WO2016134783A1 - Precoding for multiple user mimo - Google Patents

Abstract

Methods are disclosed of a wireless communication receiving device comprising N_r reception antennas and first and second wireless communication transmitting devices comprising, respectively, N_t1 and N_t2 transmission antennas. The wireless communication receiving device and is adapted to simultaneously receive a first MU-MIMO signal from the first wireless communication transmitting device over a first channel and a second MU-MIMO signal from the second wireless communication transmitting device over a second channel. The wireless communication receiving device determines a number (less than or equal to N_t1N_t2) of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and transmits an indication of the channel association values to at least one of the first and second wireless communication transmitting device. The first (and/or second) wireless communication transmitting device obtains the indication of the channel association values, determines a number of precoding coefficients based on the channel association values and a maximum available transmission power, generates a MU-MIMO signal based on the precoding coefficients, and transmits the MU-MIMO signal to the wireless communication receiving device.

Description

PRECODING FOR MULTIPLE USER MIMO

Technical Field

The present invention relates generally to the field of multiple user multiple- input multiple-output (MU-MIMO) systems. More particularly, it relates to precoding design in such systems.

Background

Linear precoder design for multiple user (multi-user) MIMO systems is typically applied in, for example, WLAN (Wireless Local Area Network) systems and 4^th generation (4G) communication systems such as the Long Term Evolution for Universal Mobile Telecommunication Standard (UMTS-LTE).

Examples of approaches for design of linear precoders for the uplink channel may be found in C-C Hu, C-L Yang, "Combined Transceiver Optimization for Uplink Multiuser MIMO with Limited CSI", International Scholarly Research Notices (ISRN) Signal Processing, Vol. 6, 2011, JW Huang, EKS Au, VKN Lau, "Linear Precoder and Equalizer Design for Uplink Multiuser MIMO Systems with Imperfect Channel State Information", IEEE Wireless Communications and Networking Conference (WCNC), March 2007, pp. 1295-1300, and H Karaa, RS Adve, AJ Tenenbaum, "Linear Precoding for Multiuser MIMO-OFDM Systems", proceedings of IEEE International Conference on Communication (ICC), pages 2797-2802, Glasgow, June 2007. In these publications, various suboptimal solutions are disclosed to the problem of designing precoders at MU-MIMO transmitting devices by minimizing the total resulting mean square error (MSE) at the MU-MIMO receiving device.

DP Palomar, Y Jiang, "MIMO Transceiver Design via Majorization Theory",

NOW Publishers, Foundations and Trends in Communication and Information Theory, Vol. 3, Nos. 4-5, 2006, pages 331-551 discloses optimal precoder solutions to a zero forcing (ZF) equalizer, but only for point-to-point MIMO systems and not for multiple user MIMO systems.

In the prior art, it is typically assumed that the MU-MIMO receiving device performs any precoder design (optimization or sub-optimization) and feeds back - to each MU-MIMO transmitting device - either an entire precoding matrix or a number of bits that denote the index of a precoder in a codebook of the MU-MIMO transmitting device.

The latter approach assumes that the MU-MIMO receiving device is aware of the precoder codebook at each MU-MIMO transmitting device.

Summary

It should be emphasized that the term "comprises/comprising" when used in this specification is taken to specify the presence of stated features, integers, steps, or components, but does not preclude the presence or addition of one or more other features, integers, steps, components, or groups thereof.

Terms like wireless communication transmitting/receiving device, MU-MIMO transmitting/receiving device, and transmitting/receiving device will be used interchangeably herein. For example, the wireless communication receiving device may be an access point (AP), a network node, a base station, or the like, and the wireless communication transmitting devices may be mobile terminals, user equipments, stations (STA) or the like. The description uses design of MU-MIMO uplink precoding as an example, but it should be noted that this is not to be considered limited. Contrarily, the wireless communication receiving/transmitting devices may be any suitable devices.

The inventors have realized that feeding back entire precoding matrices causes a large amount of overhead communication which negatively affects system capacity.

Therefore, there is a need for alternative methods and devices for MU-MIMO precoder design. Preferably, such solutions minimize the amount of feedback needed.

It is an object of some embodiments to solve or mitigate at least some of the above or other disadvantages.

In this disclosure, aspects and embodiments will be disclosed where the MU- MIMO receiving device has knowledge of (or estimates) first and second channels for reception from first and second MU-MIMO wireless communication transmitting devices, respectively. Based on the first and second channels, the receiving device calculates channel association values (arranged in a channel association matrix according to some embodiments) and feeds back an indication of the channel association values to both of first and second wireless communication transmitting devices. The first and second wireless communication transmitting devices then determine their respective precoding coefficients (arranged in precoding matrices according to some embodiments) based on the channel association values.

Hence, the receiving device does not need to determine the precoding coefficients according to some embodiments. Typically, this assumes that the receiving device can estimate the channel-precoder products (HiFi and H₂F₂), which may, for example, be accomplished by additional training after the first and second wireless communication transmitting devices have determined and applied their precoding coefficients.

In some embodiments, the receiving device does determine the precoding coefficients to avoid the need for the additional training.

According to a first aspect, this is achieved by a method of a first wireless communication transmitting device comprising a first number, N_tl, of transmission antennas and adapted to transmit a first multiple user multiple-input multiple-output (MU-MIMO) signal to a wireless communication receiving device over a first channel, while a second wireless communication transmitting device comprising a second number, N_t2, of transmission antennas is adapted to simultaneously transmit a second MU-MIMO signal to the wireless communication receiving device over a second channel.

The wireless communication receiving device comprises a third number, N_r, of reception antennas.

The method comprises obtaining an indication of a fourth number of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and wherein the fourth number is less than or equal to the first number multiplied with the second number.

The method also comprises determining a fifth number of precoding coefficients based on the channel association values and a maximum available transmission power of the first wireless communication transmitting device (wherein the fifth number is less than or equal to the first number squared), generating the first MU-MIMO signal based on the precoding coefficients, and transmitting the first MU- MIMO signal to the wireless communication receiving device.

In an example, N_ti = N_t2 = 2 and N_r = 4. Then, the fourth number of channel association values may be equal to at most N_ti N_t2 = 4, while the fifth number of precoding coefficients is equal to N_ti² = 4 for the first wireless communication transmitting device (and N_t2 ² = 4 for the second wireless communication transmitting device).

In another example, N_ti = 4, N_t2 = 2 and N_r = 8. Then, the fourth number of channel association values may be equal to at most N_ti N_t2 = 8, while the fifth number of precoding coefficients is equal to N_ti² = 16 for the first wireless communication transmitting device (and N_t2 ² = 4 for the second wireless communication transmitting device).

In typical embodiments, the third number may be larger than or equal to the first number plus the second number, where the first number plus the second number is larger than 1. Such embodiments have the advantage that convergence of the channel association values and/or the precoding coefficients may be ensured.

In some embodiments, the fourth number may be equal to the first number multiplied with the second number and the fifth number may be equal to the first number squared.

The channel association values may be organized into a channel association matrix, Q, of size N_tl ^x N_t2, and the precoding coefficients may be organized into a precoding matrix, F_ls of size N_tl ^x N_tl according to some embodiments.

In some embodiments, the channel association values may be extractable from the correlation between the first channel and the second channel by representing the first channel as a first channel matrix, Hi, of size N_r x N_ti and the second channel as a second channel matrix, H₂, of size N_r x N_t2, performing a singular value decomposition factorization of each of the first and second channel matrices, Hi = Ui ·∑i · Vi and H₂ = U₂ ·∑₂ · V₂ (wherein Ui and U₂ are N_r x N_r unitary matrices, Vi is a N_tl ^x N_tl unitary matrix, V₂ is a N_t2 ^x N_t2 unitary matrix,∑i is a N_r ^x N_ti non-negative real number rectangular diagonal matrix and∑₂ is a N_r ^x N_t2 non-negative real number rectangular diagonal matrix), and extracting the channel association matrix as an upper left part size N_tl ^x N_t2 of a result of a matrix multiplication between a Hermitian transposition of the left unitary matrix of the first channel matrix and the left unitary matrix of the second channel matrix, Ui · U₂.

The precoding coefficients may, according to some embodiments, be determined based on the channel association values and the maximum available transmission power of the first wireless communication transmitting device by determining a unitary matrix, Wi, and an eigenvalue matrix, Γι, of a symmetric matrix resulting from a matrix multiplication between a singular value matrix,∑i, of the first channel, an identity matrix minus a matrix multiplication between the channel association matrix and its Hermitian transpose, and the singular value matrix of the first channel,∑i · (I - Q · Q ) ·∑i, calculating an intermediary precoding matrix as a matrix multiplication between the right unitary matrix of the first channel, the unitary matrix of the symmetric matrix, and a square root of an inverse of the eigenvalue matrix of the

-1/2

symmetric matrix,Vi · Wi · T , and applying a scaling factor to the intermediary precoding matrix to generate the precoding matrix, wherein the scaling factor is based on the maximum available transmission power of the first wireless communication transmitting device.

In some embodiments, the channel association values may be determined by the wireless communication receiving device (e.g. based on measurements of previously transmitted MU-MIMO signals and/or channel information from the first and second wireless communication transmitting device), and obtaining the indication of the channel association values may comprise receiving the indication from the wireless communication receiving device.

A sixth number of precoding coefficients may be determinable, according to some embodiments, by the second wireless communication transmitting device based on the channel association values and a maximum available transmission power of the second wireless communication transmitting device, wherein the sixth number is less than or equal to the second number squared.

A second aspect is a method of a wireless communication receiving device comprising a third number, N_r, of reception antennas and adapted to simultaneously receive a first MU-MIMO signal from a first wireless communication transmitting device (comprising a first number, N_tl, of transmission antennas) over a first channel and a second MU-MIMO signal from a second wireless communication transmitting device (comprising a second number, N_t2, of transmission antennas) over a second channel.

The method comprises receiving MU-MIMO signals from the first and second wireless communication transmitting device, and determining a fourth number of channel association values (wherein the channel association values are extractable from a correlation between the first channel and the second channel and wherein the fourth number is less than or equal to the first number multiplied with the second number).

The method also comprises transmitting an indication of the channel association values to at least one of the first and second wireless communication transmitting device for determination of a respective number of precoding coefficients (for generation of the respective MU-MIMO signal) based on the channel association values and a maximum available transmission power of the respective wireless communication transmitting device, wherein the respective number is less than or equal to the number of transmission antennas of the respective wireless communication transmitting device squared.

The channel association values may, for example, be determined based on measurements of the received MU-MIMO signals and/or on channel information from the first and second wireless communication transmitting device.

The indication of the fourth number of channel association values may comprise the fourth number of channel association values in some embodiments.

In some embodiments, determining the channel association values may comprise estimating a distribution function of the channel association values and determining one or more (less than or equal to the first number squared (for the first wireless communication transmitting device) plus the second number squared (for the second wireless communication transmitting device)) expected values (over an ensemble of possible channel association values) of a function of the channel association values based on the distribution function.

If a stochastic process describing the channel and/or the channel association values is ergodic, estimation of the distribution function may be omitted. Thus, in some embodiments, determining the channel association values may comprise determining one or more (less than or equal to the first number squared for the first wireless communication transmitting device and less than or equal to the second number squared for the second wireless communication transmitting device) expected values (over an ensemble of possible channel association values) of a function of the channel association values by averaging the function of the channel association values over time.

The indication of the fourth number of channel association values may comprise the one or more expected values in some embodiments.

For example, the expected values may comprise one or more elements of the matrix E{Q · Q } for the first wireless communication transmitting device and one or more elements of the matrix E{Q · Q} for the second wireless communication transmitting device, where E{X} denotes the expected value of X.

In some embodiments, the method may comprise transmitting the channel association values as the indication until the distribution function has been determined and thereafter transmitting the expected values as the indication.

A third aspect is a method of a second wireless communication transmitting device corresponding to that of the first aspect of the first wireless communication transmitting device.

A fourth aspect is a computer program product comprising a computer readable medium, having thereon a computer program comprising program instructions, the computer program being loadable into a data-processing unit and adapted to cause execution of the method according to any of the first, second and third aspects when the computer program is run by the data-processing unit.

A fifth aspect is an arrangement of a first wireless communication transmitting device comprising a first number, N_tl, of transmission antennas and adapted to transmit a first multiple user multiple-input multiple-output (MU-MIMO) signal to a wireless communication receiving device over a first channel.

A second wireless communication transmitting device comprising a second number, N_t2, of transmission antennas is adapted to simultaneously transmit a second MU-MIMO signal to the wireless communication receiving device over a second channel.

The wireless communication receiving device comprises a third number, N_r, of reception antennas.

The arrangement comprises a control unit adapted to obtain an indication of a fourth number of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and wherein the fourth number is less than or equal to the first number multiplied with the second number.

The control unit is also adapted to determine a fifth number of precoding coefficients based on the channel association values and a maximum available transmission power of the first wireless communication transmitting device, wherein the fifth number is less than or equal to the first number squared, cause generation of the first MU-MIMO signal based on the precoding coefficients, and cause a transmitter of first wireless communication transmitting device to transmit the first MU-MIMO signal to the wireless communication receiving device.

A sixth aspect is an arrangement of a wireless communication receiving device comprising a third number, N_r, of reception antennas and adapted to simultaneously receive a first MU-MIMO signal from a first wireless communication transmitting device (comprising a first number, N_ti, of transmission antennas) over a first channel and a second MU-MIMO signal from a second wireless communication transmitting device (comprising a second number, N_t2, of transmission antennas) over a second channel.

The arrangement comprises a control unit adapted to determine a fourth number of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and wherein the fourth number is less than or equal to the first number multiplied with the second number.

The control unit is also adapted to cause a transmitter of the wireless communication receiving device to transmit an indication of the channel association values to at least one of the first and second wireless communication transmitting device for determination of a respective number of precoding coefficients (for generation of the respective MU-MIMO signal) based on the channel association values and a maximum available transmission power of the respective wireless communication transmitting device, wherein the respective number is less than or equal to the number of

transmission antennas of the respective wireless communication transmitting device squared.

A seventh aspect is an arrangement of a second wireless communication transmitting device corresponding to that of the fifth aspect of the first wireless communication transmitting device.

An eighth aspect is a wireless communication device comprising the arrangement of any of the fifth, sixth or seventh aspects.

In some embodiments, the various aspects may additionally have features identical with or corresponding to any of the various features as explained above for any of the other aspects.

An advantage of some embodiments is that the precoder design with a decreased amount of feedback signaling may be achieved even if the MU-MIMO receiving device is not aware of the precoding codebook of each MU-MIMO

transmitting device.

In some embodiments (e.g. when the elements of the matrix Q are fed back), the amount of feedback is limited to N_tiN_t2 complex numbers. Furthermore, the same numbers may be used as feedback to both MU-MIMO transmitting devices.

These feedback amounts are in contrast to prior art solutions where N_ti² complex numbers (precoding coefficients) are fed back to the first MU-MIMO transmitting device and N_t2 ² complex numbers (precoding coefficients) are fed back to the second MU-MIMO transmitting device.

In some embodiments (e.g. when the expected values are fed back), the amount of feedback is limited to N_ti² complex numbers for the first MU-MIMO transmitting device and N_t2 ² complex numbers for the second MU-MIMO transmitting device. In these embodiments, different numbers may need to be fed back to the different MU- MIMO transmitting devices and the amount is the same as in the prior art at each feedback occation. On the other hand, the feedback of the expected values may typically be performed more seldom (or even only once) than feedback of momentary channel association values.

Brief Description of the Drawings

Further objects, features and advantages will appear from the following detailed description of embodiments, with reference being made to the accompanying drawings, in which:

Fig. 1 is a schematic drawing illustrating an example system according to some embodiments;

Fig. 2A is a block diagram illustrating an example arrangement according to some embodiments;

Fig. 2B is a block diagram illustrating an example arrangement according to some embodiments;

Fig. 3 is a combined flowchart and signaling diagram illustrating example method steps and signaling according to some embodiments; and

Fig. 4 is a schematic drawing illustrating a computer readable medium according to some embodiments.

Detailed Description

In the following, embodiments will be described where MU-MIMO precoder design is achieved based on channel information. The channel information may, for example, comprise channel state information (CSI), channel quality indications (CQI), or similar.

Figure 1 schematically illustrates an example system scenario where embodiments may be applicable.

In this scenario wireless communication receiving device 103 comprising N_r reception antennas simultaneously receives first and second MU-MIMO signals. The first MU-MIMO signal is received from a first wireless communication transmitting device 101 comprising N_ti transmission antennas (and transmitting N_ti MIMO streams) over a first channel 1 1 1 and the second MU-MIMO signal is received from a second wireless communication transmitting device 102 comprising N_t2 transmission antennas (and transmitting N_t2 MIMO streams) over a second channel 1 12. In this example, N_r = 4 and N_ti = N_t2 = 2. Embodiments may be equally applicable when the number of transmitted streams is less than the number of transmission antennas. The first channel 1 1 1 will be denoted Hi and may be represented as an N_r x N_ti matrix and the second channel 1 12 will be denoted H₂ and may be represented as an N_r x N_t2 matrix.

Figure 2A illustrates an example arrangement according to some embodiments. The arrangement of Figure 2A may be comprised in a wireless communication transmitting device, for example any of the first and second wireless communication transmitting devices 101 and 102 of Figure 1.

The arrangement of Figure 2A comprises a control unit (CU) 240 which is adapted to determine precoding coefficients based on channel association values and a maximum available transmission power of the wireless communication transmitting device as will be elaborated on below. The precoding coefficients may, for example, be determined by a precoding determiner (PC DET) 241 of the control unit 240.

The control unit may be adapted to obtain the channel association values (or an indication thereof, such as an expected value of a function of the channel association values) from a receiver (illustrated in Figure 2A as a transceiver (RX/TX) 210) associated with or connected to the control unit 240.

The control unit 240 is also adapted to cause generation of a MU-MIMO signal based on the determined precoding coefficients. The MU-MIMO signal may, for example, be generated from an input signal 230 by a precoder (PC) 220, which receives the determined precoding coefficients from the precoding determiner 241.

The control unit 240 is also adapted to cause a transmitter (illustrated in Figure 2A as a transceiver (RX TX) 210) associated with or connected to the control unit 240 to transmit the generated MU-MIMO signal to a wireless communication receiving device.

Figure 2B illustrates an example arrangement according to some embodiments. The arrangement of Figure 2B may be comprised in a wireless communication receiving device, for example the wireless communication receiving device 103 of Figure 1.

The arrangement of Figure 2B comprises a control unit (CU) 260 which is adapted to determine channel association values (e.g. based on measurements of MU- MIMO signals received from first and second wireless communication transmitting devices over first and second channels or based on channel information regarding the first and second channels received from first and second wireless communication transmitting devices, respectively), respectively, via a receiver (illustrated in Figure 2B as a transceiver (RX/TX) 250). More precisely, the channel association values are extractable from a correlation between the first channel and the second channel, as will be elaborated on below.

The channel association values may, for example, be determined by a channel association value determiner (CAV DET) 262 of the control unit 260.

In some embodiments, the control unit 260 may be adapted to determine expected values related to the channel association values as will be elaborated on below. The expected values may, for example, be determined by an expectation determiner (EXP DET) 263 of the control unit 260, which expectation determiner receives the channel association values from the channel association value determiner 262.

The control unit 260 is also adapted to cause a transmitter (illustrated in Figure

2B as a transceiver (RX/TX) 250) associated with or connected to the control unit 260 to transmit an indication of the channel association values (e.g. the channel association values or the expected values) to at least one wireless communication transmitting device for determination of precoding coefficients at the wireless communication transmitting device.

Figure 3 is a combined flowchart and signaling diagram illustrating example method steps and signaling according to some embodiments. The method 305 of Figure 3 is performed by a wireless communication transmitting device 301 and the method 307 of Figure 3 is performed by a wireless communication receiving device 303.

The wireless communication transmitting device 301 may, for example, be any of the wireless communication transmitting devices 101, 102 of Figure 1 and/or may comprise the arrangement of Figure 2A. The wireless communication receiving device 303 may, for example, be the wireless communication receiving device 103 of Figure 1 and/or may comprise the arrangement of Figure 2B.

The wireless communication transmitting device 301 comprises N_tl

transmission antennas, the wireless communication receiving device 303 comprises N_r receiving antennas, and an other wireless communication transmitting device (not shown in Figure 3, see the scenario of Figure 1) comprises N_t2 transmission antennas.

The wireless communication transmitting device 301 transmits a MU-MIMO signal 390 to the wireless communication receiving device 303 as illustrated in step 310. The wireless communication receiving device 303 receives the MU-MIMO signal in step 350. Simultaneously, the wireless communication receiving device 303 also receives a MU-MIMO signal transmitted by the other wireless communication transmitting device.

Step 310 may, for example, be performed by the transceiver 210 of Figure 2A and step 350 may, for example, be performed by the transceiver 250 of Figure 2B.

Based on a suitable approach, the wireless communication receiving device 303 determines a number of channel association values as illustrated in step 352, and transmits an indication 392 of the channel association values to the wireless

communication transmitting device 301 as illustrated in step 355. The indication 392 of the channel association values may, for example, comprise the channel association values themselves.

Step 352 may, for example, be performed by the control unit 260 of Figure 2B (e.g. by the channel association value determiner 262) and step 355 may, for example, be performed by the transceiver 250 of Figure 2B.

The indication 392 is received by the wireless communication transmitting device 301 in step 312. In step 314, the wireless communication transmitting device 301 determines the MU-MIMO precoding coefficients based on the received indication and a maximum available transmission power of the wireless communication transmitting device 301. Then, in step 316, the wireless communication transmitting device 301 generates a MU-MIMO signal based on the precoding coefficients according to any suitable method and returns to step 310 for transmission of the generated MU-MIMO signal.

Step 312 may, for example, be performed by the transceiver 210 of Figure 2 A, step 314 may, for example, be performed by the control unit 240 (e.g. the precoding determiner 241) of Figure 2A, and step 316 may, for example, be performed by the precoder 220 of Figure 2A. Since, as will be elaborated on in the following, the number of channel association values is less than or equal to N_tiN_t2, the amount of feedback needed is decreased compared to a solution where the wireless communication receiving device 303 calculates and feeds back the precoding coefficients to the wireless communication transmitting device 301.

As will be exemplified in the following, determining the channel association values in step 352 may comprise determining a coupling matrix Q which embodies a correlation between the two MU-MIMO channels involved; the channel between the wireless communication transmitting device 301 and the wireless communication receiving device 303 and the channel between the other wireless communication transmitting device and the wireless communication receiving device 303 (compare with 111 and 112 of Figure 1).

The wireless communication receiving device 303 may, thus, perform measurements (e.g. channel estimation) of these two channels according to any suitable known or future approach and extracting the coupling matrix Q there from.

Alternatively, the wireless communication receiving device 303 may receive respective channel information (e.g. CQI, CSI) of these two channels from the wireless communication transmitting devices according to any suitable known or future approach and extracting the coupling matrix Q there from.

For example, in WLAN, the channels Hi and ¾ are typically estimated at the wireless communication transmitting devices, respectively. The wireless

communication receiving device (typically an access point - AP) transmits a sounding packet - null data packet (NDP) - in the downlink, which enables estimation of these channels. The wireless communication transmitting devices return their respective channel estimates. Hence, the wireless communication receiving device will have access to estimations of both channels, while each wireless communication transmitting device only knows its own channel estimation.

Another possibility in WLAN is that the wireless communication receiving device learns the channels during the training fields (e.g. Very high throughput-Long training field (VHT-LTF) as specified in the IEEE 802.1 lac standard) in the transmitted packets from the wireless communication transmitting devices. This approach assumes time synchronization within the cyclic prefix (CP) length and good enough frequency synchronization.

The coupling matrix (and its elements, the coupling values) may be seen as a representation of an association between the two MU-MIMO channels and may be extracted from a correlation between a representation of the two MU-MIMO channels as will be exemplified in the following.

The wireless communication receiving device 303 may additionally estimate a distribution function of the channel association values as illustrated in step 353. For example, the distribution function may be estimated based on a collection of previously determined channel association values.

Based on the estimated distribution function, the wireless communication receiving device 303 may then, in step 354, determine expected values - over the ensemble of possible channel association values - associated with the channel association values (e.g. expected values of a function of the channel association values).

If a stochastic process describing the channel and/or the channel association values is ergodic, estimation of the distribution function in step 353 may be omitted and step 354 may comprise determining the expected values by averaging over time.

In these embodiments, the indication 392 of the channel association values may, for example, comprise the expected values (or a derivation there of).

As will be exemplified in the following, the expected values may comprise

E{Q · Q } for the wireless communication transmitting device 301 and E {Q · Q} for the other wireless communication transmitting device, where E{X} denotes the expected value of X. The transmitted indication 392 may comprise elements of E {Q · Q } or of (I - E{Q · Q }) - and correspondingly for the other wireless communication transmitting device - where I denotes the identity matrix.

Since the number of expected values for the two wireless communication transmitting devices is less than or equal to N_ti² + N_t2 ² and since the expected values typically need to be transmitted more seldom, the amount of feedback needed is decreased compared to a solution where the wireless communication receiving device 303 calculates and feeds back the precoding coefficients to the wireless communication transmitting device 301. Steps 353 and 354 may, for example, be performed by the control unit 260 of Figure 2B (e.g. by the expectation determiner 263).

Steps 353 and 354 may, for example, be executed in parallel to step 352 as illustrated in Figure 3. However, steps 352, 353 and 354 (or any suitable selection there of) may be executed in any suitable order for each iteration of method 307.

In some embodiments, the wireless communication receiving device 303 iteratively executes step 352 (and iteratively transmits the channel association values in step 355) until a reliable estimation of the distribution function may be achieved (e.g. until a large enough number of channel estimation values have been determined and/or until a channel estimation value histogram has converged). Then, the wireless communication receiving device 303 determines the expected values in step 354 and transmits the expected values instead of the channel association values in step 355. The expected values may be transmitted more seldom than the channel association values, for example, only when it is detected that the distribution function has changed.

An example derivation of the channel association values and the expected values will now be given. This example may be applied to the embodiments in any of Figures 1, 2A, 2B and 3 as suitable. WLAN terminology is applied in the example for illustrative purposes only.

In this example, it is assumed that the receiving device applies a ZF equalizer and forwards the equalized symbols to a demodulator.

The aim of the example is to design the precoder matrices ¥₁ and F₂

(comprising precoding coefficients) at respective transmitting devices - stations or user equipments or users Ul and U2 in the example - such that the average ZF equalization error (averaged across data and noise) at the receiving device - AP in the example - is minimized.

The optimal precoders (that truly minimize this error) depend on both channels H-L and H₂, which may lead to the assumption that each optimal precoder depends on an N_r x N_ti matrix (which is the size of each user's channel, where N_t; is equal to N_tl or N_t2 as applicable), and that these matrices are different for the different transmitting devices. However, the dependency is very limited apart from a number (N_tlN_t2) of channel association values organized in a matrix Q, which is the same for both transmitting devices.

In the example, it is assumed that there is no significant frequency and timing offset degradation at the AP. It is also assumed that N_r = 4 and N_tl = N_t2 = 2. The received signal at the AP, for a specific OFDM (orthogonal frequency division multiplexing) subcarrier, from the two uplink transmissions, takes the following mathematical model:

+ n, (1) where s-^nd s₂ are 2 x 1 vectors representing the two symbols transmitted from each user, stacked in a vector s, and n is an N_r x 1 additive white Gaussian noise (AWGN) vector.

It is assumed that a ZF equalizer G⁺ produces an estimate s of the transmitted symbols from Ul and U2 as:

§ = G⁺y = s + G⁺n, (2)

where G⁺ denotes the pseudo-inverse of the channel-precoder matrix product G in equation (1).

To measure the error made in the estimation, the mean square error (MSE) matrix needs to be calculated for the ZF equalizer, where the averaging is across the data and the noise given a realization of the channel-precoder matrix product. Given a channel-precoder matrix product, the MSE matrix M can be calculated from the work in DP Palomar, Y Jiang, "MIMO Transceiver Design via Majorization Theory", as;

M(F, H) = E_s,n{ (s - s) (s - s)^* } = (F^*H^*HF)-\

where * denotes Hermitian transpose and E_{s n} expectation over s and n.

In this example, Theorem 3.1 of DP Palomar, Y Jiang, "MIMO Transceiver Design via Majorization Theory" is used as a starting point to produce solutions according to various embodiments. However, Theorem 3.1 cannot be directly applied to the optimization problems defined here since they include optimization across a block diagonal matrix (which is a hurdle that could not be overcome for MMSE equalizers in JW Huang, EKS Au, VK Lau, "Linear Precoder and Equalizer Design for Uplink Multiuser MIMO Systems with Imperfect Channel State Information"). Thus, additional computations need to be performed in accordance with these embodiments before applying Theorem 3.1. The expressions obtained before applying Theorem 3.1 are interesting since they reveal (among other things) the amount of feedback.

In a first part of the example the aim is to design optimal precoders for the transmitting devices based on a limited amount of feedback from the receiving device.

For this purpose, it is desirable to minimize the total mean square error (MSE) of the equalizer, which equals the sum of the mean square errors across all streams, with a power constraint on the transmitted signal from each user. In mathematical notation, the total MSE equals tr(M(F, H)), where tr stands for the trace operation. The power constraint for the two users Ul and U2 may be expressed as trCFjF-L) < P_1; tr(F₂F₂) < P₂, with P_{l 5} P₂ being the maximum transmit power for Ul and U2, respectively.

Mathematically, the problem can be formulated as:

min_Fl(F2 tr(M(F, H)) (3)

subject to trCFJFi) < P trCF^) < P₂.

Clearly, finding the two precoders ¥_lt F₂ (which make up F) that minimize the total MSE for each channel realization H_1; H₂ (which make up H) results in an improved performance of the ZF equalizer, assuming the channel H stays constant for some number of OFDM symbols (which typically holds in WLAN scenarios).

Equation (3) has been solved in H Karaa, RS Adve, AJ Tenenbaum, "Linear Precoding for Multiuser MIMO-OFDM Systems" when F is a full matrix with a power constraint on the full matrix F (in contrast to the block diagonal structure in (1) and the power constraints per user in (3)).

One can show (Theorem 3.1 mentioned above) that the optimal solution to problem (3) takes the following form:

F₁ = ^V^V;¹'², F₂ = μ₂ν₂νν₂Γ₂ ^"1/2 (4)

where V_lt V₂ are, respectively, the right unitary matrices of a singular value decomposition factorization of the channels Η_1; H₂ (Hi = Ui ·∑i · Vi and H₂ = U₂ ·∑₂ ^• V₂ ^*), WL, W₂ are unitary matrices of the symmetric matrices∑₁ (I— QQ^*)∑₁ and ∑20^— Q^*Q)∑2 > respectively, and T_1} Γ₂ are eigenvalues of the symmetric matrices ∑i0^— QQ^*)∑i ^and∑₂ (I^— Q^*Q)∑2 ' respectively.∑_1;∑₂ are the singular values of H_]_, H₂, respectively, and the coupling matrix Q is the upper left N_tl x N_t2 matrix of the product (Ui · U₂ or U₂ · Ui) between the left unitary matrices U_{l s} U₂ of F^ and H₂. The scaling factors μ₁ and μ₂ are such that the precoder power constraints in (3) are met, and these constants are easily computed once all other variables in (4) are known.

Hence, in order to construct ¥₁ at UI according to the approach of the first part of the example, the information needed is the coupling matrix Q and the knowledge of Hi (and similarly for U2). Thus, the AP needs to feedback only the matrix Q (or related information) to both users.

The second part of the example builds of the analysis of the first part and aims at constructing ergodic-optimal precoders without repeatedly having to feedback the coupling matrix Q from the AP.

A viable approach in this case is to minimize the total MSE, tr(M(F, H)) , averaged across the ensemble of possible coupling matrices Q. This approach may be justified by noting that, since the solution to (3) is optimal for every channel realization, it is also optimal when tr(M(F, H)) is averaged across the composite channel H, i.e., E_H{tr(M(F, H))}.

In this part of the example, it is assumed that the coupling matrix Q is not repeatedly fed back, and thus unknown, to the transmitting devices or users while the matrices V and∑j, 1 < j < 2, are known. Thus, determination of the precoder matrices F-! and F₂ should not depend on the coupling matrix Q. Therefore, an aim may be to find precoders minimizing the total MSE averaged across the coupling matrix

E_Q{tr(M(F, H))} = tr(E_Q{M(F, H)}). In the case of a Rayleigh distribution on and H₂ (which is a common channel model for the channel on each subcarrier), the following reduction may be applied:

EQ{M (F, H)} = EQ^ITHF) -¹} = F-¹E_Q{(H*H) -¹} (F*)-¹ =

T(F, {S_1J V_1J S_{2 J} V₂}),

where T(F, {S_lt V_lt S₂, V₂}) is an expression that only depends on the matrices that are left after averaging across the coupling matrix Q. This expression contains the matrices V_lt S that are known at Ul (from the NDP training) without any feedback from the AP, and matrices V₂, S₂ which are known at U2 (from the NDP training) without any feedback from the AP.

Hence, a problem similar to (3) may be formulated, namely minimizing the total MSE after averaging across the coupling matrix, subject to power constraints on the precoders:

min_Fl(F2 tr(T(F, {S_1; V_lt S₂ , V₂})) (5)

subject to tr(FiFi) < P₁, tr(F₂ F₂) < P₂.

Solving (5) produces a solution that is optimal ergodically after Q has been averaged out. The solution to (5) will never be a better ergodic solution than the solution to (3), since the solution to (3) is in fact an optimal ergodic solution. The same reasoning holds not only for Rayleigh distributed H_x and H₂ , but also for other distributions on H_x and H₂ for which the coupling matrix Q is independent of the other matrices in the SVD (singular value decomposition) of H_x and H₂.

One can show (Theorem 3.1 mentioned above) that the optimal solution to problem (5) in case of a Rayleigh distribution on H_1; H₂, takes the following form:

Fi = μΛΣΪ ², F₂ = μ₂ν₂∑₂ ^"1/2 . (6)

For non-Rayleigh distribution where Q is independent of the other matrices in the SVD of H and H₂ , the solution takes the following form: Έ₁ = μ₁ν₁Ζ₁Φΐ^1/2, F₂ = μ₂ν₂Ζ₂Φ^~1/2 , (7)

where Z₁ and Φ₁ are the eigenvalues and eigenvectors of the matrix ¹ EQ{I—

Q^*Q}∑i ¹, and Z₂ and Φ₂ are the eigenvalues and eigenvectors of the matrix∑₂ ¹ EQ{I—

QQ

Hence, in order to construct ¥₁ at Ul according to the approach of the second part of the example, the information needed is the expected value EQ{I — Q^*Q} and the knowledge of Hi (and similarly for U2). Thus, the AP needs to feedback only E_Q{I— Q* Q} (or related information, e.g. EQ{Q* Q}) to Ul (and similarly for U2). Since the expected values may be assumed to vary slowly, this type of information can be fed back quite seldom (e.g. when a change in the distribution is detected at the AP) compared to Q in the first part of the example.

Thus, according to some embodiments, two different types of precoder constructions for the transmitting devices are provided, aiming at minimization of the ZF equalization error at the receiving device.

The first type of precoders for minimizing the ZF equalization error may be constructed at the transmitting devices if the receiving device feedbacks N_tiN_t2 complex values, that represent a coupling between the two MU-MIMO channels, to the transmitting devices (the same values to both transmitting devices). Optimization of the ZF equalization error may refer to minimization of the average error after the data and the noise are averaged out, which implies that the channel stays constant for some time.

Since this solution is optimal for every channel realization, it is also optimal when the error is averaged across channel realizations.

The second type of precoder may be constructed based on averaging of the coupling between the two MU-MIMO channels.

The described embodiments and their equivalents may be realized in software or hardware or a combination thereof. They may be performed by general-purpose circuits associated with or integral to a communication device, such as digital signal processors (DSP), central processing units (CPU), co-processor units, field- programmable gate arrays (FPGA) or other programmable hardware, or by specialized circuits such as for example application- specific integrated circuits (ASIC). All such forms are contemplated to be within the scope of this disclosure.

Embodiments may appear within an electronic apparatus (such as a wireless communication device) comprising circuitry/logic or performing methods according to any of the embodiments.

According to some embodiments, a computer program product comprises a computer readable medium such as, for example, a CD-ROM as illustrated by 400 in Figure 4. The computer readable medium may have stored thereon a computer program comprising program instructions. The computer program may be loadable into a data- processing unit (PROC) 420, which may, for example, be comprised in a wireless communication device 410. When loaded into the data-processing unit, the computer program may be stored in a memory (MEM) 430 associated with or integral to the data- processing unit. According to some embodiments, the computer program may, when loaded into and run by the data-processing unit, cause the data-processing unit to execute method steps according to, for example, any of the methods shown in Figure 3.

Reference has been made herein to various embodiments. However, a person skilled in the art would recognize numerous variations to the described embodiments that would still fall within the scope of the claims. For example, the method

embodiments described herein describes example methods through method steps being performed in a certain order. However, it is recognized that these sequences of events may take place in another order without departing from the scope of the claims.

Furthermore, some method steps may be performed in parallel even though they have been described as being performed in sequence.

In the same manner, it should be noted that in the description of embodiments, the partition of functional blocks into particular units is by no means limiting.

Contrarily, these partitions are merely examples. Functional blocks described herein as one unit may be split into two or more units. In the same manner, functional blocks that are described herein as being implemented as two or more units may be implemented as a single unit without departing from the scope of the claims.

Hence, it should be understood that the details of the described embodiments are merely for illustrative purpose and by no means limiting. Instead, all variations that fall within the range of the claims are intended to be embraced therein.

Claims

1. A method of a first wireless communication transmitting device (101, 301) comprising a first number, N_ti, of transmission antennas and adapted to transmit a first multiple user multiple-input multiple-output - MU-MIMO - signal to a wireless communication receiving device (103, 303) over a first channel (111), wherein a second wireless communication transmitting device (102) comprising a second number, N_t2, of transmission antennas is adapted to simultaneously transmit a second MU-MIMO signal to the wireless communication receiving device (103, 303) over a second channel (112), and wherein the wireless communication receiving device comprises a third number, N_r, of reception antennas, the method comprising:

obtaining (312) an indication of a fourth number of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and wherein the fourth number is less than or equal to the first number multiplied with the second number;

determining (314) a fifth number of precoding coefficients based on the channel association values and a maximum available transmission power of the first wireless communication transmitting device, wherein the fifth number is less than or equal to the first number squared;

generating (316) the first MU-MIMO signal based on the precoding

coefficients; and

transmitting (310) the first MU-MIMO signal to the wireless communication receiving device.

2. The method of claim 1 wherein the fourth number is equal to the first number multiplied with the second number and wherein the fifth number is equal to the first number squared.

3. The method of any of claims 1 through 2 wherein the channel association values are organized into a channel association matrix, Q, of size N_tl ^x N_t2, and the precoding coefficients are organized into a precoding matrix, F_ls of size N_tl ^x N_tl.

4. The method of claim 3 wherein the channel association values are extractable from the correlation between the first channel and the second channel by: representing the first channel as a first channel matrix, Hi, of size N_r x N_ti and the second channel as a second channel matrix, H₂, of size N_r x N_t2;

performing a singular value decomposition factorization of each of the first and second channel matrices, Hi = Ui ·∑i · Vi and H₂ = U₂ ·∑₂ ' V₂ , wherein Ui and U₂ are N_r x N_r unitary matrices, Vi^* is a N_ti ^x N_ti unitary matrix, V₂ ^* is a N_t2 ^x N_t2 unitary matrix,∑i is a N_r ^x N_ti non-negative real number rectangular diagonal matrix and∑₂ is a N_r x N_t2 non-negative real number rectangular diagonal matrix; and

extracting the channel association matrix as an upper left part size N_ti ^x N_t2 of a result of a matrix multiplication between a Hermitian transposition of the left unitary matrix of the first channel matrix and the left unitary matrix of the second channel matrix, Ui^* · U₂.

5. The method of claim 4 wherein the precoding coefficients are determined based on the channel association values and the maximum available transmission power of the first wireless communication transmitting device by:

determining a unitary matrix, Wi, and an eigenvalue matrix, Γι, of a symmetric matrix resulting from a matrix multiplication between a singular value matrix,∑i, of the first channel, an identity matrix minus a matrix multiplication between the channel association matrix and its Hermitian transpose, and the singular value matrix of the first channel,∑i · (I - Q · Q*) ·∑i;

calculating an intermediary precoding matrix as a matrix multiplication between the right unitary matrix of the first channel, the unitary matrix of the symmetric matrix, and a square root of an inverse of the eigenvalue matrix of the symmetric matrix,Vi · Wi · T{^m; and

applying a scaling factor to the intermediary precoding matrix to generate the precoding matrix, wherein the scaling factor is based on the maximum available transmission power of the first wireless communication transmitting device.

6. The method of any of claims 1 through 5 wherein the channel association values are determined (352, 353, 354) by the wireless communication receiving device based on signals received from the first and second wireless communication

transmitting device, and wherein obtaining the indication of the channel association values comprises receiving (312) the indication from the wireless communication receiving device.

7. The method of any of claims 1 through 6 wherein a sixth number of precoding coefficients are determinable by the second wireless communication transmitting device based on the channel association values and a maximum available transmission power of the second wireless communication transmitting device, wherein the sixth number is less than or equal to the second number squared.

8. A method of a wireless communication receiving device (103, 303) comprising a third number, N_r, of reception antennas and adapted to simultaneously receive a first multiple user multiple-input multiple-output - MU-MIMO - signal from a first wireless communication transmitting device (101, 301) comprising a first number, N_tl, of transmission antennas over a first channel (111), and a second MU- MIMO signal from a second wireless communication transmitting device (102) comprising a second number, N_t2, of transmission antennas over a second channel (112), the method comprising:

receiving (350) MU-MIMO signals from the first and second wireless communication transmitting device;

determining (352, 353, 354) a fourth number of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and wherein the fourth number is less than or equal to the first number multiplied with the second number; and

transmitting (355) an indication of the channel association values to at least one of the first and second wireless communication transmitting device for determination of a respective number of precoding coefficients, for generation of the respective MU- MIMO signal, based on the channel association values and a maximum available transmission power of the respective wireless communication transmitting device, wherein the respective number is less than or equal to the number of transmission antennas of the respective wireless communication transmitting device squared.

9. The method of claim 8 wherein the channel association values are organized into a channel association matrix, Q, of size N_ti ^x N_t2, and the precoding coefficients of the first and second wireless communication transmitting devices are organized into respective precoding matrices, Fi and F₂, of sizes N_tl ^x N_tl and N_t2 ^x N_t2.

10. The method of claim 9 wherein the channel association values are extractable from the correlation between the first channel and the second channel by: representing the first channel as a first channel matrix, Hi, of size N_r x N_ti and the second channel as a second channel matrix, H₂, of size N_r x N_t2;

performing a singular value decomposition factorization of each of the first and second channel matrices, Hi = Ui ·∑i · Vi and H₂ = U₂ ·∑₂ ' V₂ , wherein Ui and U₂ are N_r x N_r unitary matrices, Vi^* is a N_ti ^x N_ti unitary matrix, V₂ ^* is a N_t2 ^x N_t2 unitary matrix,∑i is a N_r ^x N_ti non-negative real number rectangular diagonal matrix and∑₂ is a N_r x N_t2 non-negative real number rectangular diagonal matrix; and

extracting the channel association matrix as an upper left part size N_ti ^x N_t2 of a result of a matrix multiplication between a Hermitian transposition of the left unitary matrix of the first channel matrix and the left unitary matrix of the second channel matrix, Ui^* · U₂.

11. The method of any of claims 8 through 10 wherein determining the channel association values comprises estimating (353) a distribution function of channel association values and determining (354) one or more expected values, over an ensemble of possible channel association values, of a function of the channel association values based on the distribution function, and wherein the indication of the channel association values comprises the expected values.

12. A computer program product comprising a computer readable medium, having thereon a computer program comprising program instructions, the computer program being loadable into a data-processing unit and adapted to cause execution of the method according to any of claims 1 through 1 1 when the computer program is run by the data-processing unit.

13. An arrangement of a first wireless communication transmitting device (101) comprising a first number, N_ti, of transmission antennas and adapted to transmit a first multiple user multiple-input multiple-output - MU-MIMO - signal to a wireless communication receiving device (103) over a first channel (1 1 1), wherein a second wireless communication transmitting device (102) comprising a second number, N_t2, of transmission antennas is adapted to simultaneously transmit a second MU-MIMO signal to the wireless communication receiving device (103) over a second channel (1 12), and wherein the wireless communication receiving device comprises a third number, N_r, of reception antennas, the arrangement comprising a control unit (240) adapted to:

obtain an indication of a fourth number of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and wherein the fourth number is less than or equal to the first number multiplied with the second number;

determine a fifth number of precoding coefficients based on the channel association values and a maximum available transmission power of the first wireless communication transmitting device, wherein the fifth number is less than or equal to the first number squared;

cause generation of the first MU-MIMO signal based on the precoding coefficients; and

cause a transmitter (210) of first wireless communication transmitting device to transmit the first MU-MIMO signal to the wireless communication receiving device.

14. The arrangement of claim 13 wherein the fourth number is equal to the first number multiplied with the second number and wherein the fifth number is equal to the first number squared.

15. The arrangement of any of claims 13 through 14 wherein the channel association values are organized into a channel association matrix, Q, of size N_ti ^x N_t2, and the precoding coefficients are organized into a precoding matrix, F_ls of size N_ti ^x

16. The arrangement of claim 15 wherein the channel association values are extractable from the correlation between the first channel and the second channel by: representing the first channel as a first channel matrix, Hi, of size N_r x N_ti and the second channel as a second channel matrix, H₂, of size N_r x N_t2;

performing a singular value decomposition factorization of each of the first and second channel matrices, Hi = Ui ·∑i · Vi and H₂ = U₂ ·∑₂ ' V₂ , wherein Ui and U₂ are N_r x N_r unitary matrices, Vi^* is a N_ti ^x N_ti unitary matrix, V₂ ^* is a N_t2 ^x N_t2 unitary matrix,∑i is a N_r ^x N_ti non-negative real number rectangular diagonal matrix and∑₂ is a N_r x N_t2 non-negative real number rectangular diagonal matrix; and

extracting the channel association matrix as an upper left part size N_ti ^x N_t2 of a result of a matrix multiplication between a Hermitian transposition of the left unitary matrix of the first channel matrix and the left unitary matrix of the second channel matrix, Ui^* · U₂.

17. The arrangement of claim 16 wherein the control unit is adapted to determine the precoding coefficients based on the channel association values and the maximum available transmission power of the first wireless communication

transmitting device by:

determining a unitary matrix, Wi, and an eigenvalue matrix, Γι, of a symmetric matrix resulting from a matrix multiplication between a singular value matrix,∑i, of the first channel, an identity matrix minus a matrix multiplication between the channel association matrix and its Hermitian transpose, and the singular value matrix of the first channel,∑i · (I - Q · Q*) ·∑i;

calculating an intermediary precoding matrix as a matrix multiplication between the right unitary matrix of the first channel, the unitary matrix of the symmetric matrix, and a square root of an inverse of the eigenvalue matrix of the symmetric matrix,Vi · Wi · T{^m; and

applying a scaling factor to the intermediary precoding matrix to generate the precoding matrix, wherein the scaling factor is based on the maximum available transmission power of the first wireless communication transmitting device.

18. The arrangement of any of claims 13 through 17 wherein the control unit is adapted to obtain, from a receiver (210) of the first wireless communication transmitting device, the channel association values determined by the wireless communication receiving device based on signals received from the first and second wireless communication transmitting device, and received from the wireless communication receiving device.

19. The arrangement of any of claims 13 through 18 wherein a sixth number of precoding coefficients are determinable by the second wireless communication transmitting device based on the channel association values and a maximum available transmission power of the second wireless communication transmitting device, wherein the sixth number is less than or equal to the second number squared.

20. An arrangement of a wireless communication receiving device (103) comprising a third number, N_r, of reception antennas and adapted to simultaneously receive a first multiple user multiple-input multiple-output - MU-MIMO - signal from a first wireless communication transmitting device (101) comprising a first number, N_ti, of transmission antennas over a first channel (1 1 1), and a second MU-MIMO signal from a second wireless communication transmitting device (102) comprising a second number, N_t2, of transmission antennas over a second channel (1 12), the arrangement comprising a control unit (260) adapted to:

determine a fourth number of channel association values, wherein the channel association values are extractable from a correlation between the first channel and the second channel, and wherein the fourth number is less than or equal to the first number multiplied with the second number; and cause a transmitter (250) of the wireless communication receiving device to transmit an indication of the channel association values to at least one of the first and second wireless communication transmitting device for determination of a respective number of precoding coefficients, for generation of the respective MU-MIMO signal, based on the channel association values and a maximum available transmission power of the respective wireless communication transmitting device, wherein the respective number is less than or equal to the number of transmission antennas of the respective wireless communication transmitting device squared.

21. The arrangement of claim 20 wherein the channel association values are organized into a channel association matrix, Q, of size N_ti ^x N_t2, and the precoding coefficients of the first and second wireless communication transmitting devices are organized into respective precoding matrices, Fi and F₂, of sizes N_tl ^x N_tl and N_t2 ^x N_t2.

22. The arrangement of claim 21 wherein the channel association values are extractable from the correlation between the first channel and the second channel by: representing the first channel as a first channel matrix, Hi, of size N_r x N_ti and the second channel as a second channel matrix, H₂, of size N_r x N_t2;

performing a singular value decomposition factorization of each of the first and second channel matrices, Hi = Ui ·∑i · Vi and H₂ = U₂ ·∑₂ ' V₂ , wherein Ui and U₂ are N_r x N_r unitary matrices, Vi^* is a N_ti ^x N_ti unitary matrix, V₂ ^* is a N_t2 ^x N_t2 unitary matrix,∑i is a N_r ^x N_ti non-negative real number rectangular diagonal matrix and∑₂ is a N_r x N_t2 non-negative real number rectangular diagonal matrix; and

extracting the channel association matrix as an upper left part size N_ti ^x N_t2 of a result of a matrix multiplication between a Hermitian transposition of the left unitary matrix of the first channel matrix and the left unitary matrix of the second channel matrix, Ui^* · U₂.

23. The arrangement of any of claims 20 through 22 wherein the control unit is adapted to determine the channel association values by estimating a distribution function of channel association values and determining one or more expected values, over an ensemble of possible channel association values, of a function of the channel association values based on the distribution function, and wherein the indication of the channel association values comprises the expected values.

24. A wireless communication device comprising the arrangement of any of claims 13 through 23.