Achieve near-ML Performance Research Articles

Symbol detection based on a novel discrete harmony search algorithm in MIMO-FBMC/OQAM system

Due to its high spectral efficiency and various other advantages, filter bank multicarrier/offset quadrate amplitude modulation (FBMC/OQAM) has long been considered as a candidate waveform for the fifth generation (5G) and beyond telecommunication technologies. On the other hand, it is possible to both increase the data rate and alleviate the channel fading effects by using the multiple-input multiple-output (MIMO) antenna structure in the FBMC/OQAM transceiver. However, since the symbol detection is an indispensable task to be fulfilled in wireless communication, it is crucial to employ an efficient symbol detector at the MIMO-FBMC/OQAM receiver. Maximum likelihood (ML) detector, which always finds the optimal symbols by trying all of the possible symbol combinations likely to be transmitted, is known for its extremely high computational complexity making it impractical to be used in any system. On the other hand, it is possible to both considerably reduce the ML complexity and achieve the near-ML performance by optimizing the symbol vectors instead of implementing an exhaustive search. Since searching for the optimal symbol combination in discrete space is a combinatorial optimization problem, we developed a novel discrete harmony search (disHS) algorithm to perform this operation. According to the simulation results, the newly developed disHS algorithm not only achieves near-ML performance with lower computational complexity, but also clearly leaves behind the other symbol detectors considered in this paper.

Low Latency Energy-Efficient Neural Decoders for Block Codes

Neural decoders are being explored for 5G and beyond communication networks which have ultra-low-latency and energy-efficiency requirements. We consider several ultra-short linear and non-linear block codes and design neural decoders for them, which (i) provide near maximum-likelihood (ML) performance in terms of bit and block error rates, and (ii) have low decoding complexity (and hence, latency and energy consumption) in terms of the number of hidden layers and hidden nodes. We explore (i) single-label, (ii) multi-label, and (iii) concatenated coding based decoders. We find that single-label decoders with a single hidden layer having a sufficient number of nodes achieve near-ML performance. Since the number of output nodes required in single-label decoders is exponential in the message length, we investigate a multi-label neural decoder requiring a significantly lower number of output nodes but having decreased performance in terms of block error rate. To eliminate extra errors, we concatenate an outer code with the original code as the inner code. The inner and outer codes are decoded by multi-label and single-label neural decoders, respectively, leading to better block error performance than that is achievable using multi-label decoders.

Recursive Decoding of Reed-Muller Codes Starting With the Higher-Rate Constituent Code

Recursive list decoding of Reed-Muller (RM) codes, with moderate list size, is known to approach maximum-likelihood (ML) performance of short length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\leq 256)$ </tex-math></inline-formula> RM codes. Recursive decoding employs the Plotkin construction to split the original code into two shorter RM codes with different rates. In contrast to the standard approach which decodes the lower-rate code first, the method in this paper decodes the higher-rate code first. This modification enables an efficient permutation-based decoding technique, with permutations being selected on the fly from the automorphism group of the code using soft information from a channel. Simulation results show that the error-rate performance of the proposed algorithms, enhanced by a permutation selection technique, is close to that of the automorphism-based recursive decoding algorithm with similar complexity for short RM codes, while our decoders perform better for longer RM codes. In particular, it is demonstrated that the proposed algorithms achieve near-ML performance for short RM codes and for RM codes of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{m}$ </tex-math></inline-formula> and order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m-3$ </tex-math></inline-formula> with reasonable complexity.

Sub-Terahertz Wireless System Using Dual-Polarized Generalized Spatial Modulation With RF Impairments

In this paper, we address a multiple-input multiple-output (MIMO) communication system based on generalized spatial modulation (GSM) and dual-polarized (DP) antennas in sub-TeraHertz (sub-THz) bands to improve the Spectral Efficiency (SE) while reducing the spatial correlation effect and the space occupancy. Moreover, the joint Maximum Likelihood (ML) detector and a Modified Ordered Block Minimum Mean-Squared Error (MOB-MMSE) detector algorithm are proposed to detect jointly the complex symbols and the virtual bits conveyed by the activated polarization and the transmit antenna combination index. MOB-MMSE can achieve near-ML performance with low complexity. The performance of DP-GSM system over correlated Rayleigh/Rician fading and indoor sub-THz channels is studied. Provided results show that DP-GSM system is robust to the spatial correlation effects under Rician fading channel. In addition, an average bit-error probability (ABEP) upper bounding is derived and analyzed for the DP-GSM system over correlated Rayleigh/Rician fading channels. Since the sub-THz band suffers from many technological limitations and severe RF-impairments such as low transmit output power and important phase noise (PN), the DP-GSM system is studied by considering the sub-THz impairments. Moreover, the Dual Polarized Spatial Multiplexing (DP-SMX) and the Uni-Polarized GSM (UP-GSM) are compared with the DP-GSM system. The results reveal that DP-GSM with low order modulation schemes as QPSK outperforms the UP-GSM. Besides, DP-GSM and DP-SMX provide a good performance up to medium PN, which is interesting for sub-THz bands, but DP-GSM can reduce the transceiver cost by using a lower number of RF chains when the used transmitter architecture is based on RF-switching.

Low-Complexity Detection for Multiple-Mode OFDM with Index Modulation

Multiple-mode orthogonal frequency division multiplexing with index modulation (MM-OFDM-IM) is a recently proposed multicarrier transmission technique, which transmits distinguishable constellations (modes) according to their full permutations. For an uncoded system, the maximum-likelihood (ML) detector achieves the optimal performance, but its computational complexity is extremely high due to a large number of symbol modes. Existing low-complexity detectors may output an illegal mode permutation, which leads to catastrophic errors in the demodulation. redIt is well known that sphere decoding algorithms can reduce the computational complexity effectively and achieve near-ML bit error rate (BER) performance. In this paper, employing a sphere-decoding-like algorithm, we propose a novel detector, which can achieve near-ML performance with considerably low computational complexity. For coded MM-OFDM-IM systems, we propose a simplified log-likelihood ratio (LLR) calculation algorithm to achieve near-optimal coded BER performance with considerably low computational complexity. Computer simulation and numerical results demonstrate that the proposed detectors can achieve outstanding performance at the cost of low computational complexity.

An Efficient ZJ-Based Decoding Algorithm for Space-Time Trellis Codes in Slow Rayleigh Fading Channels

In this paper, we propose a computationally efficient decoding algorithm for space-time trellis codes in slow Rayleigh fading channels. The proposed scheme is based on a stack algorithm with two key ideas: (i) a variable stack size depending upon the signal-to-noise ratio to avoid the exhaustive search of paths and (ii) a normalized metric, which is defined as each cumulative path metric divided by its own length in the stack, to provide an appropriate comparison of the paths with different lengths. Simulation results demonstrate that the proposed algorithm achieves near-ML performance with significant reduction in complexity, compared with the conventional Viterbi algorithm.

Random-Restart Reactive Tabu Search Algorithm for Detection in Large-MIMO Systems

We present a low-complexity algorithm based on reactive tabu search (RTS) for near maximum likelihood (ML) detection in large-MIMO systems. The conventional RTS algorithm achieves near-ML performance for 4-QAM in large-MIMO systems. But its performance for higher-order QAM is far from ML performance. Here, we propose a random-restart RTS (R3TS) algorithm which achieves significantly better bit error rate (BER) performance compared to that of the conventional RTS algorithm in higher-order QAM. The key idea is to run multiple tabu searches, each search starting with a random initial vector and choosing the best among the resulting solution vectors. A criterion to limit the number of searches is also proposed. Computer simulations show that the R3TS algorithm achieves almost the ML performance in 16 × 16 V-BLAST MIMO system with 16-QAM and 64-QAM at significantly less complexities than the sphere decoder. Also, in a 32 × 32 V-BLAST MIMO system, the R3TS performs close to ML lower bound within 1.6 dB for 16-QAM (128 bps/Hz), and within 2.4 dB for 64-QAM (192 bps/Hz) at 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> BER.

Efficient Linear Programming Decoding of HDPC Codes

We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts from redundant parity checks. Second, we propose an efficient mixed integer decoder utilizing the branch and bound method. We further enhance the proposed decoders by removing inactive constraints and by adapting the parity check matrix prior to decoding according to the channel observations. Based on simulation results the proposed decoders achieve near-ML performance with reasonable complexity.

A New Signal Detection Method for Spatially Multiplexed MIMO Systems and Its VLSI Implementation

This brief proposes a new signal detection method called QR ordered successive interference cancellation (OSIC) with candidates (QOC) method for spatially multiplexed multiple-input-multiple-output (MIMO) systems. By using the OSIC algorithm and the maximum-likelihood (ML) metric, the proposed method achieves near-ML performance without requiring a large number of candidates. Although the proposed method can be used for both hard and soft decoding systems, it is particularly useful for soft decoding systems since the log-likelihood-ratio (LLR) values for all the bits can efficiently be computed without using LLR estimation. The proposed method is also suitable for very large scale integration (VLSI) implementation since it leads to a fixed throughput system. A QOC detector for a 4 times4 16-quadrature-amplitude-modulation (16-QAM) MIMO system has been designed and synthesized with a 0.13-mum complimentary metal-oxide-semiconductor (CMOS) technology. The implementation results show that the proposed detector reduces the hardware complexity by 73% relative to a K-best detector.

Reduced Complexity K-Best Sphere Decoder Design for MIMO Systems

The sphere decoding algorithm is widely used for maximum likelihood (ML) detection in multiple-input multiple-output (MIMO) systems, wherein the K-best sphere decoding algorithm is well appreciated for its fixed complexity and throughput. However, to achieve near-ML performance, K needs to be sufficiently large, which leads to large computational complexity in path expansion, sorting, and path updating. In this paper, we propose two efficient decoding schemes that can significantly reduce the average K value and thus the total computational complexity without sacrificing performance. We further present a novel sorting architecture that can save about 70% of the sorting operations compared with the bubble sort method. It is estimated that, for the example 4×4 64 QAM MIMO system, 68% of the total computational complexity can be saved over the conventional design by applying all the proposed techniques.

Low Complexity Tree Searching-Based Iterative Precoding Techniques for Multiuser MIMO Broadcast Channel

In this letter, we propose two computationally efficient precoding algorithms that achieve near-ML performance for multiuser MIMO downlink. The proposed algorithms perform tree expansion after lattice reduction. The first full expansion is tried by selecting the first level node with a minimum metric, constituting a reference metric. To find an optimal sequence, they iteratively visit each node and terminate the expansion by comparing node metrics with the calculated reference metric. By doing this, they significantly reduce the number of undesirable node visit. Monte-Carlo simulations show that both proposed algorithms yield near-ML performance with considerable reduction in complexity compared with that of the conventional schemes such as sphere encoding.

Algorithm and implementation of the K-best sphere decoding for MIMO detection

K-best Schnorr-Euchner (KSE) decoding algorithm is proposed in this paper to approach near-maximum-likelihood (ML) performance for multiple-input-multiple-output (MIMO) detection. As a low complexity MIMO decoding algorithm, the KSE is shown to be suitable for very large scale integration (VLSI) implementations and be capable of supporting soft outputs. Modified KSE (MKSE) decoding algorithm is further proposed to improve the performance of the soft-output KSE with minor modifications. Moreover, a VLSI architecture is proposed for both algorithms. There are several low complexity and low-power features incorporated in the proposed algorithms and the VLSI architecture. The proposed hard-output KSE decoder and the soft-output MKSE decoder is implemented for 4/spl times/4 16-quadrature amplitude modulation (QAM) MIMO detection in a 0.35-/spl mu/m and a 0.13-/spl mu/m CMOS technology, respectively. The implemented hard-output KSE chip core is 5.76 mm/sup 2/ with 91 K gates. The KSE decoding throughput is up to 53.3 Mb/s with a core power consumption of 626 mW at 100 MHz clock frequency and 2.8 V supply. The implemented soft-output MKSE chip can achieve a decoding throughput of more than 100 Mb/s with a 0.56 mm/sup 2/ core area and 97 K gates. The implementation results show that it is feasible to achieve near-ML performance and high detection throughput for a 4/spl times/4 16-QAM MIMO system using the proposed algorithms and the VLSI architecture with reasonable complexity.

Silicon complexity for maximum likelihood MIMO detection using spherical decoding

Multiple-input multiple-output (MIMO) wireless systems increase spectral efficiency by transmitting independent signals on multiple transmit antennas in the same channel bandwidth. The key to using MIMO is in building a receiver that can decorrelate the spatial signatures on the receiver antenna array. Original MIMO detection schemes such as the vertical Bell Labs layered space-time (VBLAST) detector use a nulling and cancellation process for detection that is sub-optimal as compared to constrained maximum likelihood (ML) techniques. This paper presents a silicon complexity analysis of ML search techniques for MIMO as applied to the HSDPA extension of UMTS. For MIMO constellations of 4/spl times/4 QPSK or lower, it is possible to perform an exhaustive ML search in today's silicon technologies. When the search complexity exceeds technology limits for high complexity MIMO constellations, it is possible to apply spherical decoding techniques to achieve near-ML performance. The paper presents an architecture for a 4/spl times/4 16QAM MIMO spherical decoder with soft outputs that achieves 38.8 Mb/s over a 5-MHz channel using only approximately 10 mm/sup 2/ in a 0.18-/spl mu/m CMOS process.

Efficient detection algorithms for mimo channels: a geometrical approach to approximate ml detection

It is well known that suboptimal detection schemes for multiple-input multiple-output (MIMO) spatial multiplexing systems (equalization-based schemes as well as nulling-and-cancelling schemes) are unable to exploit all of the available diversity, and thus, their performance is inferior to ML detection. Motivated by experimental evidence that this inferior performance is primarily caused by the inability of suboptimal schemes to deal with (i.e., poorly conditioned) channel realizations, we study the decision regions of suboptimal schemes for bad channels. Based on a simplified model for bad channels, we then develop two computationally efficient detection algorithms that are robust to bad channels. In particular, the novel sphere-projection algorithm (SPA) is a simple add-on to standard suboptimal detectors that is able to achieve near-ML performance and significantly increased diversity gains. The SPA's computational complexity is comparable with that of nulling-and-cancelling detectors and only a fraction of that of the Fincke-Phost sphere-decoding algorithm for ML detection.