Low-Complexity Soft-Output Signal Detection Based on Improved Kaczmarz Iteration Algorithm for Uplink Massive MIMO System.

In this work, we propose low-complexity detectors for massive multiple-input multiple-output (MIMO) systems. Particularly, we leverage variants of truncated polynomial expansion (TPE) in order to reduce the computational complexity of the signal detection in the uplink direction. Linear detectors such as zero-forcing (ZF) and minimum mean square error (MMSE) involve expensive matrix-matrix multiplication and matrix inversion operations. TPE-based detectors are appropriate candidates for approximating these linear detectors. However, tuning the normalization factor of TPE-based detectors may require calculating the minimum and the maximum eigenvalues of the channel Gram matrix. These calculations become computationally expensive for some massive MIMO systems, especially for systems with a large ratio of single-antenna user terminals to the number of antennas at the base station, i.e., loading factor. We propose to tune the normalization factor using appropriate approximations for the extreme eigenvalues. The proposed TPE-based detectors exhibit a bit error performance similar to that of the TPE-based detector with the optimal normalization factor. Moreover, our proposed detectors achieve the error performance of ZF and MMSE for different loading factors of spatially correlated and uncorrelated massive MIMO channels. The computational complexity of the proposed detector is proportional to the number of base station antennas and the number of users.

With a large number of antennas at the transmitter and receiver, massive multiple-input multiple-output (MIMO) systems can achieve substantially high spectral efficiency as well as high stability and reliability. Nevertheless, one of the major challenges for its practical use is its computational complexity for symbol detection that grows exponentially with the number of antennas. In this work, we focus on a low complexity implementation of massive MIMO detector based on matched filter (MF) detection with parallel interference cancellation (PIC). In general, MF-based detector performs poorly in the high SNR region. Nevertheless, with the help of powerful channel coding such as low-density parity-check (LDPC) codes and the well-designed PIC, the resulting error performance of the proposed MF-PIC can approach or even outperform the conventional minimum mean square error (MMSE)-based detector with much less complexity. Furthermore, due to its parallel structure, low latency implementation based on parallel architecture is possible and thus is suitable for practical massive MIMO systems.

Massive multiple-input multiple-output (MIMO) technology for wireless communication is considered a key technology for the future fifth-generation (5G) communication networks. To reduce the propagation loss of channel, MIMO systems with analog or digital hybrid precoders and combiners (HPC) architecture have been used. This review paper presents the various types of analog and digital HPC designs for the massive MIMO communication systems that were investigated within the last decade. The reviewed systems are useful for both single-user (SU) and multi-user MIMO (MU-MIMO) systems. The key parameter of the study was spectral efficiency (SE), signal-to-noise ratio (SNR), signal-to-interference pulse noise ratio (SINR), system sum-rate (SR) performance, computational complexity (CC), co-channel interference (CCI), inter-primary base station interference (IPBSI), multiuser interference (MUI), effective desired channel gain (EDCG), and minimum mean square error (MMSE).

Minimum mean square error (MMSE) linear detector is able to achieve the near-optimal bit error rate (BER) performance for uplink multi-user massive Multiple-Input Multiple-Output (MIMO) systems due to the increase in the number of base station (BS) antennas. However, this detector involves matrix inversion with high complexity, especially when the number of users is large. In order to reduce the complexity, in this paper, a low-complexity MMSE detector algorithm based on the Damped Jacobi (DJ) method is proposed. Further, a simple approach to determine the optimum and quasi-optimum damped parameter by exploiting the massive MIMO channel property of asymptotic orthogonality is developed. The analysis shows that the proposed algorithm can reduce the complexity of the classical MMSE detector by about one order of magnitude without performance loss. Finally, it is verified through simulation results that the proposed algorithm outperforms the recently proposed linear detector based on the conventional Jacobi method, and achieves the near-optimal performance of the classical MMSE detector with a small number of iterations in Rayleigh fading channels.

For Massive multiple-input multiple output (MIMO) systems, many algorithms have been proposed for detecting spatially multiplexed signals, such as reactive tabu search (RTS), minimum mean square error (MMSE), etc. As a heuristic neighborhood search algorithm, RTS is particularly suitable for signal detection in systems with large number of antennas. In this paper, we propose a strategy to reduce the neighborhood searching space of the traditional RTS algorithms. For this, we introduce a constellation constraints (CC) structure to determine whether including a candidate vector into the RTS searching neighborhood. By setting a pre-defined threshold on the symbol constellation, the Euclidean distance between the estimated signal and its nearest constellation points are calculated, and the threshold and distance are compared to separate the reliable estimated signal from unreliable ones. With this structure, the proposed CC-RTS algorithm may ignore a significant number of unnecessary candidates in the RTS neighborhood searching space and greatly reduce the computational complexity of the traditional RTS algorithm. Simulation results show that the BER performance of the proposed CC-RTS algorithm is very close to that of the traditional RTS algorithm, and with about 50% complexity reduction with the same signal-to-noise (SNR) ratio.

This paper considers the uplink of a single-cell large-scale multiuser multiple-input multiple-output (MU-MIMO) system. The transmitted data is detected by linear receivers at the base station (BS), that is, maximum ratio combining (MRC), zero-forcing (ZF) and minimum mean square error (MMSE). New non-asymptotic outage expressions that are valid for any number of BS antennas are derived. It is shown that the MMSE scheme always achieves the best outage performance, and the ZF scheme outperforms the MRC scheme in the high signal-to-noise-ratio (SNR) regime, while the opposite holds in the low SNR regime. We also demonstrate that when the number of BS antennas is very large and the number of users is fixed, the asymptotic outage probability tends to zero, providing that the channel state information (CSI) is perfect. However, if both the number of BS antennas and the number of users grow large, it would be a different matter. Extensive numerical results are presented to verify the theoretical analysis.

This paper focuses on the uplink (UL) of a single-cell massive multiple-input multiple-output (MIMO) systems in which the base station (BS) equipped with M antennas communicates with K single-antenna user equipments (UEs). Due to the finer spatial resolution achieved by a huge number of antennas at the base stations, these systems can substantially reduce intra-cell interference with simple signal processing. However, most precoding schemes exhibit prohibitively high computation complexity as the system dimensions increase. For example, the near-optimal minimum mean squared error (MMSE) precoding requires the inversion of a large matrix. To reduce further the complexity, the truncated polynomial expansion (TPE) is applied to approximate the inverse of large matrices that appear on the expressions of the optimal linear transceivers. A key requirement to achieve good detection performance is to find good polynomial coefficients (J), where the polynomial coefficients (J) are optimized to maximize the system performance. The simulation results show that the proposed scheme provides very close to optimal performance while reducing significantly the computational complexity.

Matrix inversion in massive multiple-input multiple-output (MIMO) precoding imposes significant burden on the energy efficiency and processing latency of baseband units. In this paper, we first propose a memristor crossbar based in-memory computing circuit capable of supporting both zero-forcing (ZF) and minimum mean square error (MMSE) precoding. The circuit features a reduced matrix size and enables faster one-step computation without the need for timing control. Secondly, to address the computational inaccuracy caused by the limited conductance range of memristors, we develop an optimized matrix-to-conductance mapping scheme that jointly considers device physical constraints and matrix statistics, achieving over 60% reduction in relative computation error compared with baseline scheme. An associated lightweight circuit enhancement ensures compatibility with practical crossbar architectures, without incurring significant hardware overhead. Thirdly, we establish a memristor programming time model grounded in device-level potentiation and depression dynamics. The analysis yields closed-form expressions for the expected programming time and its upper bound, and is further validated through Monte Carlo simulations, enabling accurate estimation of the system throughput. Simulation results demonstrate that the proposed circuit achieves a bit error rate comparable to that of 64-bit floating-point precoding, while delivering over 100× improvement in both energy and area efficiency compared with the NVIDIA RTX A2000 graphics processing unit (GPU).

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Multiple‐input multiple‐output (MIMO) technology plays a crucial role in the field of wireless communications. As one of the key technologies, MIMO signal detection ensures the reliability of communication systems and achieves high throughput transmission. In this paper, to find a high‐performance and low‐complexity detection algorithm, a hybrid detection algorithm is proposed based on the K‐best detection algorithm. The hybrid algorithm employs the minimum mean square error (MMSE) linear detection algorithm combined with sorted QR decomposition (SQRD) for preprocessing, followed by signal detection using the K‐best detection algorithm. Compared with the traditional K‐best detection algorithm, the proposed method shows significant performance improvement. To address the computational complexity issue caused by the fixed K value in each layer of the hybrid detection algorithm, an adaptive threshold algorithm is introduced to select an appropriate K value for each layer, significantly reducing the algorithm's complexity. On the hardware implementation level, not only is the overall algorithm architecture optimized but a lookup table (LUT) based sorting algorithm is also proposed to address the sorting delay issue in the hybrid detection algorithm. Comprehensive analysis shows that this detector, implemented in a 28‐nm process, achieves a throughput of 4.8 Gbps at a clock frequency of 769 MHz, presenting a significant advantage compared with other literature.

Being increasingly spectral and energy efficient, massive multiple-input multiple-output (MIMO) is envisaged as a potential technology for fifth generation (5G) wireless communication networks. Radio spectrum has become a scarce resource in wireless communications and consequently imposes excessive cost on the high data rate transmission. Several linear and non linear detection techniques such as Zero-Forcing (ZF), Minimum Mean Square Error (MMSE), and Vertical Bell-Labs Layered Space Time (VBLAST) have been introduced. The purpose of such schemes is to mitigate the signal detection problems which are based on trade-offs between the bit error rate (BER) performance and computational complexities. The challenge in the design of massive-MIMO systems is developing less complex and efficient detection algorithms. The problem in building a receiver for massive-MIMO is to de-correlate the spatial signatures on the receiver antenna array. In this paper, we propose a novel algorithm viz: Hybrid n-Bit Heuristic Assisted-VBLAST (HHAV) to perform an optimum decoding. We have simulated this structure in dynamic Rayleigh fading channel. We have also evaluated the AMP algorithm with two threshold functions which include AMP with ternary distribution (AMPT) and AMP with Gaussian distribution (AMPG). Numerical results confirm that HHAV algorithm performs significantly better than the in vogue aforementioned detection systems as introduced in recent years.

In cellular communications, recently Multi In Multi Out (MIMO) and Massive MIMO research is getting attention for the need of high data rates in Long Term Evolution Advanced(LTE-A) and 5G Communications. In MIMO baseband signal processing at physical layer, both the channel estimation and the detection algorithms play a crucial role. In this paper it is discussed the estimation algorithms least square (LS) and minimum mean square error (MMSE) and the channel detection algorithms Zero Forcing (ZF) and MMSE. Currently none of the channel estimation algorithms of LTE-A offers twin advantages of low battery consumption and very low latency, which is a key requirement of 5G. It is expected the massive MIMO with 128 or more antennas will be a norm at 5G base stations. To achieve the ultra-low latency, the matrix computations for massive MIMO are the very big bottleneck in realizing the channel estimation and massive MIMO detection algorithms. For the optimization of the 5G Massive MIMO channel estimation and detection algorithms, the prerequisite is massive complex matrix inversion speed. In this paper, a parallel processing based coding scheme is proposed by using Gauss-Jordan elimination kernel algorithm on a single instruction multiple data (SIMD) stream vector processor to realize a complex matrix inverse with optimum speed which is the need of 5G channel estimation and detection.

This work focuses on studying signal detection using three different equalization techniques, namely: Zero Forcing (ZF), Minimum Mean Square Error (MMSE) and Beam Forming (BF), for a 4×4 MIMO-system. Results show that ZF equalization is the simplest technique for signal detection, However, Beam Forming (BF) gives better Bit Error Rate (BER) performances at high Signal to Noise Ratio (SNR) values with some complexity in design. For more antennas at the base station, it is too complex to design the weight matrix for ZF, however, it is suitable for BF with the help of good quality digital signal processors. Performance of MIMO-system, with 8 antennas at the base station using BF equalization, is analysed to get BER values at different SNR. Results show a considerable improvement in BER for 8 antennas at the base station.

We present a general framework for the characterization of the packet error probability achievable in cell-free Massive multiple-input multiple output (MIMO) architectures deployed to support ultra-reliable low-latency (URLLC) traffic. The framework is general and encompasses both centralized and distributed cell-free architectures, arbitrary fading channels and channel estimation algorithms at both network and user-equipment (UE) sides, as well as arbitrary combing and precoding schemes. The framework is used to perform numerical experiments on specific scenarios, which illustrate the superiority of cell-free architectures compared to cellular architectures in supporting URLLC traffic in uplink and downlink. Also, these numerical experiments provide the following insights into the design of cell-free architectures for URLLC: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) minimum mean square error (MMSE) spatial processing must be used to achieve the URLLC targets; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) for a given total number of antennas per coverage area, centralized cell-free solutions involving single-antenna access points (APs) offer the best performance in the uplink, thereby highlighting the importance of reducing the average distance between APs and UEs in the URLLC regime; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iii</i> ) this observation applies also to the downlink, provided that the APs transmit precoded pilots to allow the UEs to estimate accurately the precoded channel.

As the promising novel multiple access scheme for the 5th generation (5G) wireless communication system, pattern division multiple access (PDMA) technology can improve the spectral efficiency and support the massive connection based on the reasonable unequal diversity between users. Compared with traditional multiple access technologies, PDMA brings more serious multiple address interference to hinder the multiuser detection. The universal detection algorithm with low complexity and high performance is one of the main challenges of PDMA technology. In this paper, we proposed a new iterative detection and decoding algorithm, which is a successive interference cancellation (SIC) iterative processing based on the minimum mean square error (MMSE) detection and channel decoding algorithm. It is essentially a SIC iterative processing based on some users' information has been correctly decoded by the MMSE detection and the channel decoder. The proposed multiuser detection algorithm can prevent the error propagation by the cyclic redundancy check (CRC). The simulation results show that the proposed algorithm can get significant performance gains over traditional multiuser detection algorithms.