Eigenvector-based method and apparatus for MIMO equalizer design via a linear integer forcing architecture

Abstract

A method and apparatus are provided, wherein a set of reference signals (2102) is received and a set of channel characteristics of a multi-antenna communication channel is estimated (2104). Channel state information including a set of quality metrics is computed (2106). In response to the set of quality metrics satisfying a criterion, a baseline receiver is selected for the multi-antenna communication channel (2108). In response to the set of quality metrics not satisfying the criterion, an alternative receiver is selected for the multi-antenna communication channel (2110). The alternative receiver selectable at a user equipment for the multi-antenna communication channel is based on a set of integer linear combinations, wherein each integer linear combination is based on at least a pair of channel signatures from the estimated set of channel signatures (2112).

Description

Technical Field

[0001] The present disclosure relates to a method and apparatus for MIMO equalizer design based on eigenvector approach involving a linear integer forcing architecture. Background Art

[0002] Currently, user equipment such as wireless communication devices communicate with other communication devices using wireless signals in a network environment that can include one or more cells. Within one or more cells, various communication connections with the network and other devices operating within the network can be supported. The network environment typically involves one or more sets of standards, each set of standards defining various aspects of any communication connection made when using the corresponding standard within the network environment. Examples of developed and / or existing standards include New Radio Access Technology (NR), Evolved Universal Terrestrial Radio Access (E-UTRA), Long Term Evolution (LTE), Universal Mobile Telecommunications Service (UMTS), Global System for Mobile Communications (GSM), and / or Enhanced Data GSM Environment (EDGE).

[0003] Each standard has various methods for constructing and organizing one or more potential communication channels between a network and one or more communication devices. In at least some instances, channels can be organized where multiple antennas at the transmitter, receiver, or both can help create diversity, which allows for a greater number of channels to be defined within the same channel space.

[0004] Correspondingly, a transmitter or receiver architecture can be selected to better support any one of the specific methods for constructing and organizing one or more potential communication channels. In certain instances, multiple potential transmitter or receiver architectures can be used.

[0005] The present inventors have recognized that it may be beneficial to develop a method that can assist in selecting between multiple different transmitter and receiver types / architectures based on one or more detectable conditions, taking into account the specific relevant methods for constructing and organizing communication channels, as well as the currently detected channel conditions. The present inventors have further recognized that in instances where an integer forcing receiver has been selected for use, an integer linear combination can be better selected. Summary of the Invention

[0006] The present application provides a method in a user equipment. The method includes receiving a set of reference signals, and estimating a set of channel signatures of multiple-antenna communication channels based on the received set of reference signals. Channel state information including a set of quality metrics is calculated. In response to the set of quality metrics satisfying a criterion, a baseline receiver is selected at the user equipment for the multiple-antenna communication channels. In response to the set of quality metrics not satisfying the criterion, an alternative receiver is selected at the user equipment for the multiple-antenna communication channels. The alternative receiver that can be selected at the user equipment for the multiple-antenna communication channels is based on a set of integer linear combinations, where each integer linear combination is based on at least a pair of channel signatures from the estimated set of channel signatures.

[0007] According to another possible embodiment, a user equipment is provided. The user equipment includes a transceiver that receives a set of reference signals and has an optional baseline receiver and an optional alternative receiver. The user equipment further includes a controller that estimates a set of channel signatures of multiple-antenna communication channels based on the received set of reference signals, and calculates channel state information including a set of quality metrics. The controller selects the baseline receiver at the user equipment for the multiple-antenna communication channels in response to the set of quality metrics satisfying the criterion, and the controller selects the alternative receiver at the user equipment for the multiple-antenna communication channels in response to the set of quality metrics not satisfying the criterion. The alternative receiver that can be selected at the user equipment for the multiple-antenna communication channels is based on a set of integer linear combinations, where each integer linear combination is based on at least a pair of channel signatures from the estimated set of channel signatures.

[0008] These and other features and advantages of the present application are apparent from the following description of one or more preferred embodiments with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 is a block diagram of an exemplary network environment suitable for operating therein;

[0010] Figure 2 is a block diagram of an exemplary integer-forcing (IF) receiver;

[0011] Figure 3 is a block diagram of a more detailed exemplary integer-forcing (IF) operation;

[0012] Figure 4 is a table providing high, medium, and low-level MIMO correlation matrices, including corresponding values for each of the transmit correlation parameter α and the receive correlation parameter β for the ULA MIMO correlation matrix;

[0013] Figure 5 is a numerical table of the integer-forcing search radius for 2×2 real MIMO;

[0014] Figure 6 It is a numerical table of the integer-forcing search radius for 2×4 real MIMO;

[0015] Figure 7 It is a numerical table of the integer-forcing search radius for 4×2 real MIMO;

[0016] Figure 8 It is a numerical table of the integer-forcing search radius for 4×4 real MIMO;

[0017] Figure 9 It is a numerical table of the integer-forcing search radius for 2×8 real MIMO;

[0018] Figure 10 It is a numerical table of the integer-forcing search radius for 8×2 real MIMO;

[0019] Figure 11 It is a numerical table of the integer-forcing search radius for 4×8 real MIMO;

[0020] Figure 12 It is a numerical table of the integer-forcing search radius for 8×4 real MIMO;

[0021] Figure 13 It is a transmitter-side block diagram constructed using a real setup with Configuration D;

[0022] Figure 14 It is a receiver-side block diagram constructed using a real setup with Configuration D;

[0023] Figure 15 It is a transmitter-side block diagram constructed using a complex setup with Configuration D;

[0024] Figure 16 It is a receiver-side block diagram constructed using a complex setup with Configuration D;

[0025] Figure 17 It is a transmitter-side block diagram constructed using a real setup with Configuration A;

[0026] Figure 18 It is a receiver-side block diagram constructed using a real setup with Configuration A;

[0027] Figure 19 It is a block diagram illustrating the codeword-to-layer mapping in LTE;

[0028] Figure 20 It is an exemplary mapping diagram illustrating the transport-block-to-layer mapping for codebook-based antenna precoding (initial transmission);

[0029] Figure 21 It is a flowchart for receiver selection in a user equipment between a baseline receiver and an alternative receiver;

[0030] Figure 22 is a flowchart for determining a preferred set of integer linear combinations used in an integer forcing receiver in a user equipment; and

[0031] Figure 23 is an exemplary block diagram of an apparatus according to a possible embodiment. Detailed Description

[0032] Although the present disclosure may adopt various forms of embodiments, the presently preferred embodiments are shown in the drawings and will be described hereinafter. It should be understood that the present disclosure should be regarded as an example of the present invention and is not intended to limit the present invention to the specific embodiments shown.

[0033] Embodiments provide various methods and apparatuses, including eigenvector-based methods and apparatuses for MIMO equalizer design via a linear integer forcing architecture.

[0034] Figure 1 is an example block diagram of a system 100 according to a possible embodiment. The system 100 can include a wireless communication device 110, such as a user equipment (UE), a base station 120, such as an evolved Node B (eNB) or a next generation Node B (gNB), and a network 130. The wireless communication device 110 can be a wireless terminal, a portable wireless communication device, a smart phone, a cellular phone, a flip phone, a personal digital assistant, a personal computer, a pager, a tablet computer, a laptop computer, or any other device capable of sending and receiving communication signals over a wireless network.

[0035] The network 130 can include any type of network capable of sending and receiving wireless communication signals. For example, the network 130 can include a wireless communication network, a cellular phone network, a time division multiple access (TDMA)-based network, a code division multiple access (CDMA)-based network, an orthogonal frequency division multiple access (OFDMA) network, a long term evolution (LTE) network, a fifth generation (5G) network, a third generation partnership project (3GPP) network, a satellite communication network, a high altitude platform network, the Internet, and / or other communication networks.

[0036] A wireless fading multiple-input multiple-output (MIMO) channel combines / mixes the input information streams of transmissions across the temporal, frequency, and spatial dimensions. In general, equalization is a meaningful part of receiver design, and particularly in MIMO operation, at least in some instances, assuming some level of channel state information (CSI) is available at the receiver, it may be preferable to cancel the combined / mixed effects of the wireless fading MIMO channel on the input signal in order to be able to separate out the original information streams. At least one class of receivers are linear receivers, such as the minimum mean square error (MMSE) receiver, where only linear operations that can be modeled as matrix operations are used in order to reduce implementation complexity.

[0037] Selecting and designing a low-complexity receiver for a user equipment (UE) is one aspect of MIMO technology that can affect the physical layer (PHY) performance of a radio access network (RAN) for wireless communications. A linear receiver applies some linear post-processing to the received signal, which is sometimes called equalization, to partially or fully separate out the multiple input information streams and facilitate single-stream decoding. This can simplify implementation because generally there is no need for joint decoding across the receive antennas as in the case of non-linear receivers such as maximum likelihood (ML) receivers. An example of a linear receiver is the minimum mean square error (MMSE) receiver, which is the baseline receiver assumed by the 3GPP 4G-LTE standard.

[0038] A concern with current linear receivers such as the MMSE receiver is that, in the open-loop case, they may perform poorly in the presence of near-singular MIMO channels where the channel state information (CSI) is not available at the base station (eNodeB). At least one reason for this is that separating out the multiple information streams of such channels can lead to noise enhancement. In such a scenario, the channel is effectively considered rank-deficient, and thus transmission of multiple information streams (i.e., spatial multiplexing) is avoided, and various copies of a small number of information streams are transmitted via the eNodeB antennas (i.e., transmit diversity).

[0039] Recently, integer-forcing (IF) receivers, as Figure 2 and 3 shown, have been introduced as a generally effective linear receiver when used with linear codes at the transmitter. For some MIMO channels, the IF receiver simplifies to the MMSE receiver and can thus provide the same general performance. However, for many MIMO channels (e.g., open-loop MIMO channels without CSI information at the transmitter and thus no CSI-based precoding selection at the transmitter), the IF receiver provides a moderately significant rate / reliability gain over the MMSE receiver by exploiting the interference generated by the multiple information streams from different eNodeB antennas and minimizing the effective noise observed by the decoder.

[0040] At least one reason for this performance improvement is that the IF receiver exploits the inter-stream interference by decoding certain integer linear combinations of the information streams, which minimize the noise observed by the decoder. Since the same linear code (i.e., the same modulation and coding scheme (MCS), and thus the same rate) is typically used at all transmit antennas, the integer linear combinations of the codewords are also valid codewords and can be decoded. An integer linear solver is then used to recover the original information bits. Note that the MMSE receiver is a special case of the IF receiver, where the integer linear combination forms the identity matrix.

[0041] Correspondingly, the IF receiver includes the MMSE receiver as a special case. Figure 2 FIG. 200 shows a block diagram of an exemplary integer-forcing (IF) receiver. Figure 3 FIG. 300 shows a more detailed block diagram of an exemplary integer-forcing (IF) operation.

[0042] At least one aspect of the IF receiver design is for the UE to run some search algorithms and find more optimized integer linear combinations that achieve more promising performance. This is generally a difficult (NP-hard) problem, and the search algorithms may sometimes involve more time-consuming and / or complex search algorithms. However, as will be discussed in the next section, for a significant portion of channels, such search algorithms may exhaust the UE's computational resources, leading to the conclusion in some instances that the optimal integer combination is (close to) the identity matrix and the MMSE receiver is indeed optimal or nearly optimal. Generally, several algorithms with different complexity levels have been proposed.

[0043] Therefore, compared with the conditions and characteristics that identify the rate / reliability gain of the IF receiver (with integer combinations that can be far from the identity matrix) to be significant enough to justify the overhead of the UE's computational resources for finding more optimal integer combinations, the conditions and characteristics of the MIMO channels that can identify that the MMSE receiver is (nearly) optimal may be somewhat advantageous. On the other hand, for cases where the IF does provide a reasonable gain, it is beneficial to achieve such a gain within a reasonable search complexity.

[0044] According to an embodiment of the present application, the present disclosure includes various combinations of at least three aspects:

[0045] - First, the present disclosure identifies two conditions for linear receiver selection based on the MIMO channel characteristics, namely the operating signal-to-noise ratio (SNR) and the interference level measured at the receiver, which determine whether the ordinary MMSE receiver is (nearly) optimal or whether the IF receiver should be used. These conditions can usually be conveniently checked to recommend the appropriate linear receiver to be selected, and can significantly save the UE's computational (and power, etc.) resources.

[0046] - Secondly, the present disclosure proposes a new algorithm with reasonable computational complexity for finding the (near) optimal integer linear combinations required for the IF receiver design. For example, a detailed description of the eigenvector-based design of the IF equalizer, where certain eigenvector pairs of the wireless MIMO channel are used to define the integer linear combinations required for the IF receiver design.

[0047] - Aspects of the implementation of the integer-forcing receiver for both real and complex channel models, including how to incorporate coded modulation techniques.

[0048] The contributions in the present disclosure are described in the context of open-loop MIMO receiver design, but can also be applied to other wireless setups, such as closed-loop MIMO receiver design, precoder design for MIMO transmitters, etc.

[0049] MIMO Receiver Selection

[0050] Through the matrix to represent the MIMO channel with N t transmit antennas and N r receive antennas, where the i-th column is given by h of length N r represented by i .

[0051] A commonly used metric for describing the singularity level of the MIMO channel is the condition number of the channel matrix, which is defined as

[0052]

[0053] where σ max (H) and σ min (H) denote the largest and smallest (non-zero) singular values of the channel matrix H, respectively. It is generally assumed that MMSE achieves good performance in well-conditioned MIMO channels (i.e., those channels with a small condition number and far from being singular), while achieving poor performance in ill-conditioned channels (i.e., those channels with a high condition number and close to being singular). Although such a conclusion provides a correct initial impression of the MIMO channel, it may be lacking in at least the following two aspects:

[0054] - The condition number κ(H) is mainly for the (very) high SNR region and may not necessarily provide an accurate description of the MIMO channel in the medium SNR region, which may also be of interest. For example, MMSE may still perform well for some ill-conditioned channels in the medium SNR region, so there is no need to use the IF receiver.

[0055] - There are certain channels with fairly good conditions, especially in those with N t ≠N rIn the non-square setting, even at high SNR, the IF receiver can significantly outperform the MMSE receiver.

[0056] Some researchers have also noted that if the MIMO channel is orthogonal or nearly orthogonal, then, regardless of how small or large the condition number is, the MMSE performance may be optimal or nearly optimal. Therefore, one would expect that, in addition to the condition number, the level of orthogonality of the MIMO channel matrix can also affect the MMSE performance. To measure the orthogonality of the channel, one can intuitively consider the matrix H T H, and compare the diagonal entries ||h i || 2 with the off-diagonal entries <h i , h j >, i ≠ j. Based on this intuition, the following measure, known as the orthogonality defect (OD), sometimes also called the lack of orthogonality Hadamard ratio, has been used in lattice and lattice reduction theory to quantify the degree of orthogonality of the matrix:

[0057]

[0058] In the literature, other variants of the above formula have also appeared, such as 1 - δ(H), 1 / δ(H), or or the Hermitian orthogonality defect of the inverse of the channel matrix For any channel with rank(H) = Nt, the Hadamard inequality can be used to show that δ(H) ≥ 1, where δ(H) = 1 if and only if the channel matrix is orthogonal. As the channel moves away from orthogonality, the value of δ(H) increases. Although OD is a useful figure of merit in some cases, it also lacks certain aspects:

[0059] - Similar to the condition number, the OD measurement is independent of the operating SNR and is therefore not very useful for the medium SNR region.

[0060] - Interestingly, OD may be more useful when rank(H) = N t . When N t > N r (which is usually the case in downlink communication), or even when N t ≤ N r but the channel rank is insufficient such that rank(H) < N t , since det(H T H) = 0, the OD measurement defined above becomes less useful.

[0061] Integer-Forcing Receiver

[0062] Denote by the matrix having N tTransmitting antenna and N r The MIMO channel of the receiving antenna, the i-th column of which is represented by h of size N r i Communication is coherent (i.e., having ideal channel state information at the receiver), but open-loop (i.e., having no channel state information at the transmitter). This concern has been addressed in non-independent MIMO streams for uplink transmission, downlink transmission, and single-user MIMO, where a capacity-approaching approach has been proposed using Construction A lattices under mild fading conditions. The present disclosure focuses more on integer-forcing receivers, where the problem is to construct the matrix This matrix consists of the integer linear combinations / vectors required by the IF receiver, each of size N t t

[0063] Some early discussions on the IF architecture have shown that the following transmission rates can be achieved through the IF architecture using optimal coding and modulation at the base station (eNodeB) and optimal post-processing or equalization at the user equipment (UE):

[0064]

[0065] where

[0066]

[0067] Since communication is open-loop, equal power allocation is used Note that the choice of A = I recovers the MMSE receiver, but it is not necessarily optimal. Some references also show the following bounds (a slightly looser version) on the length (i.e., Euclidean norm) of any potential integer combination

[0068]

[0069] where σ max (H) is the largest singular value of the channel matrix H

[0070] Based on the above formula, the optimal integer matrix A is the solution of the following

[0071]

[0072] When we consider any full-rank matrix B, called the lattice basis of G0 = B T For example, using singular value decomposition (SVD) or Cholskey decomposition, this optimization problem can be represented in a more illuminating form. Then, we can write the problem as

[0073] ​​​

[0074] This is known as the Shortest Independent Vector Problem (SIVP) in lattice theory, which is to find a set of N t linearly independent (LI) integer vectors such that the vector with the maximum length in the lattice m ||Ba m || is as short as possible. This problem for a general matrix G (alternatively B) is considered an NP-hard quadratic integer programming problem, but for the specific form and structure at hand, simplified exact or good approximate solutions can be designed.

[0075] The solution of this optimized matrix is not necessarily unique. As long as the vectors satisfy the LI condition and the length of the longest vector is minimized, there is some flexibility in choosing the lengths and values of the other vectors while still maintaining optimality.

[0076] The search is typically performed only once per coherence interval, so if the coherence interval spans multiple codeword transmissions, the complexity can become more reasonable.

[0077] In the literature, there are three approaches to this problem. The first approach simply performs some matrix operations on the lattice matrix G0 or the channel matrix H and outputs a (possibly suboptimal) solution for the A matrix. The second approach considers the entire set or a selected subset of vectors that satisfy and then extracts an (optimal or suboptimal) solution by checking the LI condition. The third approach enforces the LI condition while searching within the set or a selected subset of vectors that satisfy .

[0078] - The first approach: Several algorithms simply apply elementary or complex operations to the lattice matrix G0 or the channel matrix H or their variants. Thus, there is actually no search and selection involved. Below, we briefly explain these methods.

[0079] 1. Rounding the channel matrix: One can take the channel matrix H and construct a suboptimal integer matrix A = 「H」 by simply performing element-wise rounding.

[0080] 2. Rounding the eigenvectors: One can take the channel eigenvectors V from the SVD H = U∑V T and construct a suboptimal integer matrix A = 「H」 by performing element-wise rounding.

[0081] 3. Lattice reduction (especially the Lenstra-Lenstra Lovász (LLL) lattice reduction algorithm): Since the lattice basis is not unique, lattice reduction (LR) techniques can be performed to find a shorter and more orthogonal basis for the lattice. More precisely, if For some unimodular matrices T, i.e., square integer invertible matrices whose inverses are also integers (or equivalently have det(T) = ±1), the basis matrices B and both generate the same lattice. In the LR technique, a lattice basis satisfying G0 = B T B is considered, where the matrix G is defined above, and then lattice reduction is applied to obtain and is selected as an integer solution. At least one advantage of LR is that its computational complexity is independent of the SNR. Some well-known LR algorithms include the Minkowski and HKZ methods, whose complexity is exponential in the number of transmit antennas, but the most well-known LR method is the LLL method, whose complexity is polynomial in the number of transmit antennas. These algorithms are more optimized for small antenna arrays (e.g., 2 or 4 real transmit antennas), but become more sub-optimal for large antenna arrays.

[0082] - Second method: Some algorithms proposed in the literature for solving the optimization problem and finding the A matrix consist of three stages:

[0083] (i) Form a list of candidate short vectors based on some criteria;

[0084] (ii) Sort the candidate list in ascending order of vector length (i.e., from shortest to longest);

[0085] (iii) Starting from the top of the list, search for N in the list with the LI condition t shortest vectors.

[0086] The third stage is usually completed by one of the following methods:

[0087] · Gaussian elimination: Take the sorted candidate list as the columns of a matrix, then perform Gaussian elimination on the matrix, and finally select the candidate vectors that first define the new dimension in row-reduced echelon form, i.e., those corresponding to the pivots.

[0088] · Block LI search: Starting from the top of the list, select N t vectors at a time, and use a rank test to check the LI condition; continue until a full-rank matrix is found.

[0089] · Greedy L1 search: Starting from the top of the list, select vectors with the shortest length one by one so that they form an L1 cluster; continue until a full-rank matrix is found. Due to the greedy sequential search, this is more efficient.

[0090] For the first stage, several methods and algorithms have been proposed in the literature to form the list of candidate vectors. Below, we briefly explain these methods.

[0091] 4. Exhaustive search: By simply listing all Nt Integer vectors, for which the original IF paper proposed an exhaustive search of all size-N integer vectors satisfying t the Euclidean norm of which. This is a more optimized method, but the size of the search domain is approximately possibilities.

[0092] 5. Exhaustive tree search: The exhaustive search is performed by using a depth-first tree search algorithm (also known as sphere decoding) inspired by Fincke-Pohst (FP) or Schnorr-Euchner (SE) enumeration to find the exact solution of SIVP. This is essentially a faster implementation of the optimal exhaustive search, which forms the elements of the valid integer vectors sequentially instead of generating the entire integer vector at once.

[0093] 6. Exhaustive (tree) search via lattice reduction: Yet another exhaustive but lower-complexity method uses the following LR technique: First perform lattice reduction (e.g., LLL reduction), and then use the reduced lattice basis for the exhaustive search (possibly using an efficient tree search version) to obtain the solution It is also proposed to use as the search radius, where table does not the m-th column of. Finally, the A matrix is formed by taking The reason is that for any a vector, we can write such that or

[0094] 7. Reduced exhaustive with semi-integer induced scaling: References have recently proposed a reduced but optimal exhaustive search that describes the optimal integer vector as a properly scaled rounded version of the G0 matrix (certain variants of it) or the standard unit vectors. In particular, a = 「Wx」, where x is a real-valued vector of size rank(H), and W is an N × rank(H) matrix satisfying t This method performs an exhaustive search to find the appropriate scaling vector x, but one possible benefit is that if the number of transmit antennas strictly exceeds the rank of the channel, i.e., N t > rank(H), then the dimension of the search space will be reduced. In this case, the search algorithm only considers the real-valued scaling vectors in the dimension rank(H) space instead of the space of dimension N t Since rounding is performed, the search space of all real-valued scaling vectors can be reduced to the search space of only the semi-integer parameters that result in rounding operations, where rounding jumps to a new value. Other references have considered variations of this method.

[0095] 8. Combining method of Method 1: It is possible to consider a subset or all of the direct methods introduced in Method 1 above, and generate multiple A matrices. All column vectors in these matrices are collected into a candidate list, and the list can be sorted and the LI test can be run to generate a new A matrix, which is still suboptimal but potentially better than all the original matrices. If only a few A matrices are combined, the additional complexity of sorting the candidate list and LI processing will not be high.

[0096] 9. Search along the strongest eigenvector: The heuristic intuition conceptually suggests choosing an integer vector close to the strongest channel direction, i.e., the eigenvector corresponding to σ max (H). When σ max (H) is much larger than other singular values, this suboptimal strategy may be useful. However, no specific algorithm is mentioned in the literature.

[0097] 10. Perturbation of eigenvectors: It is considered that the integer vector with a small a T G0a value is in the form of α = 「v1 + ρ i v i 」, where y1 is the strongest channel direction, i.e., the eigenvector corresponding to σ max (H), v t with 2 ≤ i ≤ N i are other channel eigenvectors, and ρ i is a real-valued perturbation factor. Due to the rounding operation, only those perturbation factors ρ i that result in a rounding operation where the rounding jumps to a new value are considered. This suboptimal method has a relatively low complexity. To further reduce the complexity, the search is limited to a few directions rather than all possible N t -1 directions, and the search interval of the perturbation factor ρ i is also restricted. However, these are left as inputs to the algorithm, and no general recommendations are given for these modifications.

[0098] In some of the methods summarized above, the standard set of unit vectors, i.e., the columns of the default matrix are not necessarily included in the candidate vector list. In our numerical evaluation, we observed that it is best to manually add these vectors to obtain good performance, sometimes significantly better than the performance of the original method.

[0099] - The third method: Some algorithms for optimization problems and finding the A matrix have been proposed, where the LI condition is enforced when searching for a new integer vector or matrix. These algorithms are usually complex but provably find the optimal solution. Below, we briefly explain these methods.

[0100] 11. Subspace Avoidance with Tree Search: Some references propose a method based on the Subspace Avoidance Problem (SAP), which is to find the shortest non-zero lattice point Ba outside a given vector space. Thus, a series of SAP solutions are used to find the optimal A matrix as follows: The UE iteratively appends short linearly independent vectors to the A matrix, considers the subspace spanned by these vectors, and avoids looking for the next shortest vector that will trivially be linearly independent, and repeats this until N t vectors are found. To make the search more efficient, tree search methods such as a modified version of the FP or SE enumeration strategy are used. The upper bound of the complexity is exponential with the number of transmit antennas N t and is independent of the SNR.

[0101] 12. Full-Rank Matrix Update with Tree Search: Other references propose another iterative method to find the optimal A matrix, which starts from a suboptimal solution (i.e., a certain permutation of the matrix), and in each iteration, the A matrix is updated by replacing a carefully chosen column of A with a new vector a that induces a shorter lattice point Ba. Correctly choosing the replacement column involves new techniques to ensure the LI condition. The search process stops when no new vector can be found to update the A matrix. To improve the search efficiency, the algorithm (i) runs on the LLL-reduced lattice and finally converts the result back to the original lattice, and (ii) also uses tree search SE enumeration to search for new vectors. The complexity of this algorithm is again independent of the SNR and the exponential of the number of transmit antennas N t and is slightly better than the complexity of the above SAP method.

[0102] Each of the above 12 methods has its own advantages and disadvantages. In summary, the main drawbacks of existing methods are as follows:

[0103] - Suboptimal methods usually sacrifice rate performance to achieve low computational complexity. They usually perform well in smaller antenna arrays but have deteriorated performance in large antenna arrays.

[0104] - Optimal methods usually have high complexity, especially for large antenna arrays.

[0105] - Most methods fail to provide deep insights into the effects of different channel parameters (such as channel gain and channel eigenvectors) and the operating SNR.

[0106] Simple Conditions for Linear Receiver Selection in MIMO Communications

[0107] The performance of the MMSE receiver is known to be determined by the diagonal entries of the following matrix:

[0108]

[0109] wherein, denotes the identity matrix of size N t Due to open-loop communication considerations, equal power allocation is used The analysis also shows that the entire matrix G0 (not just its diagonal entries) determines the achievable rate / reliability of the IF receiver.

[0110] Hereinafter, we use a slightly modified matrix G, for which we reuse the term lattice matrix, to define the figure of merit for singularity and orthogonality as follows:

[0111]

[0112] Note that the signal-to-interference-plus-noise ratio (SINR) takes into account the total interference power estimated at the receiver (e.g., the signal channels and interference measured using reference signals such as CSI-RS in downlink transmissions and SRS (sounding reference signal) in uplink transmissions). If the interference is not measured at the receiver before transmission, the SINR reduces to SNR. Although the following new measurements are defined in a similar way to standard / conventional measurements, they are well-defined for any antenna array size; they correctly capture the role of the SINR; and they recover their standard counterparts or their variants as the limiting points for asymptotically high SINR. To our knowledge, these above-mentioned measurements have not been introduced and adopted before analyzing the MIMO wireless channel.

[0113] Modified Condition Number

[0114] A cluster of measurements of channel singularity (referred to as the modified condition number) is proposed, which is a generalization of the traditional condition number κ(H) concept and captures all channel directions and also the role of the SINR. They are a cluster of the following numbers

[0115]

[0116] where r = rank(H), and [σ1(H),..., σ r (H)] denotes the set of (non-zero) singular values of the channel matrix H in descending order. Note that for a fixed channel and SINR, the cluster of modified condition numbers

[0117] {κ mdf，1 (SINR, H),.., κ mdf，r (SINR, H)}

[0118] forms an ordered sequence in ascending order. Moreover, for a fixed channel and any fixed index i, κ mdf，i (SINR, H) is an increasing function of the SINR whose values are in the following interval range

[0119]

[0120] Specifically, for i = r, as the SINR approaches infinity, we obtain κ mdf，r (SINR, H) → κ(H), the conventional condition number of the channel.

[0121] The set of modified condition numbers provides a quantitative measure for determining the relative strength of the channel directions for any given SINR. A channel direction with a modified condition number close to 1 is a stronger direction, and a channel direction with a larger modified condition number is a weaker channel direction. Furthermore, concepts such as channel singularity, ill-conditioned channels, and well-conditioned channels should be defined in terms of the maximum modified condition number at a given SINR, i.e.,

[0122]

[0123] where σ min (H) is the smallest non-zero singular value of H. An alternative formula for the modified condition number can involve computing the eigenvalue decomposition of the G matrix (as described in Section 3.1) to obtain the eigenvalues where

[0124]

[0125] According to the definition of G, λ i can be expressed as:

[0126]

[0127] and thus, (λ1,..., λ Nt ) is in ascending order, different from (σ1,..., σ Nt ). Further modified condition numbers can also be derived that take into account the variation of all singular values rather than the largest-to-smallest singular value approach. For example,

[0128]

[0129] Note that other metrics as functions are not excluded. For ease of exposition, we adopt the previous metric κ (SINR, H) in the remainder of this disclosure. mdf，r (SINR, H).

[0130] Modified Orthogonality Defect

[0131] A channel orthogonality measure (referred to as the modified orthogonality defect) is proposed, which is a generalization of the traditional concept of the orthogonality defect δ(H) and captures the role of the SINR and different antenna array sizes. The modified OD is defined as

[0132]

[0133] Among them, the matrix G is defined as

[0134]

[0135] And G ii is the i-th diagonal entry of the matrix G. In fact, the modified orthogonality defect is the orthogonality defect of any full-rank matrix B that satisfies G = B T B, which can be constructed by, for example, using singular value decomposition (SVD) or Cholskey decomposition.

[0136] The modified orthogonality defect can also be expressed in terms of the singular values and singular vectors of the channel. Suppose V is the right singular direction of the channel (basically the channel eigenvector), we can write

[0137]

[0138] where, VoV represents the element-wise multiplication of V by itself; d 2 represents the element-wise square of the vector d; and the vector d is defined as follows:

[0139]

[0140] where r = rank(H). Note that the first r entries of the vector d, where r = rank(H), are related to the modified condition number as follows:

[0141]

[0142] It can be verified that for a channel with rank(H) = N t , when the SINR grows to infinity, δ mdf (SINR, H) → δ(H -H ), the standard orthogonality defect of the inverse or pseudo-inverse Hermitian of the channel. Note that when rank(H) < N t , δ(H) is not defined.

[0143] For any channel matrix H, regardless of the matrix size or rank, the modified OD is well-defined and satisfies

[0144] δ min ≤ δ mdf (SINR, H) ≤ δ max

[0145] where, due to the Hadamard inequality, δ min = 1, and the right-hand inequality can be proven by convex optimization to give

[0146]

[0147] where RMS(d) represents the root mean square operation

[0148]

[0149] and GeoMean(d) represents the geometric mean operation

[0150]

[0151] In fact, when the channels are orthogonal, i.e., when the channel eigenvectors form the identity matrix or its sign permutation, the lower bound is reached. The upper bound is due to the little-known observation that for a fixed set of channel gains, the maximum (modified) OD is reached when the channel eigenvectors form a Hadamard / DFT matrix or its sign permutation (after appropriate normalization). We have observed that for such channels, the IF receiver generally does not provide any rate gain compared to the MMSE receiver.

[0152] Non-square / non-symmetric N t ≠N r ) MIMO channels with different numbers of transmit and receive antennas (N t ×N r have a specific trend for the modified OD values. For the case of N t <N r , in the medium to high SINR region, the MIMO channel is likely to be almost orthogonal unless the antenna spatial correlation is significant. On the other hand, for the case of N t >N r , the MIMO channel is likely to be far from orthogonal unless the antenna spatial correlation is significant.

[0153] Those skilled in the art will understand that the above detailed description of the measurement of the impact on the SINR including the present invention is not intended to be exhaustive or to limit the present invention to the precise forms disclosed above or to the specific fields of use mentioned in this disclosure. While specific embodiments and examples of the present invention have been described above for illustrative purposes, various equivalent modifications can be made within the scope of the present invention as will be recognized by those skilled in the relevant arts. For example, the channel singularity measurement and the channel orthogonality measurement equations can be modified using square / n-th power operations, perturbations, adding regularization factors, linear / geometric means of all / subsets of values.

[0154] Proposed Algorithm for Receiver Selection

[0155] The method for linear receiver selection in the UE is as follows:

[0156] a) Calculate the maximum modified condition number κ mdf，r (SINR, H) and the modified orthogonality defect δ mdf(SINR, H), as described above.

[0157] b) If the channel is well-conditioned in the sense that κ mdf，r (SINR, H) is small, then select the MMSE receiver.

[0158] c) If the channel is completely orthogonal in the sense that δ mdf (SINR, H) reaches its lower bound (i.e., 1) or upper bound (i.e., δ max ), then select the MMSE receiver.

[0159] d) If the channel is nearly orthogonal in the sense that δ mdf (SINR, H) is close to its lower bound (i.e., 1) or upper bound (i.e., δ max ), and the channel is not highly ill-conditioned in the sense that κ mdf，r (SINR, H) is not too large, then select the MMSE receiver.

[0160] e) If the channel is far from orthogonal in the sense that δ mdf (SINR, H) is far from its lower and upper bounds, and / or the channel is in very poor condition in the sense that κ mdf，r (SINR, H) is very large, then select the IF receiver.

[0161] In summary, an IF receiver is expected to have a meaningful gain over an MMSE receiver in the following cases:

[0162] - The modified OD is sufficiently far from both limits, i.e., the eigenvectors are far from the identity matrix or its sign permutation, and also far from the Hadamard / DFT matrix or its sign permutation; and / or

[0163] - The maximum modified condition number is large enough.

[0164] Furthermore, as the number of channel directions with a large modified condition number increases, the advantage of the IF receiver over the MMSE receiver increases.

[0165] The method for linear receiver selection in the UE is as follows:

[0166] a) Identify the general singular threshold κ based on, for example, the antenna array size and antenna correlation, etc., but independent of the channel gain and SINR value thr .

[0167] b) Identify the appropriate orthogonality thresholds δ low , δ high such that δ low = δ low (SINR, H) and δ high = δhigh (SINR, H). Select these factors as δ min and δ max as the appropriate factors.

[0168] Alternatively, a function can be defined:

[0169]

[0170] where 0 ≤ δ’ ≤ 1. Regardless of δ mdf (SINR, H) approaching δ min or δ max the function approaches the value zero. Thus, a unified threshold δ thr can be used such that the IF receiver is selected when δ’ > δ thr Note that functions behaving similarly to δ’ are not excluded, which can produce a peak at the center and a zero value at the limit, and vice versa.

[0171] c) Calculate the maximum modified condition number κ mdf，r (SINR, H) and the modified orthogonality defect δ mdf (SINR, H), as described above.

[0172] d) If

[0173] κ mdf，r (SINR, H) < κ thr or (δ mdf (SINR, H) < δ low or δ mdf (SINR, H) > δ high )

[0174] then select the MMSE receiver.

[0175] e) If

[0176] x mdf，r (SINR, H) > κ thr and / or δ low < δ mdf (SINR, H) < δ high

[0177] then select the IF receiver.

[0178] From the above discussion, it can be easily concluded that the MMSE receiver should generally be selected for low SINR regions, including instances where the SINR is below 0 dB and even instances where the SINR is below 10 dB. The IF receiver is more useful for medium and high SINR regions.

[0179] For N t < Nr For non-square / non-symmetric uncorrelated MIMO channels, the MMSE receiver is usually more optimized because the channels are usually nearly orthogonal. On the other hand, for non-square / non-symmetric uncorrelated MIMO channels where N t > N, since the channels are far from orthogonal, the IF receiver is usually significantly better than the MMSE receiver. However, these effects may change due to medium to high spatial correlation between the antennas.

[0180] Although the above conditions capture many instances of MIMO channels for which the IF receiver provides less gain than MMSE, there are still some other combinations of channel eigenvectors and / or modified condition numbers that can prevent the IF receiver from having a significant rate gain over the MMSE receiver.

[0181] Note that the receiver type selection can be based on a quality metric rather than the modified condition number or the modified orthogonality defect. For example, quality metrics based on the spatial correlation of the channel or other channel-based metrics are not excluded. In addition, channel-independent metrics such as network load can also be used for receiver type selection.

[0182] New Algorithm for Integer-Forcing Design Based on Eigenvector Pairs

[0183] One element of the method we propose is to combine the strongest channel direction with other channel directions one by one using appropriate weights. The choice of weights allows us to adjust the contribution of all eigenvectors to the solution. In particular, we can appropriately align the selected integer vectors of the A matrix based on the strength of the channel directions. This not only provides profound insights into the design but also offers a near-optimal solution. The computational complexity is quite low.

[0184] In summary, aspects of the proposed method can include:

[0185] - A new method for generating candidate vectors via weighted combination of eigenvector pairs;

[0186] - A new, analytically verified, and tighter search radius;

[0187] - A modified greedy method for linear independence (L1) testing;

[0188] A direct extension of the proposed algorithm for complex MIMO channels (without converting the complex channel to a real channel via in-phase quadrature (IQ) decomposition).

[0189] Detailed Algorithm for Integer-Forcing Design Based on Eigenvector Pairs

[0190] The proposed algorithm for finding the integer linear combinations required for the integer-forcing (IF) architecture is detailed below.

[0191] Input: Estimation of the MIMO channel matrix H and the SINR at the receiver; threshold κ for identifying weak channel directions thr ; Resolution RS of the set of ρ1 values ρ or size SZ ρ ; Threshold Th of the set of ρ1 values ρ , where ρ1 represents the selection weight of the strongest channel direction

[0192] Output: (-n almost optimal) solution of matrix A

[0193] a) Calculate the matrix

[0194] b) Calculate the eigenvalue decomposition of matrix G to obtain the eigenvalues (in ascending order) and the corresponding eigenvectors Recall the above definitions of G and λ i The eigenvector corresponding to the smallest eigenvalue λ1 of G is the same as the singular vector v1 corresponding to the largest singular value of matrix H

[0195] c) Identify the search radius where λ min (G) = λ1. The proof of this search radius is given below. For speed improvement, a tighter but sub - optimal search radius can also be used based on the following 90% table

[0196] d) Identify the set {2,..., M} of strong and medium channel directions and discard any remaining weak directions. Here M is the largest index such that 2 ≤ i ≤ rank(H) and satisfies the following

[0197]

[0198] If κ mdf，2 (SINR, G) > κ thr , then select M = 2

[0199] e) Form the set of values ρ1 ∈ Ω1 based on the set resolution RS ρ as follows:

[0200]

[0201] which consists of including elements; or based on the set size SZ ρ , as follows:

[0202] Ω1 = {1} ∪ {k × Inc: k = 0, 1,..., SZ ρ - 2},

[0203] which has a size Increment. Below, refer to the multiple remarks on "Search Interval", "Search Resolution", "Exhaustive Selection", and "Optimal Selection" regarding the value of ρ1.

[0204] f) For all direction indices i = 2, …, M, and any given ρ1 ∈ Ω1, construct a set of α vectors such that a = 「ρ1v1 + ρ i v i 」, where: 「x」 represents element-wise rounding with upward rounding connection; and ρ i ∈ Ω i , where

[0205]

[0206] where and the set of half-integers Refer to the remarks below regarding the "Search Interval of ρ i Value".

[0207] g) Remove any α vectors that fall outside the search radius .

[0208] h) Put all the remaining α vectors into the candidate list.

[0209] i) Append the column vectors of the default matrix, i.e., all standard unit vectors, to the candidate list.

[0210] j) Sort the candidate list in ascending order based on their a T Ga values and discard any duplicate α vectors. Refer to the remarks below in this article regarding the usage of "Unique Sorting".

[0211] k) Remove all zero vectors.

[0212] I) Perform an improved greedy L1 test to construct the A matrix. Refer to the following.

[0213] Regarding the search interval of ρ1, the theoretical bounds and the fact that the eigenvectors have unit length imply that Since for any integer vector a, the integer vector (-a) is not linearly independent and results in the same value, (-a) T G(-a) = a T Ga, we can restrict the selection to only and can even restrict the upper bound to the 90% radius mentioned below or a small factor of it (e.g., twice the 90% radius), without losing optimality in most cases, but there may be some rate performance degradation for some ill-conditioned and non-orthogonal channels.

[0214] Regarding the search resolution for ρ1, in many cases, the selection of ρ1 can be done by considering only very low value precisions in the search interval, e.g., only integer, half-integer, or quarter-integer values. This improves the search speed and reduces the algorithm complexity, although sometimes it may sacrifice performance and / or result in long integer a vectors, which may not actually be beneficial. When our algorithm is applied to certain channels, we have also observed a saturation effect, where, regardless of how low or high the resolution of the ρ1 search selection is, the performance does not improve beyond a certain level (which may be efficient enough to achieve, e.g., 90% of the IF-optimal performance). Therefore, increasing the ρ1 precision is not necessarily a good idea.

[0215] Regarding the exhaustive selection of ρ1, a more exhaustive search of all necessary ρ1 values can be better ensured based on the half-integer intersections of all pairs of eigenvectors. In particular, for a fixed direction index 2 ≤ i ≤ M, for all pairs 1 ≤ j ≠ k ≤ N t and all half-integer pairs , the solution for ρ1 in the linear equation system can be considered:

[0216]

[0217] This can be done in a more systematic way using the "hyperplane arrangement" method. In either form, this exhaustive selection typically involves higher computational complexity and longer running times compared to the simple uniform selection above, but only provides a low to moderate improvement in terms of rate performance.

[0218] Regarding the optimal selection of ρ1, the optimal / smart selection of ρ1 values can be based on the (modified) condition number, (modified) orthogonality defect, etc. For example, for a 2×2 real MIMO channel, when the channel gain or modified condition number is small and the orthogonality or modified orthogonality defect is close to its lower or upper bound, (ρ1 = 1) can be used.

[0219] Regarding ρ i 's search interval, once again, the theoretical bounds and the fact that the eigenvectors have unit length means that at least in some cases, tighter bounds can be used Any one of the bounds can help avoid generating at least some invalid integer a vectors, and thus avoid at least some of the invalid pruning operations in step g) of the algorithm.

[0220] Regarding not needing to sort ρ i values, it may not be necessary to have the steps in the "eigenvector perturbation" algorithm corresponding to Method 10 above, i.e., "sort the ρ i values and use the average of consecutive ρ i values to construct the integer a vector".

[0221] Regarding the unique sorting of the a-vector, a technique for improving the speed of the proposed algorithm is to perform a "unique sorting" simplification in step (j) of the algorithm as follows: It is possible to sort the candidate list of integer a-vectors based on their a T Ga values, and then discard all vectors except one that achieve the same a T Ga value.

[0222] This is helpful in cases where an inappropriately high resolution in choosing the ρ1 value results in multiple repetitions in the candidate list of integer a-vectors. This technique reduces the computational complexity because it is much easier to check for duplicate scalars than for duplicate vectors. However, this technique also potentially leads to a performance loss because the possibility that two or more different linearly independent integer a-vectors achieve the same a T Ga value is relatively small, and some of them will be discarded by this "unique sorting" process.

[0223] Regarding the explicit formula, based on the above, the proposed algorithm is common enough to use potential lattice reduction as an external process as described below. Therefore, the explicit formula has been avoided. In this article, we provide these explicit formulas in the case where such lattice reduction is not performed. Here, we denote r = rank(H).

[0224]

[0225]

[0226]

[0227] Regarding LLL preprocessing and postprocessing, the UE can potentially reduce the search running time by making LLL reduction the outer layer of the proposed algorithm.

[0228] In particular, once the matrix G has been calculated in step (a), we can perform the following preprocessing:

[0229] - Consider the lattice basis B that satisfies G = BB T , for example, B = L, where L is the lower triangular matrix of the Cholskey decomposition G = LL T ; or B = V(diag(Λ)) obtained from the eigen decomposition G = Vdiag(Λ)V T 1 / 2 .

[0230] - Apply LLL reduction to B using the unimodular matrix T to obtain the reduced lattice basis and then form the reduced Gram matrix

[0231] ​While the rest of the algorithm is running, i.e., steps (b) to (1), consider the following changes:

[0232] - Replace matrix G with the matrix and call the resulting solution the matrix.

[0233] At the end of the algorithm, perform the following post - processing:

[0234] - Use to convert the result of the original lattice back to 1.

[0235] A New Search Radius for Integer Forcing

[0236] It is possible to obtain a new tight theoretical bound on the search radius for the integer - forcing problem and use it as follows.

[0237] According to the minimax theorem, for any vector a m , including the optimal vector, we have:

[0238]

[0239] where λ min (G) represents the minimum eigenvalue of matrix G. On the other hand, we know that is a valid (but not necessarily optimal) solution to this optimization problem. Here, we use the symbol e m for the standard unit vector with 1 in the m - th position and zeros elsewhere. Thus, we have

[0240]

[0241] Putting the two inequalities together, we obtain the following formula for the IF search radius:

[0242]

[0243] For a specific choice of , we have

[0244]

[0245] Therefore, the above - mentioned bound is simplified to

[0246]

[0247] To the best of our knowledge, these search radius formulas have not been reported in the literature before. These formulas tend to be particularly applicable to symmetric MIMO channels when the eNB and UE have the same number of antennas and low spatial correlation. Based on our numerical evaluation, for small values of the modified condition number (when A = I is almost optimal), the proposed search radius actually appears to be relatively tight. However, as the modified condition number increases and the optimal A matrix moves away from A = I (the more useful region of IF), this bound becomes looser. However, this is still tighter than the existing formulas for the search radius.

[0248] Numerical Table of Integer-Forcing Search Radii

[0249] In this subsection, we provide a set of tables for 90% of the IF search radius. We generated the following tables based on numerical simulations of hundreds of uncorrelated and correlated real MIMO channels, and extracted the search radius based on 90% of the norm of the actually selected integer a vectors by the optimal exhaustive selection method. For correlated MIMO channels, we used the definitions and parameters introduced in 3GPP TS 36.101 Appendix B.2.3 (and its extension to larger antenna array sizes), as follows:

[0250] where

[0251] where: vec(H) converts the matrix H to a vector by stacking columns; reshape(h, [m, n]) converts the vector h to an m×n matrix by expanding columns; denotes the Kronecker product of matrices; R eNB and R UE are the N t ×N t and N r ×N r correlation matrices at the eNB and UE, respectively, as follows:

[0252] and

[0253] where the correlation parameters are 0 ≤ α ≤ 1 and 0 ≤ β ≤ 1; and is the Cholskey decomposition of the MIMO correlation matrix R spat . For some cases of medium and high correlation, in order to better ensure that the spatial correlation matrix is positive semi - definite after rounding to 4 - digit precision, for some small scale factors, such as a = 0.00010 or a = 0.00012, the following adjustments were made:

[0254]

[0255] These tables tend to be more applicable to asymmetric MIMO channels, with unequal numbers of eNB and UE antennas, or when the MIMO spatial correlation is high.

[0256] These tables also show that if there is any gain in using an IF receiver over an MMSE receiver based on other characteristics of the channel, the average normalized received signal-to-interference-plus-noise ratio SINR / N t is more likely to have a gain when it exceeds 0 dB.

[0257] For a complex MIMO channel, the array size should be considered twice (e.g., converting a 2×2 complex channel to a 4×4 real channel), and then use the Figures 4 to 12 tables provided in. As provided in the 3rd Generation Partnership Project (3GPP) Technical Specification (TS) 36.101, "User Equipment (UE) Radio Transmission and Reception", 3GPP Technical Specification, LTE, Radio Access Network, Evolved Universal Terrestrial Radio Access (E-UTRA) (see Section B.2.3.2 in the annex), Figure 4 Table 400 is shown, which provides MIMO correlation setup matrices at high, medium, and low levels, including corresponding values for each of the transmit correlation parameter α and the receive correlation parameter β for the ULA MIMO correlation matrix.

[0258] Figure 5 Numerical Table 500 of the integer-forcing search radius for 2×2 real MIMO is shown. This table includes corresponding values associated with multiple correlation values and each of the SINR / N t values. Figure 6 Numerical Table 600 of the integer-forcing search radius for 2×4 real MIMO is shown. Figure 7 Numerical Table 700 of the integer-forcing search radius for 4×2 real MIMO is shown. Figure 8 Numerical Table 800 of the integer-forcing search radius for 4×4 real MIMO is shown. Figure 9 Numerical Table 900 of the integer-forcing search radius for 2×8 real MIMO is shown. Figure 10 Numerical Table 1000 of the integer-forcing search radius for 8×2 real MIMO is shown. Figure 11 Numerical Table 1100 of the integer-forcing search radius for 4×8 real MIMO is shown. Figure 12 Numerical Table 1200 of the integer-forcing search radius for 8×4 real MIMO is shown.

[0259] Modified Greedy Algorithm for Finding Linearly Independent Vectors

[0260] In this subsection, we provide a modified greedy method with a marked counter for finding a set of linearly independent vectors from a sorted candidate list. First, we explain the basic greedy method for the L1 test. Next, we present a modification using the marked counter that speeds up the basic greedy method via tree-like considerations and avoids testing some combinations that have already failed.

[0261] Below, we explain the basic greedy method for the L1 test.

[0262] We start from the top of the sorted list and fix the Nth t vector in the sorted candidate list as a column of the A matrix (since the IF performance is specified by the longest vector), and consider the sublist consisting of vectors with indices from 1 to N t - 1. Then, we check the LI condition of the current A matrix with the last vector in the sublist; if it passes the LI check, we append it as a column of the matrix, otherwise we discard it. We continue to check the second-to-last, third-to-last vectors, etc. in the sublist similarly one by one. We continue until we find a set of N t vectors that satisfy the LI condition, or until we have checked all the vectors in the sublist but have not formed a full-rank A matrix. In this case, we take one more step in the candidate list, change the fixed vector to the (N t + 1)st vector, and repeat the same process as before. We proceed similarly until we find a set of N t vectors that satisfy the LI condition. The algorithm will output a solution in finite time because we include the identity matrix in the candidate list, which is a valid worst-case solution.

[0263] The basic greedy LI test method may be inefficient because it fixes and updates the starting vector in the LI test sublist rather than the ending vector, which may not be optimal in general.

[0264] Below, we explain the modification of the basic greedy method using the marked counter.

[0265] In the basic method explained above, at each step, we start with the fixed vector in the list and traverse the candidate list in the reverse order, i.e., towards the top of the list, searching for a full-rank cluster of vectors. However, some of these vector clusters have already been tested and are known to fail the LI test. Therefore, we are able to store the indices of some or all of the failing clusters to speed up the upcoming checks. However, storing all of these failing clusters can be very space-consuming and may be very time-consuming. At least in some instances, we propose to store only the failing cluster pairs in the following convenient form: for the k-th integer vector a(k) in the candidate list, set a counter c(k) pointing to the next vector to be collected and checked. Initially, all counters are set to c(k) = k - 1, since the basic greedy search always traverses the candidate list in the reverse order and checks the previous vector in the list. However, we modify the counters as follows: whenever a(k) is the fixed vector in the step, and for some 2 ≤ l < k, the cluster with a(l) fails the L1 test, update the counter to c(k) = l - -1. This is because we perform the LI test in order, so if the pair [a(k), a(l)] fails the LI test, it means that all pairs [a(k), a(l + 1)], …, [a(k), a(l - 1)] have also failed, and thus the next cluster to be checked is [a(k), a(l - 1)]. When the fixed vector in the sublist changes, this counter becomes very useful as it helps to better ensure that those failing vector pairs will not be included in any upcoming clusters.

[0266] Generalization of the Proposed Algorithm for Complex MIMO Channels

[0267] In this subsection, we provide the general version of the proposed algorithm for the complex MIMO channel. There are two methods for the IF receiver design for the complex MIMO channel, both of which have the same performance:

[0268] (i) The commonly used method is to apply the I-Q decomposition to the N t ×N r complex MIMO channel and convert it to an equivalent (2N t ×2N r ) real MIMO channel, and then use the proposed algorithm for this equivalent real channel. This method generates a real integer A matrix of size (2N t ×2N r ). In this case, in order for the IF architecture to work, the same and independent MCS should be used for the real and imaginary parts, so complex or joint MCS that are not the cross product of the real and imaginary components are not allowed in this method.

[0269] (ii) A less common approach is to directly process the complex channel and use a complex integer A matrix of size N t ×N t where the entries are of the form (a + jb), where a and b are real integers; this is also called Gaussian integers. This is a more natural approach and some complexity reduction may be achieved using this method. Additionally, in this method, we are allowed to use more common complex or joint MCS for the two I-Q components, which simplifies the transmitter design. Also, note that for a complex MIMO channel, the power level per dimension per antenna should be the same as that used for a real MIMO channel.

[0270] In the following, we explain the changes to our proposed algorithm that allow for the direct design of complex MIMO channels. The aspects to note are: using conjugate transpose instead of real transpose, so the G matrix is defined as

[0271]

[0272] The weight factors ρ1,..., ρ r are now complex scalars; finally, when their real or imaginary arguments take half-integer values, the rounding vectors jump to new values. Thus, considering the above G matrix, all steps in the algorithm remain the same (including possible LLL preprocessing and postprocessing), except for steps e) and f), which are modified as follows:

[0273] a) Based on setting the resolution RS ρ to form a set of values of ρ1 ∈ Ω1 as follows:

[0274]

[0275] b) For all direction indices i = 2,..., M, and any given ρ1 ∈ Ω1, construct a set of α vectors such that α i = ⌈ρ1v1 + ρ i v i ⌉, where: ⌈x⌉ represents element-wise rounding with upward rounding connection; and ρ i ∈ Ω i，Real × jΩ i，Imag where

[0276]

[0277]

[0278] where we denote and the set of half-integers

[0279] Implementation Aspects of the IF Receiver

[0280] Coding and Modulation Aspects

[0281] IF Setting Introduction

[0282] The IF receiver has two highlighted implementation settings:

[0283] · Real number setting, where only real number channels are considered and real number lattice operations are applied. The complex channel is converted to a virtual real number channel using I-Q decomposition.

[0284] · Complex number setting, where complex number channels are directly considered and complex number lattice operations are employed.

[0285] Conversely, the lattice for the IF receiver can be constructed in at least two ways:

[0286] · Construction A: Encoding modulation via (single-stage) non-binary codes

[0287] · Construction D: Encoding modulation via multi-stage binary codes

[0288] We are more interested in binary codes such as linear block codes, convolutional codes, turbo codes, LDPC codes, polar codes, so Construction D is more preferred at least in some instances.

[0289] For the case of the real number setting with Construction D, consider the following features / aspects:

[0290] The virtual real number channel has (2×M) transmit antennas and (2×N) receive antennas. It is assumed that the channel experiences semi-static, flat fading, i.e., there is no or almost no time / frequency variation within a code block transmission. This can be achieved by restricting the mapping of modulation symbols within a resource allocation that includes a small number (e.g., 1) of RBGs (Resource Block Groups, RBG = 4 RBs, RB = 12 subcarriers), subbands (e.g., 8 RBs), and PRGs (Precoding Resource Groups, such as 2 RBs). Due to the limited number of subcarriers in the flat fading constraint in frequency, the resource allocation can be distributed across at least one time slot (e.g., including 14 OFDM symbols) or multiple time slots to support a sufficient number of information bits for communication.

[0291] All messages and codewords are binary.

[0292] All codes (i.e., encoder and decoder functions) are binary linear codes.

[0293] There are (M×2×L) independent messages / codewords, where L is the number of levels of the multi-level code. The codewords can correspond to the coded parts of one or more transport blocks. The transport block can be segmented into multiple code blocks, and each code block is encoded into a codeword using a channel code. The number of channel-coded bits in the codeword can be given by the number of data subcarriers in the resource allocation (e.g., excluding the subcarriers used for reference signals, rate matching patterns).

[0294] All (M×2) messages in the same level use the same binary code at the same rate. The code rate for each level is selected based on one of the different rules of the multi-level code scheme. The number of information bits and the number of coded bits or the codeword length are the same across all codewords in the same level. In one example, the codewords can be first mapped to the bits corresponding to a given level and antenna port (e.g., starting from the lowest level, the lowest antenna port, alternating I and Q components or starting with the I component and then the Q component), and then across the antenna ports (e.g., from the lowest antenna port to the highest antenna port), and then across the levels (e.g., to the second lowest level, the third lowest level, and so on. ) - so first (starting from the lowest level) across the antenna ports (alternating I and Q or I then Q) and then across the levels. Alternate mappings can also be considered, such as (starting from the lowest antenna port) across the levels (alternating I and Q or I then Q), and then across the antenna ports. The antenna ports can correspond to the transmission layers. Additionally, under certain space-related conditions, the case of mapping the same codeword to a subset of antenna ports with a size greater than one is not excluded.

[0295] For the modulation of the binary sequence, the messages are concatenated in the order of their levels, i.e., the MSB corresponds to the highest level (level "L"), and the LSB corresponds to the lowest level (level 1).

[0296] The mapping from bits to symbols follows the natural labeling, i.e., the Cartesian product of the mappings for each level, where the mapping for each level is a mapping from {0,1} to BPSK symbols such as {+1,-1} or {+a,-a}.

[0297] OFDM first allocates the modulation symbols in the frequency (subcarriers), and then across time (OFDM symbols). In the present disclosure, the parameter "n" refers to the total number of time-frequency allocations.

[0298] The effective channel matrix "A" should be: (i) real integers, (ii) its modulo 2 version "A2" should be full rank over Z2.

[0299] Figure 13 and 14 Shows how the transmitter and receiver sides are constructed when using the real setup with Construction D. More specifically, Figure 13FIG. 1300 shows a transmitter - side block diagram constructed using a real - number setup of Configuration D that includes a channel H, receiver noise, and OFDM demodulation, and Figure 14 FIG. 1400 shows a receiver - side block diagram constructed using a real - number setup of Configuration D.

[0300] For a complex - number setup of Configuration D, consider the following features / aspects:

[0301] The complex - number channel has (M) transmit antennas and (N) receive antennas. It is assumed that the channel experiences semi - static, flat fading, i.e., there is no or little time / frequency variation during the transmission of a code block. This can be achieved by restricting the mapping of modulation symbols within a resource allocation that includes a small number (e.g., 1) of RBGs (Resource Block Groups, RBG = 4 RBs, RB = 12 sub - carriers), sub - bands (e.g., 8 RBs), and PRGs (Precoding Resource Groups, such as 2 RBs). The resource allocation can be distributed across at least one time slot (e.g., including 14 OFDM symbols) or multiple time slots to support a sufficient number of information bits for communication, since the number of sub - carriers in the frequency for the flat - fading constraint is limited.

[0302] All messages and codewords are binary.

[0303] All codes (i.e., encoder and decoder functions) are binary linear codes.

[0304] There are (M×L) independent messages / codewords, where L is the number of levels of the multi - level code. A codeword can correspond to the coded part of one or more transport blocks. A transport block can be divided into multiple code blocks, and each code block is encoded into a codeword using a channel code. The number of channel - coded bits in a codeword can be given by the number of data sub - carriers (e.g., excluding sub - carriers used for reference signals, rate - matching patterns) in the resource allocation×2. The factor for complex - number (I and Q) modulation symbols is 2.

[0305] All (M) messages within the same level use the same binary code at the same rate. The code rate for each level is selected based on one of the different rules of the multi-level code scheme. The number of information bits and the number of coded bits or codeword length (for a transport block) are the same across all codewords within the same level. In one example, the codewords can first be mapped to bits corresponding to a given level and antenna port (e.g., starting from the lowest level, lowest antenna port, alternating I and Q components or I components first and then Q components), and then across antenna ports (e.g., from the lowest antenna port to the highest antenna port), and then across levels (e.g., to the second lowest level, third lowest level, and so on). - So first (starting from the lowest level) across antenna ports (alternating I and Q or I first and then Q) and then across levels. Alternate mappings can also be considered, such as across levels (alternating I and Q or I first and then Q) starting from the lowest antenna port, and then across antenna ports. The antenna ports can correspond to the transmission layer. Additionally, under certain space-related conditions, mapping the same codeword to a subset of antenna ports with a size greater than one is not excluded.

[0306] For the modulation of binary sequences, the messages are concatenated in the order of their levels, i.e., the MSB corresponds to the highest level (level "L"), and the LSB corresponds to the lowest level (level 1).

[0307] The mapping from bits to symbols follows natural labeling, i.e., the Cartesian product of the mappings for each level, where the mapping for each level is a mapping from {0,1} to BPSK symbols such as {+1,-1} or {+a,-a} for the I and Q components.

[0308] OFDM first allocates modulation symbols over frequency (sub-carriers) and then over time (OFDM symbols). In the present disclosure, the parameter "n" refers to the total number of time-frequency allocations.

[0309] The effective channel matrix "A" should be: (i) a complex integer, and (ii) its modulo 2 version "A2" should be full rank over Z2.

[0310] Define the multiplication of the complex integer matrix "A" with a binary sequence & complex integer / bit using modulo-2 arithmetic.

[0311] In one example, to be equivalent to the real number setting, each message can be considered to consist of two sub-messages (for the I and Q components).

[0312] Figure 15 A transmitter-side block diagram 1500 constructed using a complex number setting with construction D is shown. Figure 16 A receiver-side block diagram 1600 constructed using a complex number setting with construction D is shown.

[0313] We also note that further settings are based on:

[0314] · A lattice reduction-aided (LRA) receiver that applies IF-like operations at the symbol level (instead of the codeword level), and

[0315] · Application of an external single / multi-stage channel code

[0316] This can also be discussed for both real / complex settings.

[0317] For a real setting with Construction A, consider the following features / aspects:

[0318] For consistency, we start with binary messages. The operations are relative to a field of order p.

[0319] The codewords are p-ary. Integer matrices are applied to p-th order functions of the messages at the receiver.

[0320] All streams or layers have the same rate. Under certain arrangements, this restriction can be relaxed.

[0321] The input / output relationship in the decoding stage is non-conventional.

[0322] At the transmitter: k ≤ k b and k ≤ n but not necessarily k b ≤ n, and the code rate can be greater than 1.

[0323] OFDM first allocates modulation symbols on frequencies or subcarriers and then across time or OFDM symbols. In the figure, the parameter "n" refers to the total number of time-frequency allocations.

[0324] Extended to complex-valued channels: a virtual (2M×2N) MIMO channel, i.e., the number of streams is doubled.

[0325] Figure 17 A transmitter-side block diagram 1700 constructed using a real setting with Construction A is shown. Figure 18 A receiver-side block diagram 1800 constructed using a real setting with Construction A is shown.

[0326] For reference, at least for codebook-based operations, the codeword-to-layer mapping in LTE is recalled here as background material:

[0327] Allows up to 4 layers (8 layers in Rel.15).

[0328] N L layers, N A ports, where 1 ≤ N L ≤ N A .

[0329] The possible transport block-to-layer mapping is shown below.

[0330] For HARQ retransmission, if one transport block spans two layers, then two layers will be transmitted.

[0331] The number of symbols across layers must be equal. For example, if two transport blocks are mapped to three layers, then length (transport block 2) = 2 × length (transport block 1). This can be ensured by selecting appropriate transport block sizes in addition to rate matching.

[0332] The modulation symbols corresponding to a transport block are mapped to the layers in an alternating manner, i.e., if the transport block 1 symbols are: T1 (1) , T2 (1) , T3 (1) , T4 (1) …, then the layer 1 symbols are: T1 (1) , T3 (1) …, and the layer 2 symbols are: T2 (1) , T4 (1) ….

[0333] The current mapping does not guarantee that the decoding function is an integer combination of the messages.

[0334] Figure 19 Block diagram 1900 showing the mapping of codewords to layers in LTE is shown. Figure 20 Exemplary mapping diagram 2000 showing the mapping of transport blocks to layers for codebook-based antenna precoding (initial transmission) is shown.

[0335] IF Design for Fast-Fading MIMO Channels

[0336] In the present disclosure, it was previously discussed that the IF architecture may be useful for slow or semi-static fading scenarios. For fast fading channels, one embodiment may include performing some average ordering of matrix A over multiple coherence intervals, and another embodiment may include using IF at the symbol level, similar to a lattice reduction-aided (LRA) receiver, with or without an external FEC code.

[0337] However, if the channel fading changes faster than a certain threshold in time, it is expected that the performance of the former method will deteriorate.

[0338] Extension to Multi-User Scenarios

[0339] As can be seen from the previous description of the IF framework, the method can be extended to a multi-user (MU) system in the uplink, where each (multiple) transmit antenna or a subgroup thereof corresponds to a single user equipment (UE). This is possible because the coding process is independent across antennas, with the limitation of using the same code and modulation coding scheme (MCS) across UEs. Then, the serving cell BS will find the approximate or optimal integer linear combination required for the IF equalization / reception process and thus decode the messages sent from these UEs in a manner similar to the point-to-point case.

[0340] Use of Different Rates for Different Layers / Users via Subsets of the Same Lattice / Modulation

[0341] In some instances, the IF framework can suggest using the same code with the same rate for all layers in the point-to-point transmission (and multi-user uplink) of the IF architecture. In one embodiment, it is suggested to use a subset of the same lattice / modulation for different layers / users to facilitate transmission at different rates when their channels are different.

[0342] Downlink and Uplink Communication Frameworks

[0343] In one embodiment, a receiving node having a set of receive antenna ports may receive a reference signal from a set of transmit antenna ports of at least one transmit node. The receiving node may estimate channel characteristics, such as a set of channel signatures between the set of transmit antenna ports and the set of receive antenna ports. The receiving node may determine at least one channel quality metric based on the estimated channel characteristics, such as a modified condition number and / or a modified orthogonality defect.

[0344] In one example, the receiving node may select a receiver type from a first receiver type and a second receiver type based on the determined at least one channel quality metric and a selection criterion, where the second receiver type is an integer-forcing receiver type based on a set of integer linear combinations based on the estimated channel signatures. In one example, each integer linear combination in the set of integer linear combinations is based on a pair of channel signatures from the set of channel signatures. The first receive type may be a conventional receiver, such as MMSE-IRC or ML-SIC.

[0345] In another example, the receiving node may select an encoding / mapping type from a first encoding / mapping type and a second encoding / mapping type based on the determined at least one channel quality metric and a selection criterion for encoding the data stream. The second encoding / mapping type may support only resource allocations with a number of RBs (e.g., RBG, PRG, sub-bands) lower than a first number and at least a second number of OFDM symbols (e.g., time slots), the same channel coding scheme, the codeword length across all transport layers from a set of transmit antenna ports (at least for each modulation level), and a modulation and coding scheme (MCS). For the first encoding / mapping type, there are no such restrictions on the number of RBs, the number of OFDM symbols, the channel coding scheme, the codeword length, and the modulation and coding scheme (MCS). The second encoding / mapping type may be associated with an integer-forcing receiver type such as based on a set of integer linear combinations, a second receiver type based on a set of integer linear combinations of estimated channel characteristics. The first encoding / mapping type may be associated with a first receiving type. The first receiving type may be a conventional receiver such as MMSE-IRC or ML-SIC.

[0346] In another example, the receiving node may further select an encoding / mapping type from the first encoding / mapping type and the second encoding / mapping type based on traffic characteristics. For example, the first encoding / mapping type may support low-latency traffic regardless of whether the determined at least one channel quality metric meets the selection criterion. For normal traffic, the receiving node may select an encoding / mapping type based on the determined at least one channel quality metric and the selection criterion for encoding the data stream.

[0347] In an example of downlink communication, the transmitting node may be a network entity, a base station, a gNB, an eNB, a relay node, a TRP (transmit / receive point), etc. The receiving node may be a UE, a remote unit, etc. The reference signal may correspond to CSI-RS and CSI-IM reference signals. The receiving node may indicate the selected or recommended receiver type or encoding / mapping type to the transmitting node. The receiver node may also indicate the determined channel quality metric or a function thereof (degree of channel poor condition, degree of orthogonality defect) to the transmitting node, which may be quantized into a few bits. This indication may be signaled only when the second receiver type or encoding / mapping type is selected. The transmitting node may indicate the receiver type or encoding / mapping type for data transmission in DCI (downlink control information) on the PDCCH (physical downlink control channel) that schedules the data transmission. In one example, the receiving node may be configured as to whether the receiver type / encoding / mapping type is determined and reported by the transmitting node. In one example, the receiving node may indicate the ability to support the second receiver type / second encoding / mapping type to the transmitting node.

[0348] In another example of uplink communication, the transmitting node can be a UE, a remote unit, etc. The receiving node can be a network entity, a base station, a gNB, an eNB, a relay node, a TRP (transmit / receive point), etc. The first transmitting node (the first UE) of at least one transmitting node can include a first subset of antenna ports from a set of transmit antenna ports; and, the second transmitting node of at least one transmitting node can include a second subset of antenna ports from the set of transmit antenna ports. The reference signal can correspond to a first set of SRSs (sounding reference signals) from the first transmitting node and a second set of SRSs from the second transmitting node. For the second type of coding / mapping, the receiving node can indicate the same resource allocation (e.g., RBs and OFDM symbols), the same channel coding scheme, the codeword length, and the modulation and coding scheme (MCS) to each of at least one transmitting node from the corresponding subset of antenna ports for encoding the data stream of each transmitting node across the transport layer at least for each modulation level. The receiving node can use an integer-forcing receiver type based on a set of integer linear combinations and the received signals from the first transmitting node and the second transmitting node, and jointly decode the data from each of the first transmitting node and the second transmitting node for each modulation level.

[0349] The present disclosure proposes a new algorithm with reasonable computational complexity that finds the optimal or near-optimal integer linear combinations required for IF equalizer / receiver design.

[0350] The prominent element in the method we propose is to combine the strongest channel direction with other channel directions one by one using appropriate weights. The choice of weights allows us to adjust the contribution of all eigenvectors to the solution. In particular, we are able to appropriately align the selected integer vectors of the A matrix based on the strength of the channel directions. This not only provides profound insights into the design but also offers a near-optimal solution. The computational complexity is quite low.

[0351] In summary, the elements of the proposed method according to at least some embodiments can include:

[0352] - A method for generating candidate vectors via weighted combination of eigenvector pairs;

[0353] - A tighter search radius with analytical proof;

[0354] - A modified greedy method for linear independence (L1) testing; and

[0355] - A direct extension of the proposed algorithm to complex MIMO channels (without converting the complex channel to a real channel via in-phase quadrature decomposition).

[0356] The present disclosure discusses at least three aspects:

[0357] - First, the present disclosure identifies two conditions for linear receiver selection based on MIMO channel characteristics, namely the signal-to-interference-plus-noise ratio (SINR), which determines whether a conventional MMSE receiver is optimal or nearly optimal, or whether an IF receiver should be used. These conditions can be conveniently checked to recommend an appropriate linear receiver to be selected, and can significantly save UE computing (and power, etc.) resources.

[0358] - Second, the present disclosure proposes an algorithm with reasonable computational complexity that finds the optimal or near-optimal integer linear combinations required for IF receiver design. Specifically, the eigenvector-based design of the IF equalizer is described in detail, where certain eigenvectors of the wireless MIMO channel are used to define the integer linear combinations required for IF receiver design.

[0359] - Third, aspects of the implementation of integer-forcing receivers for both real and complex channel models, including how to incorporate coding modulation techniques.

[0360] Figure 21 FIG. 2100 shows a flow chart for receiver selection between a baseline receiver and an alternative receiver in a user equipment. According to at least one embodiment, the method can include receiving 2102 a set of reference signals and estimating 2104 a set of channel signatures of a plurality of antenna communication channels based on the received set of reference signals. Then, channel state information including a set of quality metrics can be calculated 2106. In response to the set of quality metrics satisfying a criterion, a baseline receiver can be selected 2108 at the user equipment for the plurality of antenna communication channels. In response to the set of quality metrics not satisfying the criterion, an alternative receiver can be selected 2110 at the user equipment for the plurality of antenna communication channels. The alternative receiver selectable at the user equipment for the plurality of antenna communication channels can be based on a set of integer linear combinations, where each integer linear combination can be based on at least a pair of channel signatures 2112 from the estimated set of channel signatures.

[0361] In some instances, a set of quality metrics can be based on an estimated set of channel signatures and can include one or more of at least one modified condition number and a modified orthogonality defect. In some of those instances, each of the at least one modified condition numbers includes a ratio based on one or more of the following: (i) the strongest channel signature and the weakest channel signature in the set of channel signatures, and (ii) SINR. In some of these and other instances, the modified orthogonality defect can be based on SINR. In some instances, the set of quality metrics not meeting a criterion can include one or more of the following: (i) the modified condition number of the weakest channel signature is greater than a threshold, and (ii) the modified orthogonality defect is away from its boundary value. In some instances, the set of quality metrics not meeting a criterion can include one or more of the following: (i) the modified condition number of the weakest channel signature is greater than a threshold and (ii) a function of the modified orthogonality defect is less than a threshold.

[0362] In some instances, the set of quality metrics can be independent of the estimated set of channel signatures.

[0363] In some instances, the method can further include the UE indicating whether it can support receiver selection.

[0364] In some instances, the channel signature can be based on one of eigenvector decomposition and singular value decomposition of a multi-antenna communication channel.

[0365] In some instances, a baseline receiver can be based on a MMSE receiver.

[0366] In some instances, a baseline receiver can be equivalent to an alternative receiver with integer combinations that are close to or equal to a unit vector with one non-zero entry.

[0367] In some instances, the alternative receiver can be an integer-forcing linear receiver.

[0368] In some instances, the alternative receiver can have integer combinations that can include combinations that substantially deviate from a unit vector with one non-zero entry.

[0369] In some instances, a pair of channel signatures can include the strongest channel signature and a second channel signature from the set of channel signatures. In some of those instances, the second channel signature can have a modified condition number that is not less than a threshold.

[0370] In some instances, an integer linear combination can be within a search radius, where the search radius depends on one or more of channel spatial correlation, SINR, and antenna array size at one or both of the transmitter and the receiver.

[0371] In some instances, the integer linear combination can be linearly independent.

[0372] In some instances, a user equipment is capable of communicating with a base station where channel state information is not available at the base station.

[0373] Figure 22 FIG. 2200 is a flow chart showing a preferred set of integer linear combinations used in an integer forcing receiver in a user equipment. According to at least one embodiment, the method can include determining 2202 at least one of a signal-to-interference-plus-noise ratio and an estimate of a channel matrix at the integer forcing receiver from a received signal. A lattice matrix can be computed 2204, where the lattice matrix is based on the number of transmit and receive elements, and at least one of the determined estimate of the channel matrix and the determined signal-to-interference-plus-noise ratio. A set of channel directions can be identified 2206 from the computed eigen-decomposition of the lattice matrix. A subset of the set of channel directions can be selected 2208 based on relative strength. Associated weighting values can be computed 2210 for each selected channel direction, where the weighting values are derived based on a given resolution. A set of vectors can be determined 2212 from the selected channel directions adjusted by the computed associated weighting values, and the determined set of vectors is included in a candidate list. A full-rank effective channel matrix with integer-valued entries can be formed 2214 from the vectors in the candidate list.

[0374] In some instances, the channel matrix can be a multiple-input multiple-output (MIMO) channel matrix. In some of these instances, the multiple-input multiple-output (MIMO) channel matrix can include complex channels, from which an effective channel matrix with integer-valued entries is formed without converting the complex channels to real channels via in-phase and quadrature decomposition.

[0375] In some instances, determining the set of vectors can include identifying a search radius and removing any vectors from the vectors in the candidate list that fall outside the search radius. In some of these instances, the identified search radius can be based on numerical simulations of uncorrelated and correlated real channels, where the search radius is based on a predetermined percentile of the norm of the actually selected integer vectors by an optimal exhaustive selection method, which is less than 100%. In some of these and other instances, the identified search radius can be based on one or more of a channel correlation level, the determined signal-to-interference-plus-noise ratio, and the number of transmit and receive elements.

[0376] In some instances, the candidate list can further include column vectors of an identity matrix of appropriate size.

[0377] In some instances, the candidate list can include vectors with a unique non-zero associated ɑ Τ Gɑ value, where ɑ refers to a candidate integer vector and G corresponds to the computed lattice matrix.

[0378] In some examples, when a modified condition number corresponding to a second strongest singular vector of a channel matrix is greater than a predetermined threshold condition number, a determined number of selected channel directions can be equal to 2.

[0379] In some examples, a determined number of selected channel directions can be based on eigenvalues of a lattice matrix.

[0380] In some examples, real and imaginary entries of vectors in a candidate list can be rounded element-by-element.

[0381] In some examples, an associated weighting value corresponding to a strongest channel direction can be extracted from a predetermined set of values including zero. In some of these examples, an associated weighting value corresponding to a channel direction other than the strongest channel direction can be based on eigenvectors of a lattice matrix, the associated weighting value corresponding to the strongest channel direction, and a set of half integers.

[0382] In some examples, an effective integer channel matrix can be constructed starting from a qualified vector associated with a strongest channel direction, and then qualified vectors associated with the next strongest channel directions can be added sequentially based on a linear independence test. In some of these examples, the linear independence test can include selecting qualified vectors that are linearly independent and provide the highest rate from a candidate list.

[0383] It should be understood that although specific steps as shown in the figures, various additional or different steps can be performed according to embodiments, and one or more specific steps can be completely rearranged, repeated, or eliminated according to embodiments. In addition, some steps that can be repeatedly performed on a continuous or ongoing basis can be performed while other steps are being performed. In addition, different steps can be performed by different elements or within a single element of the disclosed embodiments.

[0384] Figure 23 is an example block diagram of an apparatus 2300 such as a wireless communication device 110 according to possible embodiments. The apparatus 2300 can include a housing 2310, a controller 2320 within the housing 2310, audio input and output circuitry 2330 coupled to the controller 2320, a display 2340 coupled to the controller 2320, a transceiver 2350 coupled to the controller 2320, an antenna 2355 coupled to the transceiver 2350, a user interface 2360 coupled to the controller 2320, a memory 2370 coupled to the controller 2320, and a network interface 2380 coupled to the controller 2320. The apparatus 2300 can perform the methods described in all embodiments

[0385] The display 2340 can be a viewfinder, a liquid crystal display (LCD), a light emitting diode (LED) display, a plasma display, a projection display, a touch screen, or any other device that displays information. The transceiver 2350 can include a transmitter and / or a receiver. The audio input and output circuitry 2330 can include a microphone, a speaker, a transducer, or any other audio input and output circuitry. The user interface 2360 can include a keypad, a keyboard, buttons, a touchpad, a joystick, a touch screen display, another additional display, or any other device that provides an interface between the user and the electronic device. The network interface 2380 can be a universal serial bus (USB) port, an Ethernet port, an infrared transmitter / receiver, an IEEE 1394 port, a WLAN transceiver, or any other interface that can connect the device to a network, a device, or a computer and can transmit and receive data communication signals. The memory 2370 can include random access memory, read-only memory, optical memory, solid state memory, flash memory, removable memory, a hard disk drive, a cache, or any other memory that can be coupled to the device.

[0386] The device 2300 or the controller 2320 can implement any operating system, such as Microsoft or Android TM or any other operating system. The device operating software can be written in any programming language such as C, C++, Java, or Visual Basic. The device software can also run on an application framework such as framework, framework, or any other application framework. The software and / or the operating system can be stored in the memory 2370 or at other locations on the device 2300. The device 2300 or the controller 2320 can also use hardware to implement the disclosed operations. For example, the controller 2320 can be any programmable processor. The disclosed embodiments can also be implemented on a general or special purpose computer, a programmed microprocessor or microprocessor, peripheral integrated circuit elements, an application specific integrated circuit or other integrated circuits, a hardware / electronic logic circuit such as a discrete element circuit, a programmable logic device such as a programmable logic array, a field programmable gate array, etc. Generally, the controller 2320 can be any controller or processor device that can operate the device and implement the disclosed embodiments. Some or all of the additional elements of the device 2300 can also perform some or all of the operations of the disclosed embodiments.

[0387] The method of the present invention can be implemented on a programmed processor. However, the controller, flowchart, and modules can also be implemented on a general or special-purpose computer, a programmed microprocessor or microcontroller, and peripheral integrated circuit elements, integrated circuits, such as discrete element circuits, hardware electronics or logic circuits of programmable logic devices, etc. Generally, any device in which a finite state machine capable of implementing the flowchart shown in the figures resides can be used to implement the processor functions of the present disclosure.

[0388] Although the present disclosure has been described through its specific embodiments, it is obvious that many alternatives, modifications, and variations are obvious to those skilled in the art. For example, the various components of the embodiments can be interchanged, added, or replaced in other embodiments. In addition, all elements of each figure are not necessary for the operation of the disclosed embodiments. For example, those of ordinary skill in the art to which the embodiments of the present invention pertain will be able to make and use the teachings of the present invention by simply using the elements of the independent claims. Therefore, the embodiments of the present disclosure described herein are intended to illustrate rather than limit. Various changes can be made without departing from the spirit and scope of the present invention.

[0389] In this document, relational terms such as "first", "second", etc. may be used only to distinguish one entity or action from another entity or action, and do not necessarily require or imply any actual such relationship or order between such entities or actions. The phrases "at least one of", "at least one selected from the group of...", or "at least one selected from..." followed by a list are defined to mean one, some, or all of the elements in the list, but not necessarily all. The terms "comprising", "including", "having", or any other variants thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device that comprises a list of elements not only includes those elements, but may also include other elements not expressly listed or inherent to such process, method, article, or device. Without more constraints, an element preceded by "a", "an", etc. does not exclude the presence of additional identical elements in the process, method, article, or device that comprises the element. In addition, the term "another" is defined as at least a second or more. The terms "comprising", "having", etc. used herein are defined as "including". In addition, the background section is written as the inventor's understanding of the background of some embodiments at the time of submission, and includes the inventor's own recognition of any problems in the prior art and / or problems encountered in the inventor's own work.

Claims

1. A method for receiver selection between a baseline receiver and an alternative receiver in a user equipment, the method comprising: Receiving a set of reference signals; Estimating a set of channel signatures of multiple antenna communication channels based on the received set of reference signals; Calculating channel state information including a set of quality metrics; Selecting, at the user equipment, the baseline receiver for the multiple antenna communication channels in response to the set of quality metrics satisfying a criterion; Selecting, at the user equipment, the alternative receiver for the multiple antenna communication channels in response to the set of quality metrics not satisfying the criterion; Wherein the alternative receiver selected at the user equipment for the multiple antenna communication channels is based on a set of integer linear combinations, wherein each integer linear combination is based on at least a pair of channel signatures from the estimated set of channel signatures.

2. The method according to claim 1, wherein The set of quality metrics is based on the estimated set of channel signatures and includes one or more of at least one modified condition number and a modified orthogonality defect.

3. The method according to claim 2, wherein, Each of the at least one modified condition number includes a ratio based on one or more of: (i) the strongest channel signature and the weakest channel signature from the set of channel signatures, and (ii) the signal-to-interference-plus-noise ratio SINR.

4. The method according to claim 2, wherein, The modified orthogonality defect is based on the signal-to-interference-plus-noise ratio SINR.

5. The method according to claim 2, wherein The set of quality metrics not satisfying the criterion includes one or more of: (i) the modified condition number of the weakest channel signature is greater than a threshold, and (ii) the modified orthogonality defect is away from its boundary value.

6. The method according to claim 2, wherein The set of quality metrics not satisfying the criterion includes one or more of: (i) the modified condition number of the weakest channel signature is greater than a threshold and (ii) a function of the modified orthogonality defect is less than a threshold.

7. The method according to claim 1, wherein, The set of quality metrics is independent of the estimated set of channel signatures.

8. The method according to claim 1, further comprising indicating, by the user equipment, whether it is capable of supporting the receiver selection.

9. The method according to claim 1, wherein The channel signature is based on one of the eigenvector decomposition and singular value decomposition of the multiple antenna communication channels.

10. The method according to claim 1, wherein The baseline receiver is based on the MMSE receiver.

11. The method according to claim 1, wherein, The baseline receiver is equivalent to an alternative receiver having an integer combination close to or equal to a unit vector with one non-zero entry.

12. The method according to claim 1, wherein, The alternative receiver is an integer forced linear receiver.

13. The method according to claim 1, wherein The alternative receiver has an integer combination that includes a combination substantially deviating from a unit vector with one non-zero entry.

14. The method according to claim 1, wherein The pair of channel signatures includes the strongest channel signature and a second channel signature from the set of channel signatures.

15. The method according to claim 14, wherein The second channel signature has a modified condition number not less than a threshold.

16. The method according to claim 1, wherein, The integer linear combination is within a search radius, wherein the search radius depends on one or more of the channel spatial correlation, SINR, and antenna array size at one or both of the transmitter and the receiver.

17. The method according to claim 1, wherein, The integer linear combinations are linearly independent.

18. The method according to claim 1, wherein The user equipment communicates with a base station, wherein the channel state information is not available at the base station.

19. A user equipment in a communication network, the user equipment comprising: A transceiver, the transceiver including a selectable baseline receiver and a selectable alternative receiver, the transceiver receiving a set of reference signals; and A controller, the controller estimating a set of channel signatures of a plurality of antenna communication channels based on the received set of reference signals, and calculating channel state information including a set of quality metrics; wherein, the controller selects the baseline receiver at the user equipment for the plurality of antenna communication channels in response to the set of quality metrics satisfying a criterion, and the controller selects the alternative receiver at the user equipment for the plurality of antenna communication channels in response to the set of quality metrics not satisfying the criterion; and wherein, the alternative receiver selectable at the user equipment for the plurality of antenna communication channels is based on a set of integer linear combinations, wherein each integer linear combination is based on at least a pair of channel signatures from the estimated set of channel signatures.

20. The user equipment according to claim 19, wherein, The selectable baseline receiver and the selectable alternative receiver are part of separate signal paths within the transceiver.

21. The user equipment according to claim 19, wherein The selectable baseline receiver and the selectable alternative receiver are respectively formed as part of a digital signal processor.

22. The user equipment according to claim 21, wherein, The digital signal processor of which the selectable baseline receiver and the selectable alternative receiver are respectively formed as part includes corresponding pre-stored sets of instructions.

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