenna spacing of λ/2 (3cm), where λ denotes the wavelength, are considered. This gives 900 local measurements of the channel impulse responses (IRs). A typical Wireless Local Area Network (WLAN) frequency of 5GHz (A= 6cm) and a bandwidth (BW) of 400MHz, divided into 64 equally spaced subcarriers, has been chosen.

B. Channel Characteristics

In order to visualize the average channel behavior, the channel characteristics are provided in this section.

1 ) Channel IR and Transfer Function: The channel IR is calculated based on equa- tion (17).

L h{ϊ) = ∑A_ιx - A₁₂ - e-^δ{t - τ{).

(17)

The summation is performed over the possible scatterer combinations. The signal from the Tx gets scattered from one scatterer on the first scatter ring, hits another scatterer on the second scatter ring and then reaches the receiver. A_? and A_t2 denote the scat- tering coefficients of the first and second scatterer encountered along the Fih path (see Fig. 2). Au and Ai₂ are uniformly distributed with random amplitude between [0, 1] and

phase between [0, 2π]. L/ expresses the length of the /"thpath , thus 2π -+- is the phase

A

offset of /'th path, t_/ indicates the delay of the /'th path which equals to— '-, with c being c the speed of light. In this channel model, no path loss effects are included. 2) Channel Correlation: The NB envelope and power correlation coefficients among all links in a 2 x 2 MIMO system are below 0.1 [19].

3) Power Delay Profile and Frequency Coherence Function: The Power Delay Profile (PDP) and the Frequency Coherence Function (FCF) are the two main parameters used to characterize the delay spread (σd_S) and Coherence Bandwidth (BW_OOh), respectively. The coherence bandwidth is defined as the 50% level of the FCF, i.e.

^BW _coh [2°]- ^{l n tne} situation considered, σ_ds = 16ns and BW_coh ~ 13MHz.

IV. Performance Evaluation

In this section, the performance of the invention in terms of capacity is compared to prior art systems. The following schemes are considered:

• Orthogonal MIMO transmission (SVD, Alamouti 2 x 2), • Single stream transmission (SISO, OC 2 * 1, Alamouti 2 x 1)

• Non-orthogonal MIMO transmission (OC 2 x 2, CI-OS, CI-WF).

In the following, the first Tx and Rx antennas of the antenna arrays are selected as the reference antennas of SISO implementation.

The input signal to noise ratio of the channel is varied, and the cases where SNR_inpυt = 1OdB and SNR_ιnpυ_t = 2OdB are investigated. The Tx filter weights are normalized as in equation (18) (NB) and (19) (WB) in order to preserve the same Tx power for all schemes. The transmitted power per data stream is 1/N_RX. In the WB case, equal power is allocated to all the subcarriers.

NTX _{1 1}

NB : ∑ KJ² = — — = — — (18)

~₁ ^streams N RX

NTX Nsubcarrier .. ..

,tri jrl N_βtnams NR_X

Subsection A analyzes the narrowband situation, while Subsection B deals with the wideband case, in terms of SINR and capacity. In each case, also the number of transmitters is varied, while keeping the number of receivers NRX equal to 2, in order to investigate how many extra elements are required in non-orthogonal transmission in order to achieve the same rate performance as in 2 x 2 orthogonal transmission. A. Narrowband channel

The investigation here represents the performance of a single subcarrier in a multi carrier communication scheme.

1 ) NB SINR distributions: Figures 3 and 4 show the Cumulative Distribution Function (CDF) of the SINR over the different channel realizations for SNR_inpUt = 1OdB and

SNRi_npu_t = 2OdB, respectively. As SNR,_np,_υt increases from 1OdB to 2OdB, the SINR of most schemes increases by 7OdB. MIMO orthogonal transmission schemes (SVD and Alamouti 2 x 2) have higher SINR than non-orthogonal transmission schemes. As expected for high noise conditions (SNR_input = 1OdB), single stream transmission (Alamouti 2 * 1, OC 2 * 1 and SISO) has higher SINR than the non-orthogonal multiplexing schemes (OC 2 x 2, CI-OS and CI-WF).

It can also be observed that the proposed non-orthogonal schemes give similar performance in terms of SINR for the two data substreams. This means that the hardware requirements on the modems that will process them are the same. This does not apply, for example, in the case of SVD orthogonal transmission, where one data stream clearly has significantly higher average SINR than the other.

2) NB Capacity: The NB capacity is calculated based on equation (20). For the capac- ity considerations, both substreams need to be taken into account.

C^NB = ∑ log_a(l + SINBg^B). ft=i (20 )

Figures 5 and 6 show the distribution of the NB capacity in single and double data stream transmission for SNR_{ιnp ut} = 1OdB and SNR_{inp Ut} = 2OdB (noise- and interference dominated scenarios, respectively). As expected, the SVD method has the highest capacity. In the noise dominated scenario ( SNR_{inp ut} = 1OdB in Fig. 5), all schemes, except SVD and SISO, have similar median capacity. However, the Alamouti 2 x 2 and OC 2 x 2 exhibit more diversity around the median than the Cl schemes according to the invention (measured by the steepness of the slope of distribution). For SNRinput = 2OdB in Fig. 6, the non-orthogonal multiplexing schemes exhibit flatter dis- tributions (lower diversity), where more resources are used for interference cancellation instead of power maximizing diversity. Consequently, the median capacity level of these multiplexing schemes becomes higher than that of the single data stream transmission. Figures 7 and 8 show how the median capacity (over the channel realizations) of the different schemes increases as the number of transmit antennas N_7x increases. Data multiplexing schemes (orthogonal or not) can achieve higher capacity than single data stream approaches, as the degrees of freedom increase (as N_7x and/or the SNR_input in- crease). OC approaches the performance of SVD although the OC solution used here is not the jointly optimized one for DL transmission to multiple antennas. This is an indication that data stream isolation becomes less of an issue with increasing N_7x, and that non-orthogonality has vanishing penalty compared to perfectly orthogonal transmission.

CI-OS has performance very close to that of OC. Therefore, even simple antenna weighting architectures perform closer to SVD than to their single data stream counterparts (OC in a N_7x * 1 solution). The suboptimal Wiener weight solution according to the invention performs reasonably close to CI-OS up to about N_7x = 8. At about N_7x = 16 elements, CI-OS reaches a saturation point with respect to performance return. However, concentrating on the low noise scenario (Fig. 8), for N_7x = 4 clear benefits of the Cl Wiener filter approach compared to single data streaming are observable, with about a 50 percent capacity increase relative to the OC N_7x x 1 (SVD would have approximately 65 percent capacity increase in this case).

The plots show that having N_7x = 3-4 transmit antennas and non-orthogonal transmission in a N_7x *2 system suffices to achieve the same performance as in orthogonal 2 x 2 transmission.

B. Wideband Channel The WB investigations follow the same procedure as the NB case. Each subcarrier is treated independently, and the results are averaged over the 64 equally spaced subcar- riers within 400MHz. This way introduces some frequency diversity.

1) Spectral efficiency: The spectral efficiency C is evaluated in the WB case as the average of the subcarrier capacities:

(21 ) Figures 9 and 10 show the WB capacity for the noise and interference dominated cases (SNR_ιπput= 1OdB and 2OdB, respectively).

Due to frequency diversity, it is in general expected that all the distributions are com- pacted compared to the NB case. The relative performance order of the schemes is mostly preserved. One peculiarity is that the CI-OS marginally outperforms the OC weighting scheme. This is due to the fact that OC has larger frequency domain fading dynamics than CI-OS.

Figures 11 and 12 show the median achievable capacity for the noise and interference dominated cases (SNR_input = 1OdB and SNR_input = 2OdB) as a function of the number of transmit antennas.

Figures 7 and 8 show that in the NB case all the multiplexing techniques have similar performance, which are distinctly different from that of single stream transmission and close to that of orthogonal MIMO transmission. However in the WB case (Figures 11 and 12) the performance is different for SNR_ιnput = 1OdB and SNR_ιnput = 2OdB. In the low noise situation {SNRj_nput = 2OdB in Fig. 12), the same observations can be made as in the NB case. In the high noise situation (SNR_input = 1OdB in Fig.11), the perform- ance of the non-orthogonal transmission algorithms uniformly covers the range between single stream and orthogonal MIMO transmission. This can be attributed to the varying statistical properties of the algorithms over the frequency spectrum.

As the number of transmit antennas rises, only for /V_7x = 2 does CI-OS marginally out- perform the OC scheme. For a larger number of transmitter antennas, OC performs better than CI-OS. Again this indicates that joint optimization of the data stream weights is mostly critical for small-size systems, whereas for larger antenna systems the diversity and isolation between data streams inherently becomes so large, that it is not a critical issue anymore.

Similarly to the NB case, 3-4 transmitter antennas suffice to achieve the same performance in non-orthogonal transmission as in orthogonal 2 x 2 transmission. The results indicate that it is possible to trade off complex orthogonal 2 x 2 MIMO and filters at both terminals, for a very simple terminal in the receiving end with just 1- 2 extra (3 - 4 total) antennas at the transmitting end. This is a very promising alternative for low complexity user equipment, where the necessary extra hardware complexity can be placed on the system side terminal.

V. Conclusion

Orthogonal and non-orthogonal transmission schemes have been compared for a sys- tern that employs several transmitter antennas and two receiver antennas. The objective is to send two data streams and decode them independently on the two receivers. Orthogonal transmission in the SVD sense requires coordination of both the transmitters and the receivers and sets the upper performance limit.

The non-orthogonal schemes investigated are optimal combining and two versions of a novel scheme, denoted cancellation/inversion (Cl). In order for these schemes to achieve the same performance as orthogonal transmission, additional antenna elements would be required at the transmitter. Based on the median capacity levels, in the noise dominated situation, OC and Cl require 3-4 transmit antennas for the same per- formance as an orthogonal system with respect to N_7X= 2.

The Cl weighting scheme is a novel alternative to orthogonal channel communication schemes that dramatically reduces the required complexity of the terminals at the receiving end, since no filtering or cross branch cooperation is necessary for the detec- tion of the data substreams. Also the scalability of the schemes with respect to the number of data streams is a straight forward generalization of the algorithms as the proposed scheme effectively is an antenna pin pointing operation. Another benefit is the similarity in the quality of the data streams, which means that the same order and complexity of modem can be used for all data streams. Moreover, the weight design on the transmitter side is further simplified by the separate treatment of the diversity and the interference cancellation actions. Finally, in its simplest form, it involves a low complexity selection criterion and straight forward algebraic expressions for the calculation of the power maximizing and interference cancelling weights.

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Claims

1. A method of non-orthogonal spatial multiplexing in a multiple-input multiple-output (MIMO) communication system, - said system having an acting transmitter side comprising a transmitter with a number of transmitter antennas and an acting receiver side comprising a receiver with a number of receiver antennas, a number of non-orthogonal parallel channels for data substream spatial multiplexing being generated between the transmitter and the receiver, and wherein the method comprises the following steps: a) data intended for being sent from said transmitter to said receiver is divided into a number of data streams at the transmitter side, b) the data streams are weighted using filter weights, said weighting being applied to the transmitter side of the system only, c) the data streams are sent from the transmitter to the receiver via the non- orthogonal parallel channels, and d) the data streams are received and decoded by the receiver.

2. A method according to claim 1 , wherein the method further comprises the step of: e) said data streams are recombined at the receiver side to recreate the original data stream.

3. A method according to claim 1 or 2, wherein each of the data streams is associated with a single receiver antenna or antenna group, and wherein the filter weights are applied at the acting transmitter side only.

4. A method according to any of the preceding claims, wherein the transmitter antennas are grouped in transmitter antenna groups of two or more individual transmitter antennas, and where the weighting is performed on the transmitter antenna groups.

5. A method according to claim 4, wherein the antenna groups are constructed as a reduced subset of highest link gain and/or lowest interference and/or lowest noise.

6. A method according to claim 5, wherein the antenna groups are constructed as optimum searched groups.

7. A method according to any of the preceding claims, wherein the filter weights in step b) are divided into at least a number of power maximising weights and a number of interference reducing weights, where the power maximising weights are used for maximising the power of the transmitted data stream to an intended receiver antenna, and the interference reducing weights are used for reducing the self-interference to the receiver antennas that are associated with other substreams.

8. A method according to claim 7, wherein for each data stream one transmitter antenna is used to reduce the interference on the receiver antennas or antenna groups not associated with the particular data stream, and the rest of the transmitter antennas is used to maximize the power of the intended data stream.

9. A method according to any of the preceding claims, wherein the signal to noise and interference ratio [SINR) of the data streams is estimated and used for transmitter filter weight optimisation.

10. A method according to claim 9, wherein the SINR of an individual data stream intended for a certain receiver antenna or antenna group is estimated as the ratio between the signal strength of said individual data stream and the signal strength of the interference from the remaining data streams received plus an estimated noise term:

where S and N denote the signal and noise power, respectively, and the subscript and superscript are indices of the actual and intended receiver antenna or antenna group, respectively.

11. A method according to claim 9 or 10, wherein an optimum combining (OC) method is used for proving the optimum SINR performance on the MIMO system, so that a complete set of transmitter weights provides the best possible signal isolation for a desired receiver antenna.

12. A method according to any of the preceding claims, wherein the filter weights w_k according to an optimum combining method for a given data stream is calculated using the inverse of the spatial covariance matrix R_n+, of the noise for said given data stream plus interference from the other data streams multiplied by the conjugate of a channel transfer scalar H for the channel used for transmitting said given data stream: where k denotes /rth receiver antenna or antenna group.

•13. A method according to any of the preceding claims, wherein optimum selection (OS) of interference reducing weights and transmitter antennas to be used is used for multiplying signal to noise and interference ratios (SINRs) of the data streams and maximising the value of this multiplication.

14. A method according to any of the preceding claims, wherein a set of weights de- veloped for uplink transmission is used directly for improving downlink transmission signal to interference plus noise ratio (SINR) performance.

15. A method according to any of the preceding claims, wherein the selection of interference reducing weights and transmitter antennas to be used is performed jointly for the optimization of the metrics for all data streams.

16. A method according to any of claims 13-15, wherein the optimum selection (OS) is performed using data stream inversion weights with an additional scale parameter α.

17. A method according to claim 16, wherein a given transmit antenna q is used to cancel a certain percentage of the interference caused by the transmission of data stream k on a given receiver antenna p, and where the other antennas apply a weight corresponding to the conjugate of the channel transfer scalar H for the channel used for transmitting, so that the filter weight for the /rth data stream from the g'th antenna is given by the following expression:

where Nγx denotes the number of transmit antennas or groups, and oris the scale parameter.

18. A method according to claim 16 or 17, wherein the scale parameter is divided into discrete values, such as in the range from 0 to 1.

19. A method according to any of the preceding claims, wherein the interference reducing weights are selected by finding the minimum of a link vector difference, namely:

where H is a channel transfer scalar, the indices p and k denote the p'th and /("th receiver antenna, respectively, and q denotes the transmitter antenna.

20. A method according to any of the preceding claims, wherein the interference reducing weights are found using Wiener filters.

21. A method according to claim 20, wherein the interference reducing weights are found using the following modified Wiener filter function:

where H is a channel transfer function, N is a noise term, SNR_k is a signal to noise ratio for the /rth data stream, p and k denote the p'th and /c"th receiver antenna, respectively, q denotes the transmitter antenna index, and / = 1 /V₇*, where N_7x is the number of transmitter antennas.