Scaling up MIMO: Opportunities and Challenges with Very Large Arrays

This paper surveys recent advances in the area of very large MIMO systems. With very large MIMO, we think of systems that use antenna arrays with an order of magnitude more elements than in systems being built today, say a hundred antennas or more. Very large MIMO entails an unprecedented number of antennas simultaneously serving a much smaller number of terminals. The disparity in number emerges as a desirable operating condition and a practical one as well. The number of terminals that can be simultaneously served is limited, not by the number of antennas, but rather by our inability to acquire channel-state information for an unlimited number of terminals. Larger numbers of terminals can always be accommodated by combining very large MIMO technology with conventional time- and frequency-division multiplexing via OFDM. Very large MIMO arrays is a new research field both in communication theory, propagation, and electronics and represents a paradigm shift in the way of thinking both with regards to theory, systems and implementation. The ultimate vision of very large MIMO systems is that the antenna array would consist of small active antenna units, plugged into an (optical) fieldbus.Comment: Accepted for publication in the IEEE Signal Processing Magazine, October 201

Reduced complexity detection for massive MIMO-OFDM wireless communication systems

PhD ThesisThe aim of this thesis is to analyze the uplink massive multiple-input multipleoutput with orthogonal frequency-division multiplexing (MIMO-OFDM) communication systems and to design a receiver that has improved performance with reduced complexity. First, a novel receiver is proposed for coded massive MIMO-OFDM systems utilizing log-likelihood ratios (LLRs) derived from complex ratio distributions to model the approximate effective noise (AEN) probability density function (PDF) at the output of a zero-forcing equalizer (ZFE). These LLRs are subsequently used to improve the performance of the decoding of low-density parity-check (LDPC) codes and turbo codes. The Neumann large matrix approximation is employed to simplify the matrix inversion in deriving the PDF. To verify the PDF of the AEN, Monte-Carlo simulations are used to demonstrate the close-match fitting between the derived PDF and the experimentally obtained histogram of the noise in addition to the statistical tests and the independence verification. In addition, complexity analysis of the LLR obtained using the newly derived noise PDF is considered. The derived LLR can be time consuming when the number of receive antennas is very large in massive MIMO-OFDM systems. Thus, a reduced complexity approximation is introduced to this LLR using Newton’s interpolation with different orders and the results are compared to exact simulations. Further simulation results over time-flat frequency selective multipath fading channels demonstrated improved performance over equivalent systems using the Gaussian approximation for the PDF of the noise. By utilizing the PDF of the AEN, the PDF of the signal-to-noise ratio (SNR) is obtained. Then, the outage probability, the closed-form capacity and three approximate expressions for the channel capacity are derived based on that PDF. The system performance is further investigated by exploiting the PDF of the AEN to derive the bit error rate (BER) for the massive MIMO-OFDM system with different M-ary modulations. Then, the pairwise error probability (PEP) is derived to obtain the upper-bounds for the convolutionally coded and turbo coded massive MIMO-OFDM systems for different code generators and receive antennas. Furthermore, the effect of the fixed point data representation on the performance of the massive MIMO-OFDM systems is investigated using reduced detection implementations for MIMO detectors. The motivation for the fixed point analysis is the need for a reduced complexity detector to be implemented as an optimum massive MIMO detector with low precision. Different decomposition schemes are used to build the linear detector based on the IEEE 754 standard in addition to a user-defined precision for selected detectors. Simulations are used to demonstrate the behaviour of several matrix inversion schemes under reduced bit resolution. The numerical results demonstrate improved performance when using QR-factorization and pivoted LDLT decomposition schemes at reduced precision.Iraqi Government and the Iraqi Ministry of Higher Education and Scientific researc

Deep learning-based space-time coding wireless MIMO receiver optimization.

Doctoral Degree. University of KwaZulu-Natal, Durban.With the high demand for high data throughput and reliable wireless links to cater for real-time or low latency mobile application services, the wireless research community has developed wireless multiple-input multiple-output (MIMO) architectures that cater to these stringent quality of service (QoS) requirements. For the case of wireless link reliability, spatial diversity in wireless MIMO architectures is used to increase the link reliability. Besides increasing link reliability using spatial diversity, space-time block coding schemes may be used to further increase the wireless link reliability by adding time diversity to the wireless link. Our research is centered around the optimization of resources used in decoding space-time block coded wireless signals. There are two categories of space-time block coding schemes namely the orthogonal and non-orthogonal space-time block codes (STBC). In our research, we concentrate on two non-orthogonal STBC schemes namely the uncoded space-time labeling diversity (USTLD) and the Golden code. These two non-orthogonal STBC schemes exhibit some advantages over the orthogonal STBC called Alamouti despite their non-linear optimal detection. Orthogonal STBC schemes have the advantage of simple linear optimal detection relative to the more complex non-linear optimal detection of non-orthogonal STBC schemes. Since our research concentrates on wireless MIMO STBC transmission, for detection to occur optimally at the receiver side of a space-time block coded wireless MIMO link, we need to optimally perform channel estimation and decoding. USTLD has a coding gain advantage over the Alamouti STBC scheme. This implies that the USTLD can deliver higher wireless link reliability relative to the Alamouti STBC for the same spectral efficiency. Despite this advantage of the USTLD, to the best of our knowledge, the literature has concentrated on USTLD wireless transmission under the assumption that the wireless receiver has full knowledge of the wireless channel without estimation errors. We thus perform research of the USTLD wireless MIMO transmission with imperfect channel estimation. The traditional least-squares (LS) and minimum mean squared error (MMSE) used in literature, for imperfect pilot-assisted channel estimation, require the full knowledge of the transmitted pilot symbols and/or wireless channel second order statistics which may not always be fully known. We, therefore, propose blind channel estimation facilitated by a deep learning model that makes it unnecessary to have prior knowledge of the wireless channel second order statistics, transmitted pilot symbols and/or average noise power. We also derive an optimal number of pilot symbols that maybe used for USTLD wireless MIMO channel estimation without compromising the wireless link reliability. It is shown from the Monte Carlo simulations that the error rate performance of the USTLD transmission is not compromised despite using only 20% of the required number of Zadoff-Chu sequence pilot symbols used by the traditional LS and MMSE channel estimators for both 16-QAM and 16-PSK baseband modulation. The Golden code is a STBC scheme with spatial multiplexing gain over the Alamouti scheme. This implies that the Golden code can deliver higher spectral efficiencies for the same link reliability with the Alamouti scheme. The Alamouti scheme has been implemented in the modern wireless standards because it adds time diversity, with low decoding complexity, to wireless MIMO links. The Golden code adds time diversity and improves wireless MIMO spectral efficiency but at the cost of much higher decoding complexity relative to the Alamouti scheme. Because of the high decoding complexity, the Golden code is not widely adopted in the modern wireless standards. We, therefore, propose analytical and deep learning-based sphere-decoding algorithms to lower the number of detection floating-point operations (FLOPS) and decoding latency of the Golden code under low- and high-density M-ary quadrature amplitude modulation (M-QAM) baseband transmissions whilst maintaining the near-optimal error rate performance. The proposed sphere-decoding algorithms achieve at most 99% reduction in Golden code detection FLOPS, at low SNR, relative to the sphere-decoder with sorted detection subsets (SD-SDS) whilst maintaining the error rate performance. For the case of high-density M-QAM Golden code transmission, the proposed analytical and deep learning sphere-decoders reduce decoding latency by at most 70%, relative to the SD-SDS decoder, without diminishing the error rate performance

CSI-Free Geometric Symbol Detection via Semi-supervised Learning and Ensemble Learning

Symbol detection (SD) plays an important role in a digital communication system. However, most SD algorithms require channel state information (CSI), which is often difficult to estimate accurately. As a consequence, it is challenging for these SD algorithms to approach the performance of the maximum likelihood detection (MLD) algorithm. To address this issue, we employ both semi-supervised learning and ensemble learning to design a flexible parallelizable approach in this paper. First, we prove theoretically that the proposed algorithms can arbitrarily approach the performance of the MLD algorithm with perfect CSI. Second, to enable parallel implementation and also enhance design flexibility, we further propose a parallelizable approach for multi-output systems. Finally, comprehensive simulation results are provided to demonstrate the effectiveness and superiority of the designed algorithms. In particular, the proposed algorithms approach the performance of the MLD algorithm with perfect CSI, and outperform it when the CSI is imperfect. Interestingly, a detector constructed with received signals from only two receiving antennas (less than the size of the whole receiving antenna array) can also provide good detection performance

Low-Complexity Near-Optimal Detection Algorithms for MIMO Systems

As the number of subscribers in wireless networks and their demanding data rate are exponentially increasing, multiple-input multiple-output (MIMO) systems have been scaled up in the 5G where tens to hundreds of antennas are deployed at base stations (BSs). However, by scaling up the MIMO systems, designing detectors with low computational complexity and close to the optimal error performance becomes challenging. In this dissertation, we study the problem of efficient detector designs for MIMO systems. In Chapter 2, we propose efficient detection algorithms for small and moderate MIMO systems by using lattice reduction and subspace (or conditional) detection techniques. The proposed algorithms exhibit full receive diversity and approach the bit error rate (BER) of the optimal maximum likelihood (ML) solution. For quasi-static channels, the complexity of the proposed schemes is cubic in the system dimension and is only linear in the size of the QAM modulation used. However, the computational complexity of lattice reduction algorithms imposes a large burden on the proposed detectors for large MIMO systems or fast fading channels. In Chapter 3, we propose detectors for large MIMO systems based on the combination of minimum mean square error decision feedback equalization (MMSE-DFE) and subspace detection tailored to an appropriate channel ordering. Although the achieved diversity order of the proposed detectors does not necessarily equal the full receive diversity for some MIMO systems, the coding gain allows for close to ML error performance at practical values of signal-to-noise ratio (SNR) at the cost of a small computational complexity increase over the classical MMSE- DFE detection. The receive diversity deficiency is addressed by proposing another algorithm in which a partial lattice reduction (PLR) technique is deployed to improve the diversity order. Massive multiuser MIMO (MU-MIMO) is another technology where the BS is equipped with hundreds of antennas and serves tens of single-antenna user terminals (UTs). For the uplink of massive MIMO systems, linear detectors, such as zero-forcing (ZF) and minimum mean square error (MMSE), approach the error performances of sophisticated nonlinear detectors. However, the exact solutions of ZF and MMSE involve matrix-matrix multiplication and matrix inversion operations which are expensive for massive MIMO systems. In Chapter 4, we propose efficient truncated polynomial expansion (TPE)-based detectors that achieve the error performance of the exact solutions with a computational complexity proportional to the system dimensions. The millimeter wave (mmWave) massive MIMO is another key technology for 5G cellular networks. By using hybrid beamforming techniques in which a few numbers of radio frequency (RF) chains are deployed at the BSs and the UTs, the fully-digital precoder (combiner) is approximated as a product of analog and digital precoders (combiners). In Chapter 5, we consider a signal detection scheme using the equivalent channel consisting of the precoder, mmWave channel, and combiner. The available structure in the equivalent channel enables us to achieve the BER of the optimal ML solution with a significant reduction in the computational complexity

On Development of Some Soft Computing Based Multiuser Detection Techniques for SDMA–OFDM Wireless Communication System

Space Division Multiple Access(SDMA) based technique as a subclass of Multiple Input Multiple Output (MIMO) systems achieves high spectral efficiency through bandwidth reuse by multiple users. On the other hand, Orthogonal Frequency Division Multiplexing (OFDM) mitigates the impairments of the propagation channel. The combination of SDMA and OFDM has emerged as a most competitive technology for future wireless communication system. In the SDMA uplink, multiple users communicate simultaneously with a multiple antenna Base Station (BS) sharing the same frequency band by exploring their unique user specific-special spatial signature. Different Multiuser Detection (MUD) schemes have been proposed at the BS receiver to identify users correctly by mitigating the multiuser interference. However, most of the classical MUDs fail to separate the users signals in the over load scenario, where the number of users exceed the number of receiving antennas. On the other hand, due to exhaustive search mechanism, the optimal Maximum Likelihood (ML) detector is limited by high computational complexity, which increases exponentially with increasing number of simultaneous users. Hence, cost function minimization based Minimum Error Rate (MER) detectors are preferred, which basically minimize the probability of error by iteratively updating receiver’s weights using adaptive algorithms such as Steepest Descent (SD), Conjugate Gradient (CG) etc. The first part of research proposes Optimization Techniques (OTs) aided MER detectors to overcome the shortfalls of the CG based MER detectors. Popular metaheuristic search algorithms like Adaptive Genetic Algorithm (AGA), Adaptive Differential Evolution Algorithm (ADEA) and Invasive Weed Optimization (IWO), which rely on an intelligent search of a large but finite solution space using statistical methods, have been applied for finding the optimal weight vectors for MER MUD. Further, it is observed in an overload SDMA–OFDM system that the channel output phasor constellation often becomes linearly non-separable. With increasing the number of users, the receiver weight optimization task turns out to be more difficult due to the exponentially increased number of dimensions of the weight matrix. As a result, MUD becomes a challenging multidimensional optimization problem. Therefore, signal classification requires a nonlinear solution. Considering this, the second part of research work suggests Artificial Neural Network (ANN) based MUDs on thestandard Multilayer Perceptron (MLP) and Radial Basis Function (RBF) frameworks fo