WO2016173667A1

WO2016173667A1 - Method for determining an optimal precoding parameter and precoding device of adjustable complexity

Info

Publication number: WO2016173667A1
Application number: PCT/EP2015/059556
Authority: WO
Inventors: Luca Rose; Axel Mueller; Gaoning HE
Original assignee: Huawei Technologies Co Ltd
Current assignee: Huawei Technologies Co Ltd
Priority date: 2015-04-30
Filing date: 2015-04-30
Publication date: 2016-11-03
Anticipated expiration: 2017-10-30
Also published as: CN107408962A; CN107408962A8

Abstract

A method (400, 500, 600) for determining a value, J_opt, of a precoding parameter, J, for precoding a sequence of transmit samples, s(t), for transmission in a multi-antenna system, the method comprising: obtaining (401) values of an objective function, u(J), based on a transmission period, T_T, for transmitting the precoded sequence of transmit samples, s(t), a coherence time, T_C, of a channel and a precoding performance function, f(J), and characteristics of a precoding performance function, f(J), the transmission period T_T depending on a training period, T_TR, for channel estimation, a precoding period, T_P, for precoding the sequence of transmit samples, s(t), and the coherence time, T_C, of the channel; and applying (402) an optimality criterion to the values of the objective function, u(J), with respect to the precoding parameter, J, in order to obtain the value J_opt.

Description

Method for determining an optimal precoding parameter and precoding device of adjustable complexity

TECHNICAL FIELD

The present disclosure relates to a method for determining an optimal precoding parameter for precoding a sequence of transmit samples for transmission in a multi- antenna system and a precoding device of adjustable complexity for precoding a sequence of transmit samples for transmission in a multi-antenna system. The invention further relates to a precoding system that implements a variable complexity/variable performance precoding strategy that exploits the method in order to optimally precode considering precoding quality and contextual characteristic of the transmission medium, in particular coherence time. In particular, the disclosure relates to techniques for performance maximizing adaptive MIMO precoding based on a tradeoff between precoder complexity and quality.

BACKGROUND In modern day networks, the presence of multiple antenna devices has become a reality with the deployment of the long term evolution (LTE) infrastructure. In next generation communication system (i.e., 5G networks) this phenomenon is bound to dramatically increase, yielding to massive multiple input multiple output (MaMIMO) systems. In such systems, the number of transmitting antennas at the base stations (BSs) is much larger than the total number of receiving antennas. In MIMO systems in general, and in MaMIMO in particular, precoding occupies a prominent role. The most common types of precoding include the maximum ration transmission (MRT) (known also as matched filter (MF)), which maximizes the received signal to noise power (SNR), the zero-forcing (ZF) which minimizes the interference among the different streams, and the regularized zero forcing (RZF) (known also as maximum mean square error (MMSE) and Wiener filter

transmission), which increases the signal to noise plus interference (SINR) ratio.

Different precoding strategies yield different performance in terms of throughput and require different computation time. The complexity of the highest performing (in terms of throughput) precoding is strongly linked with the number of transmit antenna. In systems characterized by a finite computational power, limited coherence time and large number of transmit antenna, this limits severely the performance of the network. Channel conditions may vary due to mobility, which in turn, can modify the channel statistics and coherence time duration. In particular, the coherence time variation may be impacted by the scheduling of a highly mobile user, or by the uncontrollable modification of the speed of the objects around the receivers. In this case, a fixed-complexity precoding scheme may suffer from severe limitations.

In a downlink MaMI MO system as such one exemplary depicted in Figure 1 , the base station (BS) is equipped with M antennas and it is serving a total of K receiving antennas, with M»K for receiving signals from a plurality of user equipments (U E). In order to successfully serve the different users, the BS needs to retrieve the channel matrix H e £^MXK and then compute its precoder, denoted by the letter w. All the standard precoders used in the literature (e.g., MMSE, MF) are defined by some fixed function of the channel matrix. Here fixed refers to the fact that their complexity cannot be tuned. For instance, one of the most performing precoding strategy is known as RZF transmission, and its formulation is:

Here, z represents a regularization factor, in general taken as the noise variance divided by the transmit power, I_K represents an identity matrix of dimension K, and β is a normalization factor guaranteeing the power budget to be respected. It is possible to prove that the complexity of such a strategy is quite high and it grows linearly with the number of transmit antennas M and with the square of the number of receive antennas K. Given its high performance, in the following it is assumed that the baseline for precoding is the RZF precoder. However, the reasoning developed holds with any sort of linear precoder with fixed complexity.

In a single coherence time, represented in Figure 2, a BS must complete the following steps: (i) complete the training in order to obtain the channel matrix; (ii) compute the precoder; (iii) transmit until the end of the coherence time. Thus the coherence time T_c can be divided in three periods: the training period T_TR , the precoding period T_P and the transmission period T_T, yielding T_c = T_TR + T_P + r_T.The Training period is fixed, it depends on the system chosen to obtain the channel state, and for the following is considered as fixed. The precoding time, on the contrary strongly depends on the selected precoder. The channel matrix H is obtained at the end 210 of the training period T_TR. At the end 212 of the precoding period T_P the first symbol is coded and transmitted. Clearly, the overall performance of the system does not depend only on the performance of the precoder, but also on its complexity. In general, a higher complexity can bring higher precoding performance, but longer precoding times. If one imagines a variable coherence time, or variable hardware performance, it is easy to see how a fixed complexity (and hence fixed precoding time) strategy is not suitable for MaMIMO systems. For instance, if T_c < T_TR + T_P, then there would be no time to dedicate to transmission, and the overall throughput of the system would be equal to 0.

In general the problem is to maximize an objective function expressed as:

where /(^■) is a measure of performance of the precoder w, for instance it could be the average SINR level. The notation (x)⁺ indicates max(x, 0).

In MaMIMO system, one of the most performing techniques is the RZF described, for instance, by M. Joham, K. Kusume, M. H. Gzara, W. Utschick, and J. A. Nossek,

"Transmit Wiener Filter for the Downlink of TDD DS-CDMA Systems," Proceedings of ISSSTA 2002, vol. 1 , pp. 9-13, 2002. This technique balances the negative effects of interference with the useful signal maximizing the average SINR. However, this solution requires the evaluation of the following matrix:

It is possible to show that the total complexity, and hence the precoding time, of such an approach grows linearly with M and with the square of K.

In order to trade complexity with performance, Mijller, A., A. Kammoun, E. Bjornson, and M. Debbah, "Linear Precoding Based on Polynomial Expansion: Reducing Complexity in Massive Ml MO " proposed the implementation of a truncated polynomial expansion (TPE) The matrix operation according to equation (1 ) is approximated by a power series of fixed size, implemented in a pipeline, for example according to the precoder pipeline 300 as shown in Fig. 3. Such a solution shortens the precoding time of a fixed amount by decreasing the precoding performance in terms of SINR.

The precoder pipeline 300 includes a series of memory blocks 321 , 322a, 322b, 323a, 323b that are based on a channel estimate H; a weighting filter (not depicted in Fig. 3) for implementing a filter function; and a processor 301 , 302, 303. The processor including a plurality J of processing cores or precoding blocks 301 , 302, 303 configured for parallel processing drives the sequence of transmit samples 302, s(t) through the series of memory blocks to provide a series of power coefficients 331 , 332, 333 at taps 341 , 342, 343 of the series of memory blocks. The processor 301 , 302, 303 filters the series of power coefficients 331 , 332, 333 based on a filter function∑w_t to provide a precoded transmit sample y(t) (not depicted in Fig. 3). The precoder pipeline 300 includes a plurality of memory-delay units 312, 313 coupled between respective memory blocks for delaying signals at taps 341 , 342, 343 of the series of memory blocks.

However, this solution (see Fig. 3) does not account for situations in which the coherence time is not known a priori, and varies with the scheduled users, or for situations in which different hardware capabilities are available.

SUMMARY

It is the object of the invention to provide a concept for improving the precoding efficiency in MIMO antenna systems with respect to computational complexity, in particular in situations in which the coherence time is not known a priori or in which different hardware capabilities are available.

This object is achieved by the features of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures.

This invention targets the aforementioned problems by defining a family of variable complexity precoders. This variable complexity tunes the tradeoff between precoding performance and complexity, thus increasing the transmission quality. The basic concept described in this disclosure is according to the following: In a (massive) multi-antenna network the time spent computing the precoder reduces the time useful for data transmission. On the other hand, increasing the complexity, i.e., the computing time, of the precoder can yield better performance during the transmission. The optimal tradeoff depends mainly on the complexity, the performance gain obtained with a more complex precoder, the coherence time duration and the capability of hardware. Based on a power series, that is a weighted sum of channel-by-vector products, this disclosure introduces techniques for determining the optimal precoder calculation time and a system to implement it. Hence, an algorithm for determining the optimal tradeoff is derived, and also a system to actually exploit these optimal settings for precoding a sequence of transmit samples. This precoding time may be expressed as the (finite) amount of products one should compute before transmission. Different solutions are introduced depending on different levels of information available at the base station. In order to describe the invention in detail, the following terms, abbreviations and notations will be used:

M: Number of antennas at the transmitter.

K: number of receivers' antennas (for simplicity, one antenna receivers are considered; however the invention is applicable to receivers with multiple antennas).

Tc: coherence time

J: Number of the coding blocks.

BS: Base station

H: channel matrix

MIMO: multiple input multiple output

RZF: regularized zero-forcing

TPE: truncated polynomial expansion

MF: matched filter

UE: user equipment

LTE: long term evolution

MaMIMO: massive MIMO

MRT: maximum ratio transmission

SNR signal to noise power ratio

ZF: zero-forcing

MMSE: minimum mean square error SI NR: signal to noise plus interference ratio

TTR: training period

TP precoding period

TY: transmission period

In the following, devices and methods applicable in MIMO antenna systems using precoding techniques are described. MIMO is a method for multiplying the capacity of a radio link using multiple transmit and receive antennas to exploit multipath propagation. MI MO specifically refers to a practical technique for sending and receiving more than one data signal on the same radio channel at the same time via multipath propagation.

Precoding is a generalization of beamforming to support multi-stream or multi-layer transmission in MI MO wireless communications. In point-to-point systems, precoding means that multiple data streams are emitted from the transmit antennas with

independent and appropriate weightings such that the link throughput is maximized at the receiver output. In multi-user MI MO, the data streams are intended for different users and some measure of the total throughput is maximized.

According to a first aspect, the invention relates to a method for determining a value J_o t of a precoding parameter for precoding a sequence of transmit samples, for transmission in a multi-antenna system, the method comprising: obtaining values of an objective function, based on a transmission period for transmitting the precoded sequence of transmit samples, a coherence time of a channel and a precoding performance function, and characteristics of a precoding performance function, the transmission period depending on a training period for channel estimation, a precoding period for precoding the sequence of transmit samples, and the coherence time of the channel; and applying an optimality criterion to the values of the objective function with respect to the precoding parameter in order to obtain the value J_o t.

Such a method improves the precoding efficiency in MI MO antenna systems with respect to computational complexity because an optimal precoding parameter is applied for the precoding. The precoding parameter applied for the precoding is optimal in the sense that it optimizes the value of the objective function with respect to a pre-set optimality criterion, such as a minimum value, a maximum value, or a pre-determined threshold value. Since the value J_o t of the precoding parameter J is not pre-determined and hence fixed, but determined on the-fly based on the coherence time, any variations of the coherence time are taken into account and hence reflected in the determined value J_o t. This provides for a flexible, efficient, and accurate precoding of sequences of transmit samples.

In a first possible implementation form of the method according to the first aspect, the transmission period decreases with at least one of the following conditions: increasing the training period, increasing the precoding period.

In a second possible implementation form of the method according to the first aspect as such or according to the first implementation form of the first aspect, the characteristics of the precoding performance function include the precoding performance function being monotonically increasing with the precoding parameter.

Knowing the behavior of the precoding performance function provides the advantage that the value Jopt can be determined even in the case in which the exact precoding performance function is not known.

Preferably, the precoder parameter is a natural number. This provides the advantage that for computing the optimal precoding parameter only a low number of computations are required.

In a third possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the precoding parameter indicates a total number of precoding blocks of a precoder, and the value Jo t indicates the optimal number of precoding blocks of the precoder for precoding the sequence of transmit samples.

With other words, the precoder parameter corresponds to an amount of complexity of the precoding at fixed hardware capabilities. In this context, the optimal number of precoding blocks indicates the number of cores of the processor, to be activated for parallel processing of the sequences of transmit samples, to attain the most efficient precoding of the given sequence in terms of time and complexity. This provides the advantage that for a given hardware an optimal precoding parameter can be determined that maximizes the efficiency of the available hardware. In a fourth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the method comprises: precoding the sequence of transmit samples based on the optimal precoder parameter; and transmitting the precoded sequence of transmit samples over the channel.

This provides the advantage that the precoding is optimal with respect to precoding performance. When precoding the sequence of transmit samples based on the optimal precoder parameter the precoding efficiency in MIMO antenna systems is improved with respect to computational complexity, in particular in situations in which the coherence time is not known a priori or in which different hardware capabilities are available. A flexible, adaptable precoding is attained.

In a fifth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the objective function is a product of the transmission period and the precoder performance function, normalized by the coherence time.

This provides the advantage that the optimal precoding parameter is optimal for increased transmission period and/or precoder performance function and for decreased coherence time.

In a sixth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the step of applying an optimality criterion to the values of the objective function comprises:

maximizing the objective function by applying a mathematical maximization technique in case the precoding performance function is available in close form or as an estimate; and maximizing the objective function by applying a heuristic technique in case the precoding performance function is not available in close form or as an estimate.

This provides the advantage that depending on the available form of the precoding performance function different precoding strategies can be applied. Hence, the method can be flexibly applied. In an seventh possible implementation form of the method according to the sixth implementation form of the first aspect, applying the heuristic technique comprises:

successively evaluating the obtained values of the objective function for increasing values of the precoding parameter until a difference between two successive values of the objective function is below a threshold.

Applying such heuristic technique provides the advantage that the optimal precoding parameter can also be determined in cases where the precoding performance function is not available in close form or as an estimate.

In an eighth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the precoding performance function is based on a received signal to interference plus noise ratio.

This provides the advantage that the precoding performance function can be computed by evaluating the received signal.

In a ninth possible implementation form of the method according to the eight

implementation form of the first aspect, the precoding performance function is based on a logarithmic function of the received signal to interference plus noise ratio plus one.

This provides the advantage that the precoding performance function can be computed by evaluating the received signal and applying some simple mathematics.

In an tenth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the precoding performance function is received within a feedback signal from a mobile terminal.

This provides the advantage that the precoding performance function is already available and does not have to be computed.

In an eleventh possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, values of the precoding performance function are received within a feedback signal from a mobile terminal.

This provides the advantage that the value J_o t of the precoding parameter can accurately be determined even if the precoding performance function is neither available nor can be estimated.

According to a second aspect, the invention relates to a precoding device, comprising: a precoder for precoding a sequence of transmit samples, for transmission in a multi- antenna system, wherein an amount of complexity of the precoder is adjustable based on a precoding parameter; a processor for determining a value J_o t of the precoding parameter for the precoder by applying an optimality criterion to values of an objective function with respect to the precoding parameter; wherein the processor is configured to determine the objective function, based on a transmission period for transmitting the precoded sequence of transmit samples, a coherence time of a channel and a precoding performance function, the transmission period depending on a training period for channel estimation, a precoding period for precoding the sequence of transmit samples, and the coherence time of the channel.

Such a precoding device improves the precoding efficiency in Ml MO antenna systems with respect to computational complexity because an optimal precoding parameter is applied in the precoder. The precoding parameter applied for the precoding is optimal in the sense that it optimizes the value of the objective function with respect to a pre-set optimality criterion. Since the value J_o t of the precoding parameter J is not pre-determined and hence fixed, but determined on the-fly based on the coherence time, any variations of the coherence time are taken into account and hence reflected in the determined value Jopt. A flexible, efficient, and accurate precoder is provided that allows for an adaptable precoding of sequences of transmit samples, while taking into account variations of the coherence time, not known a priori.

By applying the optimal precoding parameter, the amount of complexity of the precoding device can be reduced, thereby improving the precoding efficiency.

In a first possible implementation form of the precoding device according to the second aspect, the processor is configured to successively compute values of the objective function for increasing values of the precoding parameter until a difference between two successive values of the objective function is below a threshold.

According to a third aspect, the invention relates to a multi-antenna base station, comprising: the precoding device according to the second aspect as such or according to the first implementation form of the second aspect, wherein the precoder is configured to precode the sequence of transmit samples based on the determined value of the precoding parameter; and a transmitter configured to transmit the precoded sequence of transmit samples over the channel. In such a multi-antenna base station the precoding is optimal with respect to precoding performance. When precoding the sequence of transmit samples based on the determined value of the precoder parameter the precoding efficiency of the multi-antenna base station is improved with respect to computational complexity, in particular in situations in which the coherence time is not known a priori or in which different hardware capabilities are available.

According to a fourth aspect, the invention relates to a precoding system, comprising: a precoder for precoding a sequence of transmit samples for transmission over a transmission medium; and a processor exploiting the method according to the first aspect as such or according to any one of the implementation forms of the first aspect for providing the precoder with a variable precoding strategy in order to optimally precode the sequence of transmit samples with respect to precoding quality and contextual characteristic of the transmission medium, in particular with respect to a coherence time. Such a precoding system provides the advantage that a processor can execute an algorithm for determining the optimal tradeoff which optimal tradeoff setting is then actually exploited by a precoder for precoding the transmit samples. The processor can implement the optimal tradeoff during off-line operation or during on-line operation. This provides a high degree of flexibility for implementation of the system in changing environments. Such a variable precoding strategy is adaptable in terms of complexity and performance depending on the variations of the coherence time. Employing such a variable complexity/variable performance precoding strategy leads to a highly flexible and efficient precoding system. BRIEF DESCRIPTION OF THE DRAWINGS

Further embodiments of the invention will be described with respect to the following figures, in which: Fig. 1 shows a schematic diagram illustrating a massive MIMO system 100;

Fig. 2 shows a schematic diagram 200 illustrating exploitation of the coherence time of a channel; Fig. 3 shows a block diagram illustrating an example of a pipelined implementation of a precoder 300;

Fig. 4 shows a schematic diagram illustrating a method 400 for determining an optimal precoding parameter for precoding a sequence of transmit samples for transmission in a multi-antenna system according to an implementation form;

Fig. 5 shows a flowchart illustrating a method 500 for determining an optimal precoding parameter according to an implementation form; Fig. 6 shows a flowchart illustrating a method 600 for determining an optimal precoding parameter according to an implementation form;

Fig. 7 shows a block diagram illustrating a precoding device 700 according to an implementation form; and

Fig. 8 shows a performance diagram 800 illustrating the performance of an exemplary precoding device according to an implementation form.

DETAILED DESCRIPTION OF EMBODIMENTS In the following detailed description, reference is made to the accompanying drawings, which form a part thereof, and in which is shown by way of illustration specific aspects in which the disclosure may be practiced. It is understood that other aspects may be utilized and structural or logical changes may be made without departing from the scope of the present disclosure. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present disclosure is defined by the appended claims.

It is understood that comments made in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if a specific method step is described, a corresponding device may include a unit to perform the described method step, even if such unit is not explicitly described or illustrated in the figures. Further, it is understood that the features of the various exemplary aspects described herein may be combined with each other, unless specifically noted otherwise.

In the following detailed description, reference is made to a massive MIMO downlink scenario. In a massive MIMO downlink scenario the number of base station's antennas is much greater than the number of receiving antennas, that is M»K. For simplicity of explanation the difference between channel matrix and estimated channel matrix is not considered here. However, whenever the channel matrix is employed at the base station or the receivers the estimated channel matrix is used. The method to estimate the channel matrix is outside from the scope of this disclosure.

In the following detailed description, reference is made to a system model transforming a channel matrix H by using a precoding matrix W. In such system model x(t) may represent the information vector at time instant t and y(t) may represent the transmitted vector at time instant t. They may be generally linked by the relationship y(t) = W x(t), where W is the precoding matrix. The precoding matrix can be evaluated following different strategies.

For instance, \N= H^H is the matched filter (also known as maximum ratio transmission, MRT). In general W is a function of the channel matrix H. Every coherence time, the channel matrix changes and it is re-estimated, hence the precoder changes. The base station needs to "precode", that is, evaluating an efficient matrix W at every coherence time. The time spent in computing this precoding matrix cannot be used for transmitting (since the matrix is not available yet), as shown in Fig. 2. This is particularly problematic for massive MIMO since the large dimension of the channel matrix implies large computational time. For instance if RZF according to "M. Joham, K. Kusume, M. H. Gzara, W. Utschick, and J. A. Nossek, "Transmit Wiener Filter for the Downlink of TDD DS- CDMA Systems," Proceedings of ISSSTA 2002, vol. 1, pp. 9-13, 2002" is used the computational complexity grows approximately as MK² + K³ (that is, it grows more than quadratically with the amount of receiving antennas). If one considers that the coherence time can be of the order of 5 s, it is easy to see how this computation can seriously affect the system performance.

Fig. 4 shows a schematic diagram illustrating a method 400 for determining an optimal precoding parameter for precoding a sequence of transmit samples for transmission in a multi-antenna system according to an implementation form.

The method 400 includes determining 401 an objective function u(J) and applying 402 an optimality criterion to that objective function u(J) with respect to J. Determining 401 the objective function u(J) is based on a transmission period Ττ for transmitting the precoded sequence of transmit samples s(t), based on a coherence time Tc of a channel and based on a precoding performance function f(J). The precoding performance function f(J) depends on the precoding parameter J. The transmission period Ττ depends on a training period TTR for channel estimation, a precoding period TP for precoding the sequence of transmit samples s(t) and the coherence time Tc of the channel, as exemplary illustrated in Fig. 2. Applying 402 the optimality criterion to the objective function u(J) is with respect to the precoding parameter J in order to obtain the optimal precoding parameter J_o t.

The transmission period Ττ may decrease with at least one of the following conditions: increasing the training period TTR, increasing the precoding period Tp. The precoding performance function f(J) may be monotonically increasing with the precoding parameter J. The objective function u(J) may be a product of the transmission period Ττ and the precoder performance function f(J), normalized by the coherence time Tc. The precoder parameter J may be a natural number. The precoder parameter J may correspond to an amount of complexity of the precoding at fixed hardware capabilities.

The method 400 may further include: precoding the sequence of transmit samples s(t), e.g. as described above with respect to Fig. 3 or below with respect to Fig. 7, based on the optimal precoder parameter J; and transmitting the precoded sequence of transmit samples s(t) over the channel. The method 400 may further include: maximizing the objective function u(J) by applying a mathematical maximization technique in case the precoding performance function f(J) is available in close form or as an estimate; and maximizing the objective function u(J) by applying a heuristic technique in case the precoding performance function f(J) is not available in close form or as an estimate, e.g. as described below with respect to Figures 5 and 6. Applying the heuristic technique may comprise: successively computing values of the objective function u(J) for increasing values of the precoding parameter J until a difference between two successive values of the objective function u(J) is below a threshold, e.g. as described below with respect to Figures 5 and 6. The precoding performance function f(J) may be based on a received signal to interference plus noise ratio, e.g. as described below. The precoding

performance function f(J) may be based on a logarithmic function of the received signal to interference plus noise ratio plus one. The precoding performance function f(J) may be received within a feedback signal from a mobile terminal. The objective function may be derived as described in the following. Methods and devices according to the disclosure provide techniques to adapt the quality of the precoding strategy f(w) with the length of the coherence time. In general the precoder can be written as:

where the terms ω_; are opportune parameters (matrices of the opportune dimensions or scalars) computed in order to maximize f(w). During the transmission time, several vectors are precoded using w. Denoting by n (alternatively by t) the time index, by x(n) the precoded transmit vector and by s(n) the uncoded transmit signal one obtains x(n)

By defining the following intermediate quantities:

f r₀(n) = Hs(n)

( 5 )

\ (η) = Hr^fn) 0 < i < ] one can express ( 4 ) as _x(n) = ^ ω_ί ( ).

i=o

Hence the evaluation of a coded vector is reduced to the evaluation of the intermediate vectors

and the precoder performance depends explicitly on the parameter /.

That is, larger values of J correspond to more accurate evaluations of the precoder, but also to longer precoding time. Indeed, the number of operations needed to precode grows linearly with the parameter J, and the precoder performance f(w) may be a non- decreasing function of J. Since the precoder may be univocally identified by the parameter J, and so are its performance, one can denote f(w(J)) as /(/), to ease the notation. Thus, in this disclosure the parameter / may be selected to maximize the following objective function:

Fig. 5 shows a flowchart illustrating a method 500 for determining an optimal precoding parameter according to an implementation form.

The method 500 starts from a first block 501 in which the letter Ω represents the ratio between the single operation complexity and the hardware speed, in other words, it represents the time needed to compute a single operation. In a second block 502 a first factor is evaluated as (Tc-Tp)/Tc, i.e., the difference of the coherence time Tc and the precoding time (or period) TP which difference is divided by the coherence time Tc. In a third block 503 it is checked if f(J), i.e. the precoding performance function is available in close form, or can be estimated (e.g., through feedback). If f(J) is available in close form or can be estimated, in a fourth block 504 the value J is computed that maximizes the objective function u(J) = (Ti/Tc)f(J), i.e. the transmission period divided by the coherence time and multiplied by the precoding performance function f(J). If such a function f(J) is not available in close form and cannot be estimated, in a fifth block 505 a heuristic technique is applied according to the following: successively computing values of u(J) for increasing values of J until a difference between two successive values of u(J) is below a threshold. Precoding (not shown in Fig. 5) may then be applied by using the found or computed value for J. As shown in Fig. 5, depending on the nature, and on the available information, of the function f(J), the optimal J can be computed in two different ways. In the case in which f(J) is available in close form, or it is possible to estimate it, the function u(J) can be maximized with standard maximization techniques. Maximizing a single variable function is straight forward, however, as a backup solution, in case of particularly complex functions a heuristic technique, e.g. an exhaustive search or a trial and error approach may be applied. Such a solution is possible since / is a natural (possibly small) number.

The resulting optimal J is clearly coherence time dependent. Hence, whenever the coherence time changes it needs to be reinitialized.

Fig. 6 shows a flowchart illustrating a method 600 for determining an optimal precoding parameter according to an implementation form. The method 600 starts from a first block 501 corresponding to the first block 501 described above with respect to Fig. 5. The following blocks 502, 503, 504 may correspond to respective blocks 502, 503, 504 described above with respect to Fig. 5. If the above mentioned function f(J) is not available in close form and cannot be estimated, in a fifth block 605 a heuristic technique is applied according to the following: A test value, e.g. J=1 is applied for the precoding parameter J. Then, in a sixth block 606 precoding is applied by using the applied value for J. In a subsequent seventh block 607 it is checked if the precoding parameter J was a test value. If J was not a test value, the sixth block 606 is repeated. If J was a test value, in an eighth block 608 it is checked if the current value of the objective function u(J) is greater than the previous value of u(J). If the answer is yes, in a ninth block 609, the precoding parameter J is increased, e.g. by one (or any other value): J=J+1 and the method 600 proceeds with the precoding according to the sixth block 606. If the answer is no, the method 600 directly proceeds with the precoding according to the sixth block 606. As shown in Fig. 6, depending on the nature, and on the available information, of the function ^"(/), the optimal J can be computed in two different ways. In the case in which f(J) is available in close form, or it is possible to estimate it, the function u(J) can be maximized with standard maximization techniques. Maximizing a single variable function is straight forward, however, as a backup solution, in case of particularly complex functions a heuristic technique, e.g. an exhaustive search or a trial and error approach may be applied. Such a solution is possible since / is a natural (possibly small) number. In the case in which such a function is not available, the method 600 resorts to a trial and error approach. It may begin with a value of J:=1 , and it evaluates u(l), then in the next coherence time it tries u(2). If u(2) < u(l), then the optimal J is equal to 1 , if, instead, u(2) > u(l), the algorithm tries /: = 3, and evaluates u(3). Now, if u(3) < u(2), the optimal / is equal to 2, otherwise the algorithm keeps increasing J. A pseudo-code implementing such an algorithm is provided in table 1.

Trial and Error algorithm evaluating the optimal J

BEGIN

SET /: = l;

Precode and measure u(J);

SET u := 0

REPEAT

SET u ·■= uQ);

SET /: = / + l;

Precode and measure u(J);

UNTIL u < u(J)

END REPEAT SET /: = / - l;

END

Table 1 : Pseudo code of the trial and error algorithm evaluating the optimal J

Fig. 7 shows a block diagram illustrating a precoding device 700 according to an implementation form. The precoding device 700 may implement one of the methods 400, 500, 600 as described above with respect to Figures 4-6. The precoding device 700 includes a precoder 701 and a processor 707. The precoder 701 precodes a sequence of transmit samples s(t) 702 for transmission in a multi-antenna system, wherein an amount of complexity of the precoder 701 is adjustable based on a precoding parameter J.

The precoder 701 may include a series of memory blocks 705, e.g. corresponding to the memory blocks 321 , 322a, 322b, 323a, 323b as described above with respect to Fig. 3, wherein outputs 721 of the series of memory blocks 705 are coupled with a weighting filter 703 for implementing a filter function to compute the precoded transmit sample y(t) 704.

The processor 707 determines an optimal precoding parameter J_o t for the precoder 701 by applying an optimality criterion to an objective function u(J) with respect to the precoding parameter J, e.g. as described above with respect to Figures 4-6. The processor 707 is configured to determine the objective function u(J) based on a transmission period Ττ for transmitting the precoded sequence of transmit samples s(t), a coherence time Tc of a channel and a precoding performance function f(J). The precoding performance function f(J) depends on the precoding parameter J. The transmission period TT depends on a training period TTR for channel estimation, a precoding period TP for precoding the sequence of transmit samples s(t) and the coherence time Tc of the channel. The processor 707 may successively compute values of the objective function u(J) for increasing values of the precoding parameter J until a difference between two successive values of the objective function u(J) is below a threshold, e.g. as described above with respect to Figures 5 and 6. The precoding device 700 may be implemented in a multi-antenna base station, e.g. a device BS as depicted in Fig. 1 which includes the precoding device 700, wherein the precoder 701 is configured to precode the sequence of transmit samples s(t) based on the optimal precoding parameter J_o t. The base station may further include a transmitter to transmit the precoded sequence of transmit samples s(t) over the channel.

Fig. 8 illustrates the results of a numerical simulation. A precoding performance function /(/) = log_e(l + SINR) is considered. The precoding device 700 described in Fig. 7 is implemented on a machine equipped with an exemplary number of N=6 cores at an exemplary speed of C=1 GHz. The MIMO system simulated has an exemplary number of M=200 transmit antennas and an exemplary number of K=80 receive antennas, generating around 256K operations per second. The first curve 801 depicts spectral efficiency in nats over SNR in dB for a precoding parameter J=3. The second curve 802 depicts spectral efficiency in nats over SNR in dB for a precoding parameter J=2. The third curve 803 depicts spectral efficiency in nats over SNR in dB for a precoding parameter J=4. Fig. 8 illustrates that increasing the value of J does not always yield an improvement in the total performance of the system, and selecting the optimal J can clearly improve the system performance.

The present disclosure also supports a computer program product including computer executable code or computer executable instructions that, when executed, causes at least one computer to execute the performing and computing steps described herein, in particular the methods 400, 500 and 600 as described above with respect to Figs. 4 to 6. Such a computer program product may include a readable storage medium storing program code thereon for use by a computer. The program code may perform the method 400, 500, 600 as described above with respect to Figs. 4-6.

While a particular feature or aspect of the disclosure may have been disclosed with respect to only one of several implementations, such feature or aspect may be combined with one or more other features or aspects of the other implementations as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms "include", "have", "with", or other variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term "comprise". Also, the terms "exemplary", "for example" and "e.g." are merely meant as an example, rather than the best or optimal. The terms "coupled" and "connected", along with derivatives may have been used. It should be understood that these terms may have been used to indicate that two elements cooperate or interact with each other regardless whether they are in direct physical or electrical contact, or they are not in direct contact with each other.

Although specific aspects have been illustrated and described herein, it will be

appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations may be substituted for the specific aspects shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific aspects discussed herein. Although the elements in the following claims are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence.

Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. Of course, those skilled in the art readily recognize that there are numerous applications of the invention beyond those described herein. While the present invention has been described with reference to one or more particular embodiments, those skilled in the art recognize that many changes may be made thereto without departing from the scope of the present invention. It is therefore to be understood that within the scope of the appended claims and their equivalents, the invention may be practiced otherwise than as specifically described herein.

Claims

CLAIMS:

1 . A method (400, 500, 600) for determining a value, J_o t, of a precoding parameter, J, for precoding a sequence of transmit samples, s(t), for transmission in a multi-antenna system, the method comprising: obtaining (401 ) values of an objective function, u(J), based on a transmission period, TV, for transmitting the precoded sequence of transmit samples, s(t), a coherence time, Tc, of a channel and a precoding performance function, f(J), and characteristics of a precoding performance function, f(J), the transmission period Ττ depending on a training period, TTR, for channel estimation, a precoding period, TP, for precoding the sequence of transmit samples, s(t), and the coherence time, Tc, of the channel; and applying (402) an optimality criterion to the values of the objective function, u(J), with respect to the precoding parameter, J, in order to obtain the value J_o t.

2. The method (400, 500, 600) of claim 1 , wherein the transmission period, Ττ, decreases with at least one of the following conditions: increasing the training period, TTR, increasing the precoding period, Tp.

3. The method (400, 500, 600) of claim 1 or 2, wherein the characteristics of the precoding performance function, f(J), include the precoding performance function, f(J), being monotonically increasing with the precoding parameter, J.

4. The method (400, 500, 600) of one of the preceding claims, wherein the precoding parameter, J, indicates a total number of precoding blocks of a precoder, and the value Jopt indicates the optimal number of precoding blocks of the precoder for precoding the sequence of transmit samples s(t).

5. The method (400, 500, 600) of one of the preceding claims, comprising: precoding the sequence of transmit samples, s(t), based on the value J_o t of the precoder parameter J; and transmitting the precoded sequence of transmit samples (s(t)) over the channel.

6. The method (400, 500, 600) of one of the preceding claims, wherein the objective function, u(J), is a product of the transmission period, TV, and the precoder performance function, f(J), normalized by the coherence time, Tc.

7. The method (400, 500, 600) of one of the preceding claims, wherein the step of applying an optimality criterion to the values of the objective function, u(J), comprises: maximizing the objective function, u(J), by applying a mathematical maximization technique in case the precoding performance function, f(J), is available in close form or as an estimate; and maximizing the objective function, u(J), by applying a heuristic technique in case the precoding performance function, f(J), is not available in close form or as an estimate.

8. The method (400, 500, 600) of claim 7, wherein applying the heuristic technique comprises: successively evaluating the obtained values of the objective function, u(J), for increasing values of the precoding parameter, J, until a difference between two successive values of the objective function, u(J), is below a threshold.

9. The method (400, 500, 600) of one of the preceding claims, wherein the precoding performance function, f(J), is based on a received signal to interference plus noise ratio.

10. The method (400, 500, 600) of claim 9, wherein the precoding performance function, f(J), is based on a logarithmic function of the received signal to interference plus noise ratio plus one.

1 1 . The method (400, 500, 600) of one of the preceding claims, wherein the precoding performance function, f(J), is received within a feedback signal from a mobile terminal.

12. The method (400, 500, 600) of one of the preceding claims, wherein values of the precoding performance function, f(J), are received within a feedback signal from a mobile terminal.

13. A precoding device (700), comprising: a precoder (701 ) for precoding a sequence of transmit samples, s(t), for transmission in a multi-antenna system, wherein an amount of complexity of the precoder is adjustable based on a precoding parameter, J; a processor (707) for determining a value J_o t of the precoding parameter, J_o t, for the precoder by applying an optimality criterion to values of an objective function, u(J) with respect to the precoding parameter, J, wherein the processor (707) is configured to determine the objective function, u(J), based on a transmission period, TV, for transmitting the precoded sequence of transmit samples, s(t), a coherence time, Tc, of a channel and a precoding performance function f(J), the transmission period, TV, depending on a training period, TTR, for channel estimation, a precoding period, TP, for precoding the sequence of transmit samples, s(t), and the coherence time, Tc, of the channel.

14. The precoding device (700) of claim 13, wherein the processor (707) is configured to successively compute values of the objective function (u(J)) for increasing values of the precoding parameter (J) until a difference between two successive values of the objective function (u(J)) is below a threshold.

15. A multi-antenna base station, comprising: the precoding device (700) of claim 13 or 14, wherein the precoder (701 ) is configured to precode the sequence of transmit samples, s(t), based on the determined value Jo t of the precoding parameter J_o t; and a transmitter configured to transmit the precoded sequence of transmit samples

(s(t)) over the channel.

16. A precoding system, comprising:

a precoder for precoding a sequence of transmit samples for transmission over a transmission medium; and a processor exploiting the method according to any one of claims 1 to 12 for providing the precoder with a variable precoding strategy in order to optimally precode the sequence of transmit samples with respect to precoding quality and contextual characteristic of the transmission medium.