Devices and methods for MIMO transmission using nonlinear downlink precoding

Abstract

A transmitter (110) configured to communicate for MlMO transmission to a plurality of receivers (140) using a final sequence vector based on a target signal vector s is disclosed. The transmitter (110) is configured to generate one or more sequence vectors based on a precoding matrix W and the target signal vector s and perform an iterative vector perturbation, VP, scheme (200, 300, 400, 500) for determining the final sequence vector by iteratively refining the one or more sequence vectors. The iterative VP scheme (200, 300, 400, 500) is configured to: (a) generate a plurality of candidate perturbation vectors based on the precoding matrix W and the one or more sequence vectors from a previous iteration; (b) determine for each of the candidate perturbation vectors one or more sequence correlation values between the respective candidate perturbation vector and the one or more sequence vectors from the previous iteration; (c) select, based on the plurality of sequence correlation values, one or more perturbation vectors from the plurality of candidate perturbation vectors for obtaining one or more selected perturbation vectors; and (d) refine the one or more sequence vectors based on the one or more selected perturbation vectors for determining the final sequence vector.

Description

[0001]DEVICES AND METHODS FOR MIMO TRANSMISSION USING NONLINEAR DOWNLINK PRECODING TECHNICAL FIELD The present invention relates to wireless communications. More specifically, the present invention relates to devices and methods for MIMO transmission using nonlinear downlink precoding based on vector perturbation (VP). BACKGROUND Multi-antenna precoding is an important transmitter technology which pre-cancels interferences for multiuser MIMO (MU-MIMO) downlink communications. Channel knowledge is essential for the transmitter in order to perform channel inversion. This may lead to issues when the channel is not-well conditioned, because the inversion of an ill-conditioned channel matrix results in a waste of transmitter energy and, thus, a significant signal-to-noise ratio (SNR) loss at the receivers. Vector perturbation (VP) schemes can improve the transmitter’s energy efficiency in such a case. SUMMARY It is an objective of the present disclosure to provide improved devices and methods for MIMO transmission using nonlinear downlink precoding based on vector perturbation (VP). The foregoing and other objectives are achieved by the subject matter of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures. According to a first aspect a transmitter is provided for energy-efficient MIMO transmission to a plurality of receivers using a final sequence vector based on a target signal vector ^. The transmitter is configured to generate one or more initial sequence vectors based on a MIMO precoding matrix ^ and the target signal vector ^. Moreover, the transmitter is configured to perform an iterative vector perturbation, VP, scheme for determining the final sequence vector by iteratively refining the one or more initial sequence vectors. The iterative VP scheme is configured to: (a) generate a plurality of candidate perturbation vectors based on the precoding matrix ^ and the one or more sequence vectors from a previous iteration; (b) determine for each of the candidate perturbation vectors one or more sequence correlation values between the respective candidate perturbation vector and the one or more sequence vectors from the previous iteration; (c) select, based on the plurality of sequence correlation values, one or more perturbation vectors from the plurality of candidate perturbation vectors for obtaining one or more selected perturbation vectors; and (d) refine the one or more sequence vectors based on the one or more selected perturbation vectors for determining the final sequence vector. In the following several implementation forms of the iterative VP scheme implemented by the transmitter according to the first aspect will be described in more detail. As all of these implementation forms make use of the sequence correlation values between the candidate perturbation vectors and the one or more sequence vectors of a previous iteration for “guiding” the refinement of the one or more sequence vectors, these iterative VP schemes are herein also referred to as correlation-matching pursuit, CMP, VP schemes. As will be appreciated from the more detailed description below, implementation forms of the CMP VP schemes disclosed herein may significantly improve the transmitter energy efficiency by leveraging column-wise correlation in the linear precoder. Moreover, implementation forms of the CMP VP schemes disclosed herein may significantly reduce the computational complexity by calculating the perturbation entries instead of searching in the lattice space. Implementation forms of the CMP VP schemes disclosed herein are well-suited for a parallel-computing implementation. Moreover, implementation forms of the CMP VP schemes disclosed herein may exploit the path diversity for performance improvement (enabled by list encoding). Implementation forms of the CMP VP schemes disclosed herein may flexibly balance the computational costs and the performance by enabling various selectable operation modes. In a further possible implementation form, the one or more sequence vectors comprise a single sequence vector and the transmitter is configured to generate the sequence vector based on the MIMO precoding matrix ^ and the target signal vector ^ by applying the precoding matrix ^ to the target signal vector ^. In a further possible implementation form, the iterative VP scheme comprises a first iterative VP scheme (herein also referred to as a single-path CMP or short S-CMP VP scheme), wherein the first iterative VP scheme is configured to select, based on the plurality of sequence correlation values, one perturbation vector from the plurality of candidate perturbation vectors for obtaining one selected perturbation vector by selecting the candidate perturbation vector having the largest sequence correlation value. In a further possible implementation form, the first iterative VP scheme is configured to refine the sequence vector based on the selected perturbation vector by adding the selected perturbation vector to the sequence vector of the previous iteration. In a further possible implementation form, the first iterative VP scheme is configured to generate the plurality of candidate perturbation vectors ^^(^)for the ^-th iteration based on the following equation: wherein: ^ denotes a scaling factor; ^^denotes the ^-th column vector of the precoding matrix ^; and ^^(^) denotes a complex integer weight factor for the ^-th column vector of the precoding matrix ^. In a further possible implementation form, the first iterative VP scheme is configured to determine the complex integer weight factor ^^(^) for the ^-th column vector of the precoding matrix ^ for the ^-th iteration based on the following equation: ^^(^) = round wherein: ^(^ − 1) denotes the sequence vector of the previous iteration. In a further possible implementation form, the first iterative VP scheme is configured to stop iteratively refining the one or more sequence vectors at the ^-th iteration, if for each of the plurality of candidate perturbation vectors the sequence correlation value for the ^-th iteration is smaller than a threshold value. In an implementation form, this threshold value is about 0.5. In a further possible implementation form, the first iterative VP scheme is configured to determine for each of the candidate perturbation vectors the respective sequence correlation value ^^(^) for the ^-th iteration between the respective candidate perturbation vector and the sequence vector of the previous iteration based on the following equation: In a further possible implementation form, the iterative VP scheme comprises a second iterative VP scheme (herein also referred to as multipath CMP or short M-CMP VP scheme), wherein the second iterative VP scheme comprises a plurality of parallel implementations of the first iterative VP scheme, i.e. the S-CMP VP scheme, wherein each of the plurality of parallel implementations of the first iterative VP scheme is configured to iteratively refine a different sequence vector of the plurality of sequence vectors. In a further possible implementation form, the second iterative VP scheme is configured to generate the plurality of sequence vectors based on the MIMO precoding matrix ^, the target signal vector ^ and a predefined set of complex-integer values. In a further possible implementation form, the second iterative VP scheme is configured to generate the plurality of sequence vectors based on the precoding matrix ^, the target signal vector ^ and the pre-defined set of complex integers ^^based on the following equation: ^^,^(0)= ^(0)+ ^^,^, with ^(0) = ^ ∙ ^ and ^^,^= ^ ∙ ^^∙ ^^, ^ ^ [1, N], ^ ^[1, L]. In a further possible implementation form, the second iterative VP scheme is configured to determine the final sequence vector by selecting the refined sequence vector from the plurality of refined sequence vectors provided by the converged plurality of parallel implementations of the first iterative VP scheme based on a selection criterion, for instance, having the smallest energy. In a further implementation form, additional or alternative selection criteria may be used by the second iterative VP scheme for determining the final sequence vector. For instance, in an implementation form, the second iterative VP scheme may be configured to determine the final sequence vector by selecting the refined sequence vector provided by the implementation of the first iterative VP scheme that required the smallest number of iterations to converge. In a further possible implementation form, the iterative VP scheme comprises a third iterative VP scheme (herein also referred to as a single-path list CMP or short S-list CMP VP scheme), wherein the third iterative VP scheme is configured to sort the plurality of sequence correlation values in an descending order and to select those ^^perturbation vectors from the plurality of candidate perturbation vectors with the largest sequence correlation values as the selected perturbation vectors. In a further possible implementation form, the third iterative VP scheme is configured to refine the sequence vectors based on the plurality of selected perturbation vectors and to retain the refined sequence vectors in the form of a list of sequence vectors in a buffer. As will be described in more detail below, the third VP scheme may be configured to generate the initial sequence vector based on the MIMO precoding matrix ^ and the target signal vector ^ as ^(^) = ^ ∙ ^.(suggested changes for the more generalized case: the initial sequence is not limited to ^(^) = ^ ∙ ^), it could be initialized by any one of the starting points, i.e., ^^,^(0), based on the equation above) At each iteration, the S-list-CMP VP scheme retains multiple perturbation vectors instead of a single perturbation vector (which is the case for the S-CMP scheme described above) and then updates, accordingly, multiple sequence vectors. The sequence vectors updated at the current iteration are used for computing candidate perturbation vectors for the next iteration. In a further possible implementation form, the third iterative VP scheme is configured to stop iteratively refining the one or more sequence vectors at the ^-th iteration, if for each of the plurality of candidate perturbation vectors the sequence correlation value for the ^-th iteration is smaller than a threshold value and / or if the plurality of sequence vectors stored in the buffer remain the same for two consecutive iterations. In a further possible implementation form, the third iterative VP scheme is configured to generate the plurality of candidate perturbation vectors ^^(^)for the ^-th iteration based on the following equation: wherein: ^ denotes a scaling factor; ^^denotes the ^-th column vector of the precoding matrix ^; and ^^,^(^) denotes a complex integer weight factor for the ^-th column vector of the precoding matrix ^ and the ^-th retained sequence vector ^^(^ − 1). In a further possible implementation form, the third iterative VP scheme is configured, at the ^- th iteration, to determine the complex integer weight factor ^^,^(^) for the ^-th column vector of the precoding matrix ^ and the ^-th sequence vector retained from the previous iteration based on the following equation: wherein: ^^(^ − 1), ^ ∈ [1, ^^] denotes the sequence vector retained from the previous iteration and ^^denotes the size of the list configured for the ^-th iteration. In a further possible implementation form, the third iterative VP scheme is configured to determine for each of the candidate perturbation vectors the respective sequence correlation value ^^,^(^) for the ^-th iteration between the respective candidate perturbation vector and the one or more sequence vectors of the previous iteration based on the following equation: In a further possible implementation form, the iterative VP scheme comprises a fourth iterative VP scheme (herein also referred to as M-list-CMP VP scheme) and the fourth iterative VP scheme comprises a plurality of parallel implementations of the third iterative VP scheme, i.e. the S-list-CMP VP scheme, wherein each of the plurality of parallel implementations of the third iterative VP scheme is configured to iteratively refine a different sequence vector of the plurality of sequence vectors. In a further possible implementation form, the fourth iterative VP scheme is configured to generate the plurality of sequence vectors based on the precoding matrix ^, the target signal vector ^ and a predefined set of complex-integer values. In a further possible implementation form, the fourth iterative VP scheme is configured to determine the final sequence vector by selecting the refined sequence vector from the plurality of refined sequence vectors provided by the plurality of parallel implementations of the third iterative VP scheme based on a selection criterion. In a further possible implementation form, the transmitter is further configured to generate the precoding matrix ^ based on channel state information. In a further possible implementation form, the transmitter is a base station. According to a second aspect a method is provided for energy-efficient MIMO transmission to a plurality of receivers using a final sequence vector based on a target signal vector ^. The method comprises: generating one or more initial sequence vectors based on a MIMO precoding matrix ^ and the target signal vector ^; and performing an iterative vector perturbation, VP, scheme for determining the final sequence vector by iteratively refining the one or more initial sequence vectors. The iterative VP scheme comprises: generating a plurality of candidate perturbation vectors based on the precoding matrix ^ and the one or more sequence vectors from a previous iteration; determining for each of the candidate perturbation vectors one or more sequence correlation values between the respective candidate perturbation vector and the one or more sequence vectors from the previous iteration; selecting, based on the plurality of sequence correlation values, one or more perturbation vectors from the plurality of candidate perturbation vectors for obtaining one or more selected perturbation vectors; and refining the one or more sequence vectors based on the one or more selected perturbation vectors for determining the final sequence vector. The method according to the second aspect of the present disclosure can be performed by the transmitter according to the first aspect of the present disclosure. Thus, further features of the method according to the second aspect of the present disclosure result directly from the functionality of the transmitter according to the first aspect of the present disclosure as well as its different implementation forms described above and below. According to a third aspect a computer program product is provided, comprising a computer- readable storage medium for storing program code which causes a computer or a processor to perform the method according to the second aspect, when the program code is executed by the computer or the processor. Details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description, drawings, and claims. BRIEF DESCRIPTION OF THE DRAWINGS In the following, embodiments of the present disclosure are described in more detail with reference to the attached figures and drawings, in which: Fig. 1 shows a schematic diagram illustrating a MIMO communication system including a transmitter according to an embodiment and a plurality of receivers; Fig. 2 shows a schematic diagram illustrating an iterative vector perturbation scheme implemented by the transmitter according to an embodiment; Fig. 3 shows a schematic diagram illustrating an iterative list encoding vector perturbation scheme implemented by the transmitter according to an embodiment; Fig. 4 shows a schematic diagram illustrating an iterative vector perturbation scheme implemented by the transmitter according to an embodiment including a plurality of parallel threads of the iterative vector perturbation scheme of figure 2; Fig. 5 shows a schematic diagram illustrating an iterative vector perturbation scheme implemented by the transmitter according to an embodiment including a plurality of parallel threads of the iterative list encoding vector perturbation scheme of figure 3; Fig. 6 shows a flow diagram illustrating steps of a transmission method according to an embodiment; Fig. 7 shows phase diagrams illustrating an empirical probability of the integer perturbation entry for the transmitter according to different embodiments; Fig.8 shows graphs illustrating the BLER as a function of the bit-energy-to-noise ratio for the VP schemes implemented by the transmitter according to different embodiments in comparison with conventional VP schemes with perfect channel state information; Fig.9 shows graphs illustrating the BLER as a function of the bit-energy-to-noise ratio for the VP schemes implemented by the transmitter according to different embodiments in comparison with conventional VP schemes with imperfect channel state information; and Fig.10 shows graphs illustrating the BLER as a function of the bit-energy-to-noise ratio for the VP schemes implemented by the transmitter according to different embodiments in comparison with conventional VP schemes. In the following, identical reference signs refer to identical or at least functionally equivalent features. DETAILED DESCRIPTION OF THE EMBODIMENTS In the following description, reference is made to the accompanying figures, which form part of the disclosure, and which show, by way of illustration, specific aspects of embodiments of the present disclosure or specific aspects in which embodiments of the present disclosure may be used. It is understood that embodiments of the present disclosure may be used in other aspects and comprise structural or logical changes not depicted in the figures. 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. For instance, it is to be understood that a disclosure 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 one or a plurality of specific method steps are described, a corresponding device may include one or a plurality of units, e.g. functional units, to perform the described one or plurality of method steps (e.g. one unit performing the one or plurality of steps, or a plurality of units each performing one or more of the plurality of steps), even if such one or more units are not explicitly described or illustrated in the figures. On the other hand, for example, if a specific apparatus is described based on one or a plurality of units, e.g. functional units, a corresponding method may include one step to perform the functionality of the one or plurality of units (e.g. one step performing the functionality of the one or plurality of units, or a plurality of steps each performing the functionality of one or more of the plurality of units), even if such one or plurality of steps are not explicitly described or illustrated in the figures. Further, it is understood that the features of the various exemplary embodiments and / or aspects described herein may be combined with each other, unless specifically noted otherwise. Figure 1 shows a schematic diagram illustrating a MIMO communication system 100 including a transmitter 110 according to an embodiment and a plurality of receivers 140. In the embodiment shown in figure 1 the transmitter 110 is implemented as an access point 110 communicating via a plurality of communication channels 130 with the plurality of receivers 140, which are implemented as a plurality of user equipment (or short users) 140. As illustrated in figure 1, the transmitter 110 may implement a transmission processing chain, including a FEC encoding block 113, a Bit-to-Symbol mapping block 115, linear precoder 117 and a VP processing block 120. In an embodiment, the transmitter 110 may comprise processing circuitry and / or a communication interface implementing one or more of these processing blocks. The processing circuitry of the transmitter 110 may be implemented in hardware and / or software and may comprise digital circuitry, or both analog and digital circuitry. Digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), or general-purpose processors. The transmitter 110 may further comprise a memory configured to store executable program code which, when executed by the processing circuitry, causes the transmitter 110 to perform the functions and methods described herein. As illustrated in figure 1, the FEC coding block 113 of the transmitter 110 is configured to encode a data bit stream defining a target signal into an encoded data bit stream using a suitable forward-error-correction (FEC) scheme. The encoded data bit stream is mapped by the Bit-to-Symbol mapping block 115 of the transmitter into a plurality of symbols. The linear precoder 117 of the transmitter 110 is configured to precode the output of the Bit-to-Symbol mapping block 115 based on a precoding matrix ^ (also referred to as precoder ^). As will be described in more detail below, the VP processing block 120 (which in figure 1 for reasons described in more detail below is referred to as Correlation-Matching Pursuit, CMP-based VP processing block 120) to apply a vector perturbation to the output of the liner precoder 117 for achieving a more energy efficient transmission by means of a plurality of antennas 111 of the transmitter 110. As will be described in more detail below, for retrieving the original data signal received by its antenna 111 each receiver 140 may comprise a modulo operation block 143. Moreover, each receiver 140 may comprise a demapping processing block 145 and a decoding processing block 147 for retrieving the decoded bits representing the original data signal. In an embodiment, each receiver 140 may comprise processing circuitry and / or a communication interface implementing one or more of these processing blocks. The processing circuitry of each receiver 140 may be implemented in hardware and / or software and may comprise digital circuitry, or both analog and digital circuitry. Digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), or general-purpose processors. Each receiver 140 may further comprise a memory configured to store executable program code which, when executed by the processing circuitry, causes each receiver 140 to perform the functions and methods described herein. Before describing more detailed embodiments of the transmitter 110 as well as the vector perturbation schemes implemented by the VP processing block 120 of the transmitter 110, some technical and mathematical background helpful for better understanding these embodiments will be explained in the following. In the MU-MIMO downlink communication scenario illustrated in figure 1 the transmitter 110, which, as already mentioned, may be implemented as an access point (AP) 110, deploys, by way of example, antennas 111 to simultaneously serve the receivers 140 (referred to as users 140 in figure 1). Each receiver 140 may be equipped with antennas 141 so that the total number of receiving antennas is given by . As will be appreciated, the aim of vector perturbation (VP) schemes is generally to find an integer-valued perturbation vector that minimizes the precoded sequence energy: As already mentioned above, in this equation ^ denotes the precoding matrix (also referred to as precoder ^), ^ denotes the target signal vector and ^ denotes a constant scaling factor. The received signal of each receiving antenna 141 may be expressed in the following form: In order to successfully detect the desired signal vector ^ with its components ^^, each receiver 140 has to remove the impact introduced by the vector perturbation. To this end, as already described above, the modulo operation block 143 of each receiver 140 may be configured to perform a modulo operation with a suitably chosen scaling factor (e.g., ) as follows (wherein denotes a rounding operation): As will be described in more detail below, the transmitter 110, for instance, the VP processing block 120 thereof is configured to generate one or more initial sequence vectors based on a MIMO precoding matrix ^ and a target signal vector ^ representing the desired signal, i.e. the target signal. The VP processing block 120 of the transmitter 110 is further configured to perform an iterative vector perturbation, VP, scheme 200, 300, 400, 500 for determining a final sequence vector by iteratively refining the one or more initial sequence vectors. As will be described in more detailed in the context of figure 2 to 5, the iterative VP scheme 200, 300, 400, 500 is configured to: (a) generate a plurality of candidate perturbation vectors based on the precoding matrix ^ and the one or more sequence vectors from a previous iteration; (b) determine for each of the candidate perturbation vectors one or more sequence correlation values between the respective candidate perturbation vector and the one or more sequence vectors from the previous iteration; (c) select, based on the plurality of sequence correlation values, one or more perturbation vectors from the plurality of candidate perturbation vectors for obtaining one or more selected perturbation vectors; and (d) refine the one or more sequence vectors based on the one or more selected perturbation vectors for determining the final sequence vector to be used for the MIMO transmission to the plurality of receivers 140. Thus, in the following several embodiments of the CMP-based VP processing block 120 of the transmitter 110 will be described in more detail. As will be appreciated from the detailed description below, in contrast to conventional VP schemes embodiments of the CMP-based VP processing block 120 of the transmitter 110 disclosed herein neither rely on the conventional matrix decomposition to assist nor require the conventional closest-lattice search for finding the perturbation vector and, thus, allow reducing the computational complexity of perturbation vectors resulting in an energy efficient MIMO communication. In addition to the significantly reduced computational complexity, embodiments of the CMP-based VP processing block 120 of the transmitter 110 disclosed herein allow the precoder to offer significantly improved nonlinear precoding performance, i.e., near-VP-optimum performance. Figure 2 shows a schematic diagram illustrating a first embodiment of an iterative vector perturbation scheme 200 implemented by the VP processing block 120 of the transmitter 110. The iterative vector perturbation scheme 200 illustrated in figure 2 is herein also referred to as single-path CMP VP scheme (or short S-CMP VP scheme 200). As will be appreciated, if denotes the precoded signal vector (herein also referred to as precoded sequence or sequence vector) provided by the linear precoder 117 of the transmitter 110 and the perturbation vector, the energy reduction due to the perturbation vector can be written as As can be taken from equation (1), the energy reduction is strongly related to real part of the product between the precoded sequence vector and the perturbation vector , which is herein regarded as a type of correlation measure, which will be defined in more detail in the following. Instead of directly finding the perturbation vector , the CMP-based VP schemes disclosed herein, such as the S-CMP VP scheme 200 illustrated in figure 2, are configured to iteratively find single-entry perturbation vectors which jointly contribute to the energy reduction. For the S-CMP VP scheme 200 illustrated in figure 2, for instance, at the iteration, the energy reduced by the perturbation vector can be written as where denotes the precoded sequence vector obtained during the previous iteration ( ) and denotes the integer-valued perturbation entry. If holds, it indicates that the calculated perturbation entry contributes to the energy reduction and vice versa. By re-arranging the inequality, one obtains the following equivalent form in which is defined as the sequence correlation between the precoded sequence vector obtained from the iteration and the perturbation vector (which is computed in block 202 of figure 2): As will be appreciated, the threshold value of 0.5 indicates whether the perturbation vector is able to reduce the sequence energy. The maximization of equation (2) can be regarded as a convex optimization with respect to By solving the convex optimization problem, the continuous-valued perturbation entry may be expressed as And the integer-valued perturbation entry can be obtained by the VP processing block 120 as . Since in this embodiment, as candidate perturbation vectors are calculated by the VP processing block 120, the VP processing block 120 of the transmitter 110 is further configured to make a selection from the set of candidate perturbation vectors. As already described above, the VP processing block 120 is configured to make this selection based on transmission energy efficiency considerations. More specifically, in an embodiment, the VP processing block 120 of the transmitter 110 is configured to make the selection from the set of candidate perturbation vectors based on the sequence correlation in the following way (as illustrated by block 203 of figure 2), In other words, according to equation (5) the VP processing block 120 of the transmitter 110 is configured in block 203 of figure 2 to select for the i-th iteration that candidate perturbation vector from the plurality of candidate perturbation vectors that has the strongest sequence correlation with the precoded sequence obtained from the iteration. Having determined based on equation (5) for the embodiment shown in figure 2 the VP processing block 120 of the transmitter 110 is further configured to determine the updated, i.e. refined precoded sequence vector in the following way (as illustrated by block 204 of figure 2): As illustrated in block 201 of figure 2, the refined sequence vector is used in the next iteration of the iterative S-CMP VP scheme 200 to compute a new plurality of candidate perturbation vectors in the way described above. If holds in the iteration i.e., none of the candidate perturbation vectors can further reduce the sequence energy, the iterative S-CMP VP scheme 200 implemented by the VP processing block 120 of the transmitter 110 according to an embodiment stops, i.e. converges and the VP processing block 120 is configured to return as the final precoded sequence vector used for the MIMO transmission of the data signal vector ^ to the plurality of receivers 140 (as illustrated by block 202 of figure 2). It can be shown that the computational complexity of the S-CMP VP scheme 200 of figure 2 at each iteration scales with order of , which can be mainly attributed to the calculation of the sequence correlations. In the S-CMP VP scheme 200 of figure 2 multiple candidate perturbation vectors are calculated in each iteration, while only a single vector is selected for the update. Although it is true that some of the vectors do not contribute to the energy reduction jointly, they may offer significant energy reduction, which is herein referred to as multipath diversity. As due to the lack multipath diversity exploitation the S-CMP VP scheme 200 of figure 2 under certain circumstances might not determine the most optimal solution, further embodiments of CMP VP schemes implemented by the VP processing block 120 of the transmitter 110 are described in the following, which allow for multipath diversity. These further embodiments are based on the general idea to select, at the iteration, multiple (e.g., ) candidate perturbation vectors for a parallel update, i.e. refinement of multiple precoded sequence vectors, which may be based on different initial precoded sequence vectors. These further embodiments of CMP VP schemes making use of multipath diversity are herein also referred to as list encoding VP schemes, because the selected perturbation vectors may form a list at each iteration. Thus, according to a further embodiment the VP processing block 120 of the transmitter 110 is configured to implement a list encoding VP scheme only for the first iteration, i.e. (this embodiment may be also referred to as multipath initialization scheme). More specifically, instead of following the S-CMP VP scheme 200 described above in the context of figure 2 for calculating the perturbation entries, in accordance with the multipath initialization scheme the VP processing block 120 of the transmitter 110 according to this further embodiment is configured to extract the perturbation entries from a pre-defined complex integer set, e.g., . By way of example, this pre-defined complex integer set may, for instance, comprise the integers {-1, -j, 1, j}, where j denotes the imaginary unit. As will be appreciated, pre-defined complex integer set may define more and / or different complex integers than the ones used for this illustrative example. In a subsequent stage the VP processing block 120 may be configured to generate the set of initial precoded sequence vectors by . As will be appreciated, each initialized sequence, i.e., , may be regarded as an initial node or starting point. According to embodiments disclosed herein these initial nodes may be combined with the S-CMP VP scheme 200 described above in the context of figure 2 (resulting in the M-CMP VP scheme 400, which will be described in more detail in the context of figure 4) or with a list encoding VP scheme implemented for the further iterations (leading to the M- list-CMP VP scheme 500, which will be described in more detail in the context of figure 5). According to an embodiment, the basic principle for list encoding may remain the same for each subsequent iteration ( ) and may be conducted by the VP processing block 120 of the transmitter 110 separately for each initial node, i.e. independently from the other initial nodes. Therefore, the basic list encoding principle implemented by the VC processing block 120 of the transmitter 110 according to an embodiment will be described in the following for the iteration and for an arbitrary initial node. For the sake of illustration in the following the precoded sequence, vectors being selected by the VP processing block 120 of the transmitter 110 from the iteration for further development in the iteration are referred to as “retained nodes”, while the sequence vectors developed from their corresponding retained node are referred to as “derived nodes”. As already mentioned above, the list encoding VP schemes disclosed herein are configured to retain at a current iteration a list of nodes for further development during the next iteration. Assuming that there are nodes, denoted by being retained by the VP processing block 120 of the transmitter 110 according to an embodiment at the iteration, each retained node may develop derived nodes according to embodiments of the VP scheme disclosed herein, i.e.: where (similar to the above description) and denotes the calculated integer-valued perturbation entry. In the following will be used to denote the derived nodes that can further reduce the energy of their retained node, i.e., with denoting the number of derived nodes satisfying this criterion. Accordingly, the VP processing block 120 of the transmitter 110 according to an embodiment may collect the derived nodes to form a set, i.e., . For generating the list, the VP processing block 120 of the transmitter 110 according to an embodiment may be configured to use the sequence correlation (already defined above) as a metric for node selection. In other words, in an embodiment the VP processing block 120 of the transmitter 110 may be configured to select those derived nodes that have a large sequence correlation value. If the list to be formed and the retained nodes therein are denoted as , the criterion used by the VP processing block 120 of the transmitter 110 according to an embodiment for generating the list may be defined as follows: where . As will be appreciated, equation (8) makes sure that the list is generated to collect the updated precoded sequences whose corresponding sequence correlation defining the largest sequence correlation values. In order to obtain the precoded sequence with the minimized energy, the VP processing block 120 of the transmitter 110 according to an embodiment is configured to implement a stopping mechanism. In an embodiment, the stopping mechanism may be implemented by the VP processing block 120 of the transmitter 110 using a buffer (denoted by whose memory size is pre-configurable (e.g., ). Given the list obtained at the iteration, the VP processing block 120 of the transmitter 110 according to an embodiment is configured to store the node (denoted by ) offering the minimal sequence energy in the buffer: As will be appreciated, the buffer set keeps being updated by the VP processing block 120 of the transmitter 110 according to an embodiment throughout the iterations so that the buffer preserves the best candidate perturbation vectors. In the case the buffer memory is fully occupied, the VP processing block 120 of the transmitter 110 according to an embodiment may replace the node therein with the largest energy by the most recent node having a lower energy. According to an embodiment, if any of the following events are triggered, the list-encoding VP scheme implemented by the VP processing block 120 of the transmitter 110 may stop at the iteration and the node (denoted by ) having the minimal energy may be selected from the buffer as the final precoded sequence: (a) the derived nodes cannot further reduce the energy, i.e., and / or (b) the buffer set remains unchanged for two consecutive iterations, i.e., . As already mentioned above, figure 3 illustrates a S-list-CMP VP scheme 300 implemented by the VP processing block 120 of the transmitter 110 according to an embodiment. Given the initial sequence, i.e. the S-list-CMP VP scheme 300 implemented by the VP processing block 120 of the transmitter 110 according to an embodiment comprises the following processing stages illustrated in figure 3. In a first stage a processing block 301 is configured to determine the integer-valued perturbation entry In a second stage a processing block 302 is configured to determine whether the sequence correlation . holds. If this is the case, the VP processing scheme 300 continues at a third stage, or otherwise returns the final precoded sequence as output. In a third stage a processing block 303 is configured to sort the sequence correlations in descending order. In a fourth stage a processing block 304 is configured to select the derived nodes to form the list as already described above. In a fifth stage a processing block 305 is configured to find the best retained node. In a sixth stage a processing block 306 is configured to update the buffer set in the way described above. In a seventh stage a processing block 307 is configured to return as result the final precoded sequence based on Otherwise, the VP processing scheme 300 returns to the processing block 301 for the next iteration ^ = ^ + 1. It can be shown that for each iteration the computational complexity for the S-list-CMP VP scheme 300 illustrated in figure 3 and described above scales with order of , assuming . However, this increased computational complexity compared with the S-CMP VP scheme 200 illustrated in figure 2, may provide improved, i.e. better optimized perturbation vectors due to the multipath diversity exploitation. As already mentioned above, figure 4 illustrates a M-CMP VP scheme 400 implemented by the VP processing block 120 of the transmitter 110 according to a further embodiment. Basically, the M-CMP VP scheme 400 illustrated in figure 4 is a parallel implementation of a plurality of the S-CMP VP schemes 200 shown in figure 2, which already have been described above. In an embodiment, as already mentioned above, the VP processing block 120 of the transmitter 110 may be configured to implement the plurality of S-CMP VP schemes 200 in parallel such that the number of parallel S-CMP VP schemes 200 (used by the initialization block 401 of the M-CMP VP scheme 400) is equal to the product of the cardinality of the pre- defined complex integer set, i.e., and the number of columns of the precoding matrix, i.e. equal to . Thus, by letting all the parallel S-CMP VP schemes 200 converge the VP processing block 120 of the transmitter 110 implementing the M-CMP VP scheme 400 illustrated in figure 4 obtains precoded sequences. A decision processing block 402 of the M-CMP VP scheme 400 illustrated in figure 4 is configured to select from these precoded sequences the precoded sequence with the minimal sequence energy as the final precoded sequence, i.e., It can be shown that at each iteration the computational complexity of the M-CMP VP scheme 400 illustrated in figure 4 scales approximately with the order of , depending on the number of the parallel S-CMP VP schemes 200 yet to converge. Due to the multipath initialization and the processing of the plurality of S-CMP VP schemes 200 in parallel the M- CMP VP scheme 400 implemented by the VP processing block 120 of the transmitter 110 according to an embodiment may obtain a performance close to the VP-optimum, as will be illustrated in more detail further below. Figure 5 illustrates a M-list-CMP VP scheme 500 implemented by the VP processing block 120 of the transmitter 110 according to an embodiment. As illustrated in figure 5, the M-list-CMP VP scheme 500 basically consists of a plurality of parallel processed S-list-CMP VP schemes 300 of figure 3. In this embodiment, each of the plurality of parallel S-list-CMP VP schemes 300 is initialized by an initialization block 501 with a different initial node. Once all of the parallel S-list-CMP VP schemes 300 have converged, the VP processing block 120 is configured to select by means of a decision block 502, the node, i.e. sequence that has the minimal energy as the final precoded sequence. At each iteration, there will be at maximum parallel S-list- CMP VP schemes 300 and retained nodes for each scheme 300. Therefore, the computing complexity for the M-list-CMP VP scheme 500 illustrated in figure 5 at each iteration scales with the order of . As already described above, each of the VP schemes 200, 300, 400 and 500 illustrated in figures 2 to 5 may be implemented by the VP processing block 120 of the transmitter 110 according to an embodiment. According to further embodiments the VP processing block 120 of the transmitter 110 may combine the results of several of these schemes or select one of these schemes based on a desired performance-complexity trade-off. In other words, in an embodiment, the transmitter 110 may be configured to operate in different operation modes, wherein in a first low computational complexity operation mode the transmitter 110 is configured to implement, for instance, the S-CMP VP scheme 200, while in a second high energy reduction operation mode the transmitter 110 is configured to implement, for instance, the computationally more complex M-CMP VP scheme 400. In the following some similarities and some important differences between the VP schemes 200, 300, 400 and 500 illustrated in figures 2 to 5 and described above will be highlighted and summarized. As already described above, the iterative VP schemes 200, 300, 400, 500 are configured to compute the candidate perturbation vectors based on the following equations: The iterative VP schemes 200, 300, 400, 500 differ either in the initialization process, which distinguishes the single path VP schemes 200, 300 from the multipath VP schemes 400, 500, or whether the respective scheme employs list-encoding, which leads to a different selection criterion of the candidate perturbation vectors for each iteration. As already described above, in the S-CMP VP scheme 200 the VP processing block 120 of the transmitter 110 is configured to compute the complex-valued integers at the ^-th iteration, which are denoted as ^^, ^^(^), ^ ∈ {1, … , ^}, wherein ^ also denotes the number of columns of the precoding matrix ^. Based on the equations (A1) and (A3), the VP processing block best perturbation vector ^⋆(^)from the set of candidate perturbation vectors for the ^ -th iteration by: argmax ^^(^), ^^, ^^(^) > 0.5 (A4) ^^(^)Based on the best perturbation vector ^⋆(^) the target precoded sequence is updated by the VP processing block 120 as: ^(^ + 1)= ^(^)+ ^⋆(^)(A5) As described above, the S-CMP VP scheme 200 implemented by the VP processing block 120 of the transmitter 110 according to an embodiment will stop, i.e. converge at the ^-th iteration if ^^, ^^(^) < 0.5 holds. In other words, the S-CMP VP scheme 200 will stop, i.e. converge, if none of the candidate perturbation vectors leads to a further energy reduction. As already described above, the M-CMP VP scheme 400 illustrated in figure 4 consists of multiple parallel S-CMP VP schemes 200. For ^^^parallel S-CMP VP schemes 200, the S- CMP VP schemes 200 differ from each other by their initialized starting point or initial node, i.e., ^^(0) . In an embodiment, the initialized starting point may be obtained by the VP processing block 120 of the transmitter according to an embodiment based on the following equation: ^^,^(0)= ^(0)+ ^^,^, ^ ∈[1, ^], ^ ∈ [1, ^^] (A6) As already described above, ^(0)= ^ ∙ ^ denotes the linearly-precoded sequence and, ^^,^= ^ ∙ ^^∙ ^^, ^ ^ [1, N], ^ ^[1, L^], (A7) denotes the perturbation vectors used for the initialization, where the ^^are taken from the pre- defined complex integer set described above, i.e. . As will be appreciated, for this example there are in total ^ ∙ ^^initialized S-CMP paths. When the ^^^parallel S-CMP VP schemes 200 converge, there will be ^^^nonlinearly-precoded sequences serving as candidate sequences (i.e., ^⋆ ^ , ^ ^[1, N^^]). As already described above, the VP processing block 120 of the transmitter 110 implementing the M-CMP VP scheme 400 is configured to select the nonlinearly-precoded sequence having the minimum sequence energy as the final precoded sequence, i.e., ^⋆= argmin ||^⋆ ^||^, ^ ^[1, N^^](A8) ^⋆ ^ As to the relationship between the S-list-CMP VP scheme 300 and the M-list-CMP VP scheme 500, it can be taken from the detailed description above that the S-list-CMP VP scheme 300 only possesses a single path (starting point), which is initialized by ^(0)= ^ ∙ ^, whereas the M-list-CMP VP scheme 500 consists of multiple S-list-CMP VP schemes 300 that are executed in parallel. Each S-list-CMP VP scheme 300 thereof differs from the others by its initialized starting point (initial node), i.e., ^^,^(0). Similar to the M-CMP VP scheme 400, the final precoded sequence is selected in the M-list-CMP VP scheme 500 according to a minimum sequence energy criterion, as defined by equation (A8). As to the relationship between the S-list-CMP VP scheme 300 and the S-CMP VP scheme 200, it can be taken from the detailed description above that the S-CMP VP scheme 200 only selects a single perturbation vector (from a plurality of candidate perturbation vectors) at each iteration (according to the criterion in equation (A4)), while the S-list-CMP VP scheme 300 selects multiple perturbation vectors (from multiple pluralities of candidate perturbation vectors) at each iteration (instead of selecting a single perturbation vector and doing the update). Each selected perturbation vector is then used, separately, to update the corresponding precoded sequence. This results in a plurality of, for instance, 10 precoded sequences obtained at each iteration. At the next iteration, each of these, for instance, 10 precoded sequences will be used to compute their own candidate perturbation vectors. Such procedure will basically follow the same as illustrated by equations (A1) - (A3) above. Thus, there will be, for instance, 10 ∙ ^ candidate perturbation vectors computed in total for each iteration. And there will be, for instance, 10 candidates being selected among them for updating their corresponding precoded sequence. The, for instance, 10 updated precoded sequence vectors are then forwarded to the next iteration. The, for instance, 10 candidate perturbation vectors are selected by first ordering the sequence correlation values of the, for instance, 10 ∙ ^ candidate perturbation vectors and by selecting those having the, for instance, 10 largest sequence correlation values. At each iteration, the sequence vector that has the smallest sequence energy among the, for instance, 10 precoded sequence candidates may be stored by the buffer, as already described above. As already described above, the buffer may be used for the list-encoding VP schemes. In an embodiment, a separate buffer may be used for each path (starting point). Thus, if there are multiple paths, such as for the M-list-CMP VP scheme 500, the VP processing lock 120 of the transmitter 110 may be configured to implement multiple buffers. Considering the list-encoding for a specific path, the buffer is configured to collect the best precoded sequence candidate obtained at each iteration. If the buffer has a memory size it can store precoded sequence candidates. When a new candidate is about to be stored in the buffer, but the buffer is full, i.e., candidates already are stored in the buffer, the candidate in the buffer that has the largest sequence energy will be compared with the new candidate. If the new candidate has a smaller sequence energy, it will replace the candidate that has the largest energy in the buffer. As already described above, if the precoded sequence candidates in the buffer remain unchanged for two consecutive iterations, the list-encoding procedure for that path is said to have converged and may be stopped. Figure 6 shows a flow diagram illustrating steps of a method 600 for energy-efficient MIMO transmission to the plurality of receivers 140 using a final sequence vector based on a target signal vector ^. The method 600 comprises the steps of: generating 601 one or more initial sequence vectors based on the MIMO precoding matrix ^ and the target signal vector ^; and performing 603 an iterative VP scheme 200, 300, 400, 500 for determining the final sequence vector by iteratively refining the one or more initial sequence vectors. As already described above the iterative VP scheme 200, 300, 400, 500 comprises: generating 603a a plurality of candidate perturbation vectors based on the precoding matrix ^ and the one or more sequence vectors from a previous iteration; determining 603b for each of the candidate perturbation vectors one or more sequence correlation values between the respective candidate perturbation vector and the one or more sequence vectors from the previous iteration; selecting 603c, based on the plurality of sequence correlation values, one or more perturbation vectors from the plurality of candidate perturbation vectors for obtaining one or more selected perturbation vectors; and refining 603d the one or more sequence vectors based on the one or more selected perturbation vectors for determining the final sequence vector. Figure 7 shows phase diagrams illustrating an empirical probability of the integer perturbation entry for the transmitter 110 implementing the S-CMP VP scheme 200. For conventional VP schemes, the integer-valued perturbation entries are commonly bounded, because otherwise the search for the closest lattice would be generally computationally too complex. As will be appreciated from the detailed description above, for the CMP VP schemes 200, 300, 400 and 500 the value of the calculate perturbation entry may be unbounded, because its value may depend on the channel conditions as reflected by the precoding matrix. In figure 7 the x-axis represents the real part of the value of a perturbation entry, while the y-axis represents the imaginary part. Figures 8 to 10 show graphs illustrating the BLER as a function of the bit-to-noise ratio for the VP schemes implemented by the transmitter 110 according to different embodiments in comparison with conventional VP schemes. For the results illustrated in figures 8 to 10 the exemplary parameters listed in the following table have been used. Antenna number 32 Coding method Polar code ( ) Single-antenna 32 Coding rate 1 / 2 user number ( ) MIMO Channels i.i.d. Rayleigh Codeword length 1024 Modulation order 256-QAM Decoding successive cancellation method decoding The results illustrated in figures 8 and 9 are for the S-CMP VP scheme 300, the M-CMP VP scheme 400 and the M-list-CMP VP scheme 500 of figures 3, 4 and figure 5, respectively. As will be appreciated, the best performance is offered by the M-list-CMP VP scheme 500 with the maximized path diversity exploitation. The S-CMP VP scheme 300 offers the simplest implementation but with less optimal performance. The M-CMP VP scheme 400 achieves the best balance between computational complexity and performance. As will be appreciated, in the presence of imperfect channel state information (as illustrated in figure 8), the list-based VP schemes disclosed herein still outperform the conventional VP schemes. The results illustrated in figure 10 are for the M-list CMP scheme 500 of figure 5. As will be appreciated, the M-list CMP scheme 500 of figure 5 achieves near-VP-optimum performance with significantly reduced computational complexity. The results in figure 10 are based on the following exemplary parameters: 8x8 MIMO system with 16-QAM modulation scheme, FEC coding scheme is polar code with ½ code rate. As will be appreciated, the performance provided by embodiments disclosed herein is close to the VP-optimum regardless of the MIMO size, because the performance gap variation between AWGN and the embodiments disclosed herein is nearly negligible in different MIMO systems (as illustrated in figure 8). As will be appreciated from the detailed description above, embodiments of the VP processing block 120 of the transmitter 110 disclosed herein may significantly improve the transmitter energy efficiency by leveraging column-wise correlation in the linear precoder. Moreover, embodiments of the VP processing block 120 of the transmitter 110 disclosed herein may significantly reduce the computational complexity by calculating the perturbation entries instead of searching in the lattice space. Embodiments of the VP processing block 120 of the transmitter 110 disclosed herein are well-suited for a parallel-computing implementation. Moreover, embodiments of the VP processing block 120 of the transmitter 110 disclosed herein may exploit the path diversity for performance improvement (enabled by list encoding). Embodiments of the VP processing block 120 of the transmitter 110 disclosed herein may flexibly balance the computational costs and the performance by implementing various selectable operation modes. The person skilled in the art will understand that the "blocks" ("units") of the various figures (method and apparatus) represent or describe functionalities of embodiments of the present disclosure (rather than necessarily individual "units" in hardware or software) and thus describe equally functions or features of apparatus embodiments as well as method embodiments (unit = step). In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus, and method may be implemented in other manners. For example, the described embodiment of an apparatus is merely exemplary. For example, the unit division is merely a logical function division and may be another division in an actual implementation. For example, a plurality of units or components may be combined or integrated into another system, or some features may be ignored or not performed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections may be implemented by using some interfaces. The indirect couplings or communication connections between the apparatuses or units may be implemented in electronic, mechanical, or other forms. The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the objectives of the solutions of the embodiments. In addition, functional units in the embodiments of the disclosure may be integrated into one processing unit, or each of the units may exist alone physically, or two or more units may be integrated into one unit.

Claims

CLAIMS 1. A transmitter (110) for MIMO transmission to a plurality of receivers (140) using a final sequence vector based on a target signal vector ^, wherein the transmitter (110) is configured to: generate one or more sequence vectors based on a precoding matrix ^ and the target signal vector ^; and perform an iterative vector perturbation, VP, scheme (200, 300, 400, 500) for determining the final sequence vector by iteratively refining the one or more sequence vectors, wherein the iterative VP scheme (200, 300, 400, 500) is configured to: (a) generate a plurality of candidate perturbation vectors based on the precoding matrix ^ and the one or more sequence vectors from a previous iteration; (b) determine for each of the candidate perturbation vectors one or more sequence correlation values between the respective candidate perturbation vector and the one or more sequence vectors from the previous iteration; (c) select, based on the plurality of sequence correlation values, one or more perturbation vectors from the plurality of candidate perturbation vectors for obtaining one or more selected perturbation vectors; and (d) refine the one or more sequence vectors based on the one or more selected perturbation vectors for determining the final sequence vector.

2. The transmitter (110) of claim 1, wherein the one or more sequence vectors comprise a single sequence vector and wherein the transmitter (110) is configured to generate the sequence vector based on the precoding matrix ^ and the target signal vector ^ by applying the precoding matrix ^ to the target signal vector ^.

3. The transmitter (110) of claim 1 or 2, wherein the iterative VP scheme (200, 300, 400, 500) comprises a first iterative VP scheme (200) and wherein the first iterative VP scheme (200) is configured to select, based on the plurality of sequence correlation values, one perturbation vector from the plurality of candidate perturbation vectors for obtaining oneselected perturbation vector by selecting the candidate perturbation vector having the largest sequence correlation value.

4. The transmitter (110) of claim 3, wherein the first iterative VP scheme (200) is configured to refine the sequence vector based on the selected perturbation vector by adding the selected perturbation vector to the sequence vector of the previous iteration.

5. The transmitter (110) of claim 3 or 4, wherein the first iterative VP scheme (200) is configured to generate the plurality of candidate perturbation vectors ^^(^)for the ^-th iteration based on the following equation: wherein: ^ denotes a scaling factor; ^^denotes the ^-th column vector of the precoding matrix ^; and ^^(^) denotes a complex integer weight factor for the ^-th column vector of the precoding matrix ^.

6. The transmitter (110) of claim 5, wherein the first iterative VP scheme (200) is configured to determine the complex integer weight factor ^^(^) for the ^-th column vector of the precoding matrix ^ for the ^-th iteration based on the following equation: ^^(^) = roundwherein: ^(^ − 1) denotes the sequence vector of the previous iteration.

7. The transmitter (110) of claim 5 or 6, wherein the first iterative VP scheme (200) is configured to stop iteratively refining the one or more sequence vectors at the ^-th iteration, if for each of the plurality of candidate perturbation vectors the sequence correlation value for the ^-th iteration is smaller than a threshold value.

8. The transmitter (110) of any one of claims 5 to 7, wherein the first iterative VP scheme (200) is configured to determine for each of the candidate perturbation vectors the respectivesequence correlation value ^^(^)for the ^ -th iteration between the respective candidate perturbation vector and the sequence vector of the previous iteration based on the following equation:^ ^^^^{^(^^^)∙^^(^)} ^( )=‖^^(^)‖^ .

9. The transmitter (110) of any one of claims 3 to 8, wherein the iterative VP scheme (200, 300, 400, 500) comprises a second iterative VP scheme (400) and wherein the second iterative VP scheme (400) comprises a plurality of parallel implementations of the first iterative VP scheme (200), wherein each of the plurality of parallel implementations of the first iterative VP scheme (200) is configured to iteratively refine a different sequence vector of the plurality of sequence vectors.

10. The transmitter (110) of claim 9, wherein the second iterative VP scheme (400) is configured to generate the plurality of sequence vectors based on the precoding matrix ^, the target signal vector ^ and a predefined set of complex-integer values.

11. The transmitter (110) of claim 9 or 10, wherein the second iterative VP scheme (400) is configured to determine the final sequence vector by selecting the refined sequence vector from the plurality of refined sequence vectors provided by the plurality of parallel implementations of the first iterative VP scheme (200) based on a selection criterion.

12. The transmitter (110) of claim 1 or 2, wherein the iterative VP scheme (200, 300, 400, 500) comprises a third iterative VP scheme (300), wherein the third iterative VP scheme (300) is configured to sort the plurality of sequence correlation values in a descending order and to select those ^^perturbation vectors from the plurality of candidate perturbation vectors with the largest sequence correlation values as the selected perturbation vectors.

13. The transmitter (110) of claim 12, wherein the third iterative VP scheme (300) is configured to refine the sequence vectors based on the plurality of selected perturbation vectors and to retain the refined sequence vectors in the form of a list of sequence vectors in a buffer.

14. The transmitter (110) of claim 13, wherein the third iterative VP scheme (300) is configured to stop iteratively refining the one or more sequence vectors at the ^-th iteration, if for each of the plurality of candidate perturbation vectors the sequence correlation value forthe ^-th iteration is smaller than a threshold value and / or if the plurality of sequence vectors stored in the buffer remain the same for two consecutive iterations.

15. The transmitter (110) of any one of claims 12 to 14, wherein the third iterative VP scheme (300) is configured to generate the plurality of candidate perturbation vectors ^^(^) for the ^-th iteration based on the following equation: wherein: ^ denotes a scaling factor; ^^denotes the ^-th column vector of the precoding matrix ^; and ^^,^(^) denotes a complex integer weight factor corresponding to the ^-th column vector of the precoding matrix ^ and the ^-th retained sequence vector ^^(^ − 1).

16. The transmitter (110) of any one of claims 12 to 15, wherein the third iterative VP scheme (300) is configured, at the ^-th iteration, to determine the complex integer weight factor ^^,^(^) for the ^-th column vector of the precoding matrix ^ and the ^-th sequence vector retained from the previous iteration based on the following equation:wherein: ^^(^ − 1), ^ ∈ [1, ^^] denotes the sequence vector retained from the previous iteration and ^^denotes the size of the list configured for the ^-th iteration.

17. The transmitter (110) of any one of claims 12 to 16, wherein the third iterative VP scheme (300) is configured to determine for each of the candidate perturbation vectors the respective sequence correlation value ^^,^(^) for the ^ -th iteration between the respective candidate perturbation vector and the one or more sequence vectors of the previous iteration based on the following equation:

18. The transmitter (110) of any one of claims 12 to 17, wherein the iterative VP scheme (200, 300, 400, 500) comprises a fourth iterative VP scheme (500) and wherein the fourth iterative VP scheme (500) comprises a plurality of parallel implementations of the third iterative VP scheme (300), wherein each of the plurality of parallel implementations of the third iterative VP scheme (300) is configured to iteratively refine a different sequence vector of the plurality of sequence vectors.

19. The transmitter (110) of claim 18, wherein the fourth iterative VP scheme (400) is configured to generate the plurality of sequence vectors based on the precoding matrix ^, the target signal vector ^ and a predefined set of complex-integer values.

20. The transmitter (110) of claim 18 or 19, wherein the fourth iterative VP scheme (500) is configured to determine the final sequence vector by selecting the refined sequence vector from the plurality of refined sequence vectors provided by the plurality of parallel implementations of the third iterative VP scheme (300) based on a selection criterion.

21. The transmitter (110) of any one of the preceding claims, wherein the transmitter (110) is further configured to generate the precoding matrix ^ based on channel state information.

22. The transmitter (110) of any one of the preceding claims, wherein the transmitter (110) is a base station.

23. A method (600) for MIMO transmission to a plurality of receivers (140) using a final sequence vector based on a target signal vector ^, wherein the method (600) comprises: generating (601) one or more sequence vectors based on a precoding matrix ^ and the target signal vector ^; and performing (603) an iterative vector perturbation, VP, scheme (200, 300, 400, 500) for determining the final sequence vector by iteratively refining the one or more sequence vectors, wherein the iterative VP scheme (200, 300, 400, 500) comprises: generating (603a) a plurality of candidate perturbation vectors based on the precoding matrix ^ and the one or more sequence vectors from a previous iteration;determining (603b) for each of the candidate perturbation vectors one or more sequence correlation values between the respective candidate perturbation vector and the one or more sequence vectors from the previous iteration; selecting (603c), based on the plurality of sequence correlation values, one or more perturbation vectors from the plurality of candidate perturbation vectors for obtaining one or more selected perturbation vectors; and refining (603d) the one or more sequence vectors based on the one or more selected perturbation vectors for determining the final sequence vector.

24. A computer program product comprising a computer-readable storage medium for storing program code which causes a computer or a processor to perform the method (600) of claim 23, when the program code is executed by the computer or the processor.

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