Lattice-reduction-aided Research Articles

Lattice Reduction Aided Probability Data Association Detector for MIMO Systems

The performance of symbol detection in multiple-input multiple-output (MIMO) systems is largely determined by the achievable diversity order. The inter antenna interference (IAI), however, can limit detectors’ ability to take full advantage of diversity. This occurs because off-diagonal channel coefficients of the MIMO channel matrix are not mutually orthogonal. Nevertheless, this can be mitigated with the aid of lattice reduction (LR), which aims to increase the orthogonality among these coefficients. We propose a LR aided probability data association (PDA) detector that achieves a similar diversity order to that of the optimum detector but with significant less computational complexity.

Out-of-Bound Signal Demapping for Lattice Reduction-Aided Iterative Linear Receivers in Overloaded MIMO Systems

Out-of-Bound Signal Demapping for Lattice Reduction-Aided Iterative Linear Receivers in Overloaded MIMO Systems

A 3.85-Gb/s 8 × 8 Soft-Output MIMO Detector With Lattice-Reduction-Aided Channel Preprocessing

This article presents an 8 × 8 lattice-reduction-aided (LRA) soft-output multiple-input multiple-output (MIMO) detector for Chinese enhanced ultrahigh throughput (EUHT) wireless local area network (LAN) standard. The preprocessing algorithm combining simplified-sorting Cholesky decomposition and low-complexity decoupled lattice reduction (LDLR) is proposed to reduce computational complexity and latency with parallelism improvement. In addition, K-best detection adopts a sorting-reduced strategy utilizing approximate ordered sequence. Compared with other published LRA K-best detection algorithms, simulation results show that our proposed algorithm has performance improvement. In addition, in order to save hardware resources, a folded K-best architecture and an optimized intermediate storage strategy are introduced. Furthermore, a fully pipelined VLSI architecture is designed in Semiconductor Manufacturing International Corporation (SMIC) 40-nm 1P9M technology to support the 8 × 8.64 -QAM MIMO-OFDM system. The detector can achieve 3.85-Gb/s data throughput at 641-MHz clock frequency with 0.71-μs latency. The proposed detector is competitive in terms of latency, throughput, and area efficiency to state-of-the-art works and can meet the data-rate requirement of the EUHT standard.

Reduced complexity lattice‐based multiple‐input multiple‐output schemes

Multiple-input multiple-output is being considered as a highly interesting topic for the new generation of wireless communication systems. The major challenge is how to enhance the link reliability while neither affecting the spectral efficiency nor the quality of service. To reduce the complexity of the maximum likelihood (ML) receiver, efforts have been focused on zero forcing (ZF) decoder using lattice reduction-aided (LRA) techniques. In this study, the authors propose a method that improves performance using the LRA-based precoding technique without increasing the decoder complexity. Their approach is to exploit the channel matrix to generate matrices for both the precoding and LRA detection technique. This makes it possible to achieve maximum orthogonality for the generated channel matrices while reducing considerably the noise effect. They focus on the use of the LRA-ZF for the ease of its implementation and low complexity. The proposed method outperforms LRA-minimum mean square error-based receiver and gets closer to ML receiver performance. The performance and complexity of the proposed scheme are discussed.

A Novel Low Complexity Lattice Reduction-Aided Iterative Receiver for Overloaded MIMO

A Novel Low Complexity Lattice Reduction-Aided Iterative Receiver for Overloaded MIMO

Lattice-Reduction-Aided Equalization for MIMO-FBMC Systems

In this letter, we propose use of a lattice reduction (LR) approach to enhance the performance of spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems using filter-bank multicarrier (FBMC) modulation. It is known that lattice-reduction-aided (LRA) MIMO receivers can achieve full spatial diversity. On the other hand, the presence of intrinsic interference in FBMC is widely regarded as a factor that prevents the system from taking advantage of spatial diversity when combined with SM-MIMO. We will show that with an adequate adaptation to FBMC modulation, the LR approach can be performed in a straightforward manner. Simulation results show that an LRA equalizer allows an FBMC-MIMO system to benefit more from the available spatial diversity and offers an interesting performance gain compared to the existing solutions with reasonable complexity.

Lattice-reduction-aided signal detection in spatial multiplexing MIMO–GFDM systems

Generalized Frequency Division Multiplexing (GFDM) is a promising candidate waveform for the air interface of the Fifth Generation (5G) communication networks. The flexibility of GFDM enables it to meet different application requirements of future networks. Nevertheless, the combination of GFDM and Multiple-Input Multiple-Output (MIMO) systems using Spatial Multiplexing (SM) is a necessity to achieve high spectral efficiency. However, spatial demultiplexing using common SM detection algorithms becomes an even more challenging task due to the inherent self-interference of GFDM. In this paper, we investigate a class of Lattice-Reduction-Aided (LRA) signal detection algorithms that can achieve an attractive tradeoff between performance and complexity in MIMO–GFDM systems. Simulation results show that with less increase in complexity, LRA algorithms can greatly improve the performance of the classical linear detector.

Joint algebraic coded modulation and lattice‐reduction‐aided preequalisation

Lattice-reduction-aided (LRA) preequalisation for the multiple-input/multiple-output broadcast channel has most often been considered for the uncoded case so far. However, recent advantages in the closely related field of integer-forcing equalisation, where the cancellation of the multiuser interference and the channel coding are combined, create doubt to this separated point of view. In this Letter, the philosophy of matching both the channel code and the complex-valued signal constellation to the same finite-field arithmetic is proposed. The consequences on the factorisation task present in LRA preequalisation are discussed and covered by numerical performance evaluations based on non-binary low-density parity-check codes.

A 3.1 Gb/s 8<inline-formula> <tex-math notation="LaTeX">$\,\times\,$ </tex-math></inline-formula>8 Sorting Reduced K-Best Detector With Lattice Reduction and QR Decomposition

This paper presents the VLSI implementation of a lattice-reduction-aided (LRA) detection system. The proposed system includes a QR decomposition, lattice reduction (LR) processor, and sorting-reduced (SR) K-best detector for 8 × 8 multiple-input multiple-output (MIMO) systems. The bit error rate of the proposed MIMO detection system only incurs approximately 3 dB of implementation loss compared with optimal maximum likelihood detection with 64-quadratic-amplitude modulation. The proposed processor can also support different throughput requirements by adjusting the stage number of LR. The SR K-best detector can achieve 3.1 Gb/s throughput with 0.24-ns latency. The throughput of the system reaches 585 Mb/s if one channel preprocessing can support 72 symbol detections. The corresponding energy per bit is 63 pJ/bit, which is the smallest value achieved to date. This paper presents the first VLSI implementation of a complete LRA K-best detector with an 8 × 8 dimension.

Lattice-Reduction-Aided Conditional Detection for MIMO Systems

We introduce a low-complexity detector with near-optimal performance for transmission over multi-antenna systems. By using lattice basis reduction for generating almost orthogonal channel submatrices, we enhance the conditional optimization technique to implement a fast yet efficient detector. The lattice-reduction-aided (LRA) conditional method is presented as a general detection technique over fading channels to yield significant saving in computational complexity while achieving close to Maximum Likelihood (ML) error performance. By employing the orthogonality defect factor as a universal measure to select a near-orthogonal channel submatrix for conditional detection, we implement efficient detectors for MIMO systems. In particular, an almost optimal decoder with linear complexity for the Golden code is presented over quasi-static channels.

Lattice Reduction-Aided Successive Interference Cancelation for MIMO Interference Channels

In multiple-input-multiple-ouput (MIMO) interference channels (IFCs), interference alignment (IA) with zero-forcing (ZF) linear detection can be used to achieve the maximum degrees of freedom (DoFs). However, ZF linear detection usually degrades the performance due to the noise enhancement in practical systems. In this paper, we propose lattice reduction (LR)-aided successive interference cancelation (SIC) in conjunction with IA over lattice for three-user (and extendable to $K$-user) MIMO IFCs in which the interfering signals aligned over the lattices are detected and canceled rather than nulled out. To complete the proposed LR-aided SIC method, the detection ordering and the precoding matrix that minimize the mean square error are also determined.

Algorithm and hardware design of a 2D sorter-based K-best MIMO decoder

In the field of multiple input multiple output (MIMO) decoder, K-best has been well investigated because it guarantees an SNR-independent fixed-throughput with a performance close to the optimal maximum likelihood detection (MLD). However, the complexity of its expansion and sorting tasks is significantly affected by the constellation size W. In this paper, we propose an algorithm and hardware design of a 2D sorter-based K-best MIMO decoder whose complexity is negligibly affected by W. The main novelties of the algorithm are the following: (1) Direct expansion and parent node grouping ideas are proposed for reducing the expansion task’s complexity. (2) Two-dimensional (2D) sorter is proposed for simplifying the sorting task. The hardware design of the decoder supports up to 256-QAM modulation, which aims to apply into 4 × 4 MIMO 802.11n and 11ac systems. The paper shows that the proposed decoder outperforms the Bell Labs layered space-time (BLAST) minimum mean square error (MMSE) and lattice-reduction aided (LRA) MMSE, and is close to the full K-best in terms of bit error rate (BER) performance. The hardware design of the decoder is synthesized in application specific integrated circuit (ASIC) and compared with the previous works. As a result, it achieves the highest throughput (up to 2.7 Gbps), consumes the least power (56 mW), obtains the best hardware efficiency (15.2 Mbps/Kgate), and has the shortest latency (0.07 µs).

Lattice-Reduction-Aided Detection with Successive Interference Cancelation for Multiuser Space-Time Block Coded Systems

Effective detectors with low-complexity are considered for the Alamouti’s multiuser space-time block coded (STBC) systems. Viewing the noiseless received signals from Q users as a lattice with basis vectors being the columns of the total channel matrix H, we apply lattice reduction to transform the original basis into a nearly orthogonal one which improves the decision regions against noise. Then, linear detection using zero-forcing (ZF) and minimum-mean-square-error (MMSE) methods is performed on the transformed basis to detect transmitted signals from the Q users. These lattice-reduction-aided (LRA) linear detectors significantly improve BER of the linear detectors and, more importantly, allow us to achieve full diversity at high Eb/N0 regions.

Low-Complexity Lattice Reduction-Aided Regularized Block Diagonalization for MU-MIMO Systems

By employing the regularized block diagonalization (RBD) preprocessing technique, the MU-MIMO broadcast channel is decomposed into multiple parallel independent SU-MIMO channels and achieves the maximum diversity order at high data rates. The computational complexity of RBD, however, is relatively high due to two singular value decomposition (SVD) operations. In this letter, a low-complexity lattice reduction-aided RBD is proposed. The first SVD is replaced by a QR decomposition, and the orthogonalization procedure provided by the second SVD is substituted by a lattice-reduction whose complexity is mainly contributed by a QR decomposition. Simulation results show that the proposed algorithm can achieve almost the same sum-rate as RBD, substantial bit error rate (BER) performance gains and a simplified receiver structure, while requiring a lower complexity.

Loop‐Reduction LLL Algorithm and Architecture for Lattice‐Reduction‐Aided MIMO Detection

We propose a loop‐reduction LLL (LR‐LLL) algorithm for lattice‐reduction‐aided (LRA) multi‐input multioutput (MIMO) detection. The LLL algorithm is an iterative algorithm that contains many check and process operations; however, the traditional LLL algorithm itself possesses a lot of redundant check operations. To solve this problem, we propose a look‐ahead check technique that not only reduces the complexity of the LLL algorithm but also produces the lattice‐reduced matrix which obeys the original LLL criterion. Simulation results show that the proposed LR‐LLL algorithm reduces the average number of loops or computation complexity. Besides, it also shortens the latency of clock cycles about 19.4%, 29.1%, and 46.1% for 4 × 4, 8 × 8, and 12 × 12 MIMO systems, respectively.

Quantization Error Correction Schemes for Lattice-Reduction Aided MIMO Detectors

Lattice reduction aided (LRA) linear detectors have been known to achieve near optimal performance at low complexity. However, one weakness of LRA detector is that the quantization step in LRA detector is not optimal. Based on simulation results, we show that most of detection errors in LRA linear detectors are due to quantization errors. We then propose two methods to correct the quantization errors. In the first method, sphere detectors are introduced to correct quantization errors at low additional complexity. As a second approach, we propose a list quantization scheme which can generate a list of candidate symbols from the original LRA estimated symbols. From these listed symbols, decisions are made according to the minimum Euclidean distance between the received and estimated points. It is shown by simulations that both methods provide significant BER performance improvements with only a small additional complexity.

Gram-Schmidt Combined LLL Lattice-Reduction Aided Detection in MIMO Systems

This paper proposes an improved lattice-reduction aided (LRA) MMSE detection scheme, based on the Gram-Schmidt (GS) procedure. The proposed scheme reduces the column vectors of the MIMO channel matrix, by using the LLL algorithm followed by the GS procedure in order to transform the channel matrix into a new one which has mutually purely orthogonal column vectors. Compared to the conventional LRA MMSE detector, the proposed detector achieves a very good BER performance, almost equivalent to those using the ML detector in the 4 × 4 MIMO system at the cost of a slightly larger computational complexity.

Low complexity lattice reduction scheme for STBC two-user uplink MIMO systems

Abstract Recently, a lattice reduction-aided (LRA) multiple-input multiple-output detection scheme has been proposed in junction with linear (as well as nonlinear) detectors. It is well known that these schemes provide a full diversity, and its complexity is comparable to that of linear detectors for the block fading channels. For the fast varying channels, however, the decoding complexity of LRA detection scheme is unreasonably high. This article proposes an efficient iterative lattice reduction (LR) scheme for an uplink system with two receive antennas at the base station and two users, each employing the Alamouti space-time block code (STBC). By taking advantage of the certain inherent STBC structure of transmitted symbols from users, the proposed scheme provides the same performance as a conventional LR while saving about 80% computational complexity. We also show that it can be successfully extended to handle the scenario where another interfering user, who is also employing the Alamouti STBC, is present.

A Reduced Complexity Quantization Error Correction Method for Lattice Reduction Aided Vector Precoding

A reduced complexity quantization error correction method for lattice reduction aided (LRA) vector precoding is proposed. For LRA vector precoding, Babai's approximation procedure can generate quantization errors leading to performance loss. Instead of making a list to correct all possible errors as is done in the existing scheme, we propose a novel method in which only a subset of all possible errors are corrected. The size of the subset is determined by the probability distribution of the number of actual errors. Thus, the computation complexity of our correction procedure is reduced with little performance loss compared with the existing correction scheme.

Pre-Processed Recursive Lattice Reduction for Complexity Reduction in Spatially and Temporally Correlated MIMO Channels

In this letter, a pre-processed lattice reduction (PLR) scheme is developed for the lattice reduction aided (LRA) detection of multiple input multiple-output (MIMO) systems in spatially correlated channel. The PLR computes the LLL-reduced matrix of the equivalent matrix, which is the product of the present channel matrix and unimodular transformation matrix for LR of spatial correlation matrix, rather than the present channel matrix itself. In conjunction with PLR followed by recursive lattice reduction (RLR) scheme [7], pre-processed RLR (PRLR) is shown to efficiently carry out the LR of the channel matrix, especially for the burst packet message in spatially and temporally correlated channel while matching the performance of conventional LRA detection.