This paper presents an optimized low-complexity and high-throughput multiple-input multiple-output (MIMO) signal detector core for detecting spatially-multiplexed data streams. The core architecture supports various layer configurations up to 4, while achieving near-optimal performance, as well as configurable modulation constellations up to 256-QAM on each layer. The core is capable of operating as a soft-input soft-output log-likelihood ratio (LLR) MIMO detector which can be used in the context of iterative detection and decoding. High area-efficiency is achieved via algorithmic and architectural optimizations performed at two levels. First, distance computations and slicing operations for an optimal 2-layer maximum a posteriori (MAP) MIMO detector are optimized to eliminate the use of multipliers and reduce the overhead of slicing in the presence of soft-input LLRs. We show that distances can be easily computed using elementary addition operations, while optimal slicing is done via efficient comparisons with soft decision boundaries, resulting in a simple feed-forward pipelined architecture. Second, to support more layers, an efficient channel decomposition scheme is presented that reduces the detection of multiple layers into multiple 2-layer detection subproblems, which map onto the 2-layer core with a slight modification using a distance accumulation stage and a post-LLR processing stage. Various architectures are accordingly developed to achieve a desired detection throughput and run-time reconfigurability by time-multiplexing of one or more component cores. The proposed core is applied as well to design an optimal multi-user MIMO detector for LTE. The core occupies an area of 1.58MGE and achieves a throughput of 733 Mbps for 256-QAM when synthesized in 90 nm CMOS.
In this paper, performance of a dual-hop cooperative multiple-input and multiple-output (MIMO) system is analyzed over Rayleigh faded channels. For the considered system model, non-regenerative MIMO scheme with transmit antenna selection strategy (TAS) is employed. In this scheme, a single transmit antenna which maximizes the total received signal power at the receiver is selected for transmission. Useful insights from average symbol error rate for various quadrature amplitude modulation (QAM) schemes such as general order hexagonal QAM (HQAM), general order rectangular QAM (RQAM) and 32-cross…
In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the input-output mutual information for a general Multiple-Input Multiple-Output (MIMO) system as well as its corresponding gradients is presented, based on the Gauss-Hermite quadrature rule. Then, the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the MIMO input-outpu…
This paper proposes a new detection algorithm for MIMO communication systems employing high order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward application of the Belief Propagation (BP) algorithm yields very poor results. Our algorithm is based on an optimal tree approximation of the Gaussian density of the unconstrained linear system. The finite-set constraint is then applied to obtain a loop-free discrete distribution. It is shown that even though the approximation is not directly applied to the…
Today, MIMO has become an indispensable scheme for providing significant spectral efficiency in wireless communication and for future wireless system, recently, it goes to two extremes: massive MIMO and single-RF MIMO. This paper, which is put in the latter, utilizes load-modulated arrays with only reactance loads for single-RF transmission of spatially multiplexed QAM signals. To alleviate the need for iterative processes while considering mutual coupling in the compact antenna, we present a novel design methodology for the loading network, which enables the exact computation of the three rea…
Low-complexity near-optimal detection of large-MIMO signals has attracted recent research. Recently, we proposed a local neighborhood search algorithm, namely `reactive tabu search' (RTS) algorithm, as well as a factor-graph based `belief propagation' (BP) algorithm for low-complexity large-MIMO detection. The motivation for the present work arises from the following two observations on the above two algorithms: $i)$ RTS works for general M-QAM. Although RTS was shown to achieve close to optimal performance for 4-QAM in large dimensions, significant performance improvement was still possible f…
In this paper, we propose algorithms for signal detection in large-scale multiuser {\em spatial modulation multiple-input multiple-output (SM-MIMO)} systems. In large-scale SM-MIMO, each user is equipped with multiple transmit antennas (e.g., 2 or 4 antennas) but only one transmit RF chain, and the base station (BS) is equipped with tens to hundreds of (e.g., 128) receive antennas. In SM-MIMO, in a given channel use, each user activates any one of its multiple transmit antennas and the index of the activated antenna conveys information bits in addition to the information bits conveyed through …
Precoding for multiple-input, multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For 2 transmit antennas and QAM constellations, an approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) real-valued precoder based on the singular value decomposition (SVD) of the channel is proposed, and it is shown to offer a maximum-likelihood (ML)-decoding complexity of $\mathcal{O}(\sqrt{M})$ for square $M$-QAM. The proposed precoder is obtainable easily for arbitr…
In this letter, we develop an $\ell_2$-box maximum likelihood (ML) formulation for massive multiple-input multiple-output (MIMO) quadrature amplitude modulation (QAM) signal detection and customize an alternating direction method of multipliers (ADMM) algorithm to solve the nonconvex optimization model. In the $\ell_2$-box ADMM implementation, all variables are solved analytically. Moreover, several theoretical results related to convergence, iteration complexity, and computational complexity are presented. Simulation results demonstrate the effectiveness of the proposed $\ell_2$-box ADMM dete…
The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper-bound for SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpret…
This work studies multiuser detection for one-bit massive multiple-input multiple-output (MIMO) systems in order to diminish the power consumption at the base station (BS). A low-complexity near-maximum-likelihood (nML) multiuser detection algorithm is designed, assuming that each BS antenna port is connected with a pair of single-bit resolution analog-to-digital converters (ADCs) and each user equipment (UE) transmits symbols from a quadrature amplitude modulation (QAM) constellation. First, a novel convex program is formulated as a convex surrogate of the ML detector and subsequently solved …
In this paper, we propose a low complexity graph-based linear minimum mean square error (LMMSE) equalizer in order to remove inter-symbol and inter-stream interference in multiple input multiple output (MIMO) communication. The proposed state space representation inflicted on the graph provides linearly increasing computational complexity with block length. Also, owing to the Gaussian assumption used in the presented cycle-free factor graph, the complexity of the suggested equalizer structure is not affected by the size of the signalling space. In addition, we introduce an efficient way of com…
This paper presents a novel data detector ASIC for massive multiuser multiple-input multiple-output (MU-MIMO) wireless systems. The ASIC implements a modified version of the large-MIMO approximate message passing algorithm (LAMA), which achieves near-optimal error-rate performance (i) under realistic channel conditions and (ii) for systems with as many users as base-station (BS) antennas. The hardware architecture supports 32 users transmitting 256-QAM simultaneously and in the same time-frequency resource, and provides soft-input soft-output capabilities for iterative detection and decoding. …
Coarsely quantized massive Multiple-Input Multiple-Output (MIMO) systems are gaining more interest due to their power efficiency. We present a new precoding technique to mitigate the Multi-User Interference (MUI) and the quantization distortions in a downlink Multi-User (MU) MIMO system with coarsely Quantized Constant Envelope (QCE) signals at the transmitter. The transmit signal vector is optimized for every desired received vector taking into account the QCE constraint. The optimization is based on maximizing the safety margin to the decision thresholds of the receiver constellation modulat…
Spectrally efficient multi-antenna wireless communication systems are a key challenge as service demands continue to increase. At the same time, powering up radio access networks is facing environmental and regulation limitations. In order to achieve more power efficiency, we design a directional modulation precoder by considering an $M$-QAM constellation, particularly with $M=4,8,16,32$. First, extended detection regions are defined for desired constellations using analytical geometry. Then, constellation points are placed in the optimal positions of these regions while the minimum Euclidean …
In multi-input-multi-output (MIMO) detection, semidefinite relaxation (SDR) has been shown to be an efficient high-performance approach. Developed initially for BPSK and QPSK, SDR has been found to be capable of providing near-optimal performance (for those constellations). This has stimulated a number of recent research endeavors that aim to apply SDR to the high-order QAM cases. These independently developed SDRs are different in concept and structure, and presently no serious analysis has been given to compare these methods. This paper analyzes the relationship of three such SDR methods, na…
In this paper we analyze the performance of 2*4 MIMO-MC-CDMA system in MATLAB which highly reduces BER. In this paper we combine MIMO and MC-CDMA system to reduce bit error rate in which MC-CDMA is multi user and multiple access schemes which is used to increase the data rate of the system. MC-CDMA system is a single wideband frequency selective carrier which converts frequency selective to parallel narrowband flat fading multiple sub-carriers to enhance the performance of system. Now MC-CDMA system further improved by grouping with 2*4 MIMO system which uses ZF (Zero Forcing) decoder at the r…
This paper (Part of the content of this manuscript has been accepted for presentation in IEEE Globecom 2008, to be held in New Orleans) deals with low maximum likelihood (ML) decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna ($2\times 2$) and the 4 transmit antenna, 2 receive antenna ($4\times 2$) MIMO systems. Presently, the best known STBC for the $2\times2$ system is the Golden code and that for the $4\times2$ system is the DjABBA code. Following the approach by Biglieri, Hong a…
In wireless communication systems, there are many stages for signal transmission. Among them, mapping and demapping convert a sequence of bits into a sequence of complex numbers and vice versa. This operation is performed by a system of constellations~ -- by a set of labeled points on the complex plane. Usually, the geometry of the constellation is fixed, and constellation points are uniformly spaced, e.g., the same quadrature amplitude modulation (QAM) is used in a wide range of signal-to-noise ratio (SNR). By eliminating the uniformity of constellations, it is possible to achieve greater val…
In this paper, the problem of designing a forward link linear precoder for Massive Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, we employ a novel and efficient methodology that allows for a sparse representation of multiple users and groups in a fashion similar to Joint Spatial Division and Multiplexing. Then, the method is generalized to include Orthogonal Frequency Division Multiplexing (OFDM) for frequency selective channels, resulting in Combined Frequency and Spatial Division and Multiplexing, a configuration …
This paper is concerned with SC/FDE for bandwidth-efficient uplink block transmission, with QAM schemes, in a MU MIMO system. The number of BS receiver antennas is assumed to be large, but not necessarily much larger than the overall number of transmitter antennas jointly using the same time/frequency resource at MT. In this context, we consider several detection techniques and evaluate, in detail, the corresponding detection performances (discussed with the help of selected performance bounds), for a range of values regarding the number of available BS receiver antennas. From our performance …
We propose a modulus based zero-forcing (MZF) detection for multi-input multi-output (MIMO) channels. Traditionally, a ZF detector nulls out all interferences from other layers when detecting a current layer, which can yield suboptimal detection-performance due to the noise-enhancement issue. In many communication systems, finite alphabets such as M quadrature-amplitude-modulation (QAM) are widely used, which comprises \sqrt{M} pulse-amplitude-modulation (PAM) symbols for the real and imaginary parts. With finite alphabets, one feasible way to improve ZF detection is to allow controllable inte…
This paper presents the first network-coded multiple access (NCMA) system prototype operated on high-order modulations up to 16-QAM. NCMA jointly exploits physical-layer network coding (PNC) and multiuser decoding (MUD) to boost throughput of multipacket reception systems. Direct generalization of the existing NCMA decoding algorithm, originally designed for BPSK, to high-order modulations, will lead to huge performance degradation. The throughput degradation is caused by the relative phase offset between received signals from different nodes. To circumvent the phase offset problem, this paper…
Optimal data detection in multiple-input multiple-output (MIMO) communication systems with a large number of antennas at both ends of the wireless link entails prohibitive computational complexity. In order to reduce the computational complexity, a variety of sub-optimal detection algorithms have been proposed in the literature. In this paper, we analyze the optimality of a novel data-detection method for large MIMO systems that relies on approximate message passing (AMP). We show that our algorithm, referred to as individually-optimal (IO) large-MIMO AMP (short IO-LAMA), is able to perform IO…
We consider the problem of designing low latency and low complexity schemes for channel state feedback over the MIMO-MAC (multiple-input multiple-output multiple access channel). We develop a framework for analyzing this problem in terms of minimizing the MSE distortion, and come up with separated source-channel schemes and joint source-channel schemes that perform better than analog feedback. We also develop a strikingly simple code design based on scalar quantization and uncoded QAM modulation that achieves the theoretical asymptotic performance limit of the separated approach with very low …
Massive multi-user (MU) multiple-input multiple- output (MIMO) is widely believed to be a core technology for the upcoming fifth-generation (5G) wireless communication standards. The use of low-precision digital-to-analog converters (DACs) in MU-MIMO base stations is of interest because it reduces the power consumption, system costs, and raw baseband data rates. In this paper, we develop novel algorithms for downlink precoding in massive MU-MIMO systems with 1-bit DACs that support higher-order modulation schemes such as 8-PSK or 16-QAM. Specifically, we present low-complexity nonlinear precod…
In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the metrics of all neighboring vectors are computed to determine the best one to move to. This strategy requires high computational complexity, especially in large MIMO systems with high-order modulation schemes such as 16- and 64-QAM signaling. This paper proposes a novel reduced-complexity TS detection algorithm called neighbor-grouped TS (NG-TS), which divides the neighbors into groups and finds the best neighbor by using a simplified cost function. Furthermore, based on the complexit…
In this work, a new fast-decodable space-time block code (STBC) is proposed. The code is full-rate and full-diversity for 4x2 multiple-input multiple-output (MIMO) transmission. Due to the unique structure of the codeword, the proposed code requires a much lower computational complexity to provide maximum-likelihood (ML) decoding performance. It is shown that the ML decoding complexity is only O(M^{4.5}) when M-ary square QAM constellation is used. Finally, the proposed code has highest minimum determinant among the fast-decodable STBCs known in the literature. Simulation results prove that th…
Hardware impairments in radio-frequency components of a wireless system cause unavoidable distortions to transmission that are not captured by the conventional linear channel model. In this paper, a 'binoisy' single-user multiple-input multiple-output (SU-MIMO) relation is considered where the additional distortions are modeled via an additive noise term at the transmit side. Through this extended SU-MIMO channel model, the effects of transceiver hardware impairments on the achievable rate of multi-antenna point-to-point systems are studied. Channel input distributions encompassing practical d…
This paper presents a hardware architecture of complex K-best Multiple Input Multiple Output (MIMO) decoder reducing the complexity of Maximum Likelihood (ML) detector. We develop a novel low-power VLSI design of complex K-best decoder for 8x8 MIMO and 64 QAM modulation scheme. Use of Schnorr-Euchner (SE) enumeration and a new parameter, Rlimit in the design reduce the complexity of calculating K-best nodes to a certain level with increased performance. The total word length of only 16 bits has been adopted for the hardware design limiting the bit error rate (BER) degradation to 0.3 dB with li…
The 3D MIMO code is a robust and efficient space-time block code (STBC) for the distributed MIMO broadcasting but suffers from high maximum-likelihood (ML) decoding complexity. In this paper, we first analyze some properties of the 3D MIMO code to show that the 3D MIMO code is fast-decodable. It is proved that the ML decoding performance can be achieved with a complexity of O(M^{4.5}) instead of O(M^8) in quasi static channel with M-ary square QAM modulations. Consequently, we propose a simplified ML decoder exploiting the unique properties of 3D MIMO code. Simulation results show that the pro…
This paper investigates the linear precoder design for $K$-user interference channels of multiple-input multiple-output (MIMO) transceivers under finite alphabet inputs. We first obtain general explicit expressions of the achievable rate for users in the MIMO interference channel systems. We study optimal transmission strategies in both low and high signal-to-noise ratio (SNR) regions. Given finite alphabet inputs, we show that a simple power allocation design achieves optimal performance at high SNR whereas the well-known interference alignment technique for Gaussian inputs only utilizes a pa…
In our recent work, we reported an exhaustive study on the simulated bit error rate (BER) performance of a low-complexity likelihood ascent search (LAS) algorithm for detection in large multiple-input multiple-output (MIMO) systems with large number of antennas that achieve high spectral efficiencies. Though the algorithm was shown to achieve increasingly closer to near maximum-likelihood (ML) performance through simulations, no BER analysis was reported. Here, we extend our work on LAS and report an asymptotic BER analysis of the LAS algorithm in the large system limit, where $N_t,N_r \to \in…
Approximate matrix inversion based methods is widely used for linear massive multiple-input multiple-output (MIMO) received symbol vector detection. Such detectors typically utilize the diagonally dominant channel matrix of a massive MIMO system. Instead of diagonal matrix, a stair matrix can be utilized to improve the error-rate performance of a massive MIMO detector. In this paper, we present very large-scale integration (VLSI) architecture and field programmable gate array (FPGA) implementation of a stair matrix based iterative detection algorithm. The architecture supports a base station w…
We introduce a revised derivation of the bitwise Markov Chain Monte Carlo (MCMC) multiple-input multiple-output (MIMO) detector. The new approach resolves the previously reported high SNR stalling problem of MCMC without the need for hybridization with another detector method or adding heuristic temperature scaling factors. Another common problem with MCMC algorithms is the unknown convergence time making predictable fixed-length implementations problematic. When an insufficient number of iterations is used on a slowly converging example, the output LLRs can be unstable and overconfident. Ther…
We investigate the performance of mismatched data detection in large multiple-input multiple-output (MIMO) systems, where the prior distribution of the transmit signal used in the data detector differs from the true prior. To minimize the performance loss caused by this prior mismatch, we include a tuning stage into our recently-proposed large MIMO approximate message passing (LAMA) algorithm, which allows us to develop mismatched LAMA algorithms with optimal as well as sub-optimal tuning. We show that carefully-selected priors often enable simpler and computationally more efficient algorithms…
This paper deals with SC/FDE within a MU-MIMO system where a large number of BS antennas is adopted. In this context, either linear or reduced-complexity iterative DF detection techniques are considered. Regarding performance evaluation by simulation, appropriate semi-analytical methods are proposed. This paper includes a detailed evaluation of BER performances for uncoded 4-Quadrature Amplitude Modulation (4-QAM) schemes and a MU-MIMO channel with uncorrelated Rayleigh fading. The accuracy of performance results obtained through the semi-analytical simulation methods is assessed by means of p…
We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2 by 2 multiple-antenna case, for a Wiener phase-noise p…
In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov Random Field (MRF) ba…
We consider a multi-user multiple-input multiple-output (MU-MIMO) system that uses orthogonal frequency division multiplexing (OFDM). Several receivers are developed for data detection of MU-MIMO transmissions where two users share the same OFDM time and frequency resources. The receivers have partial state information about the MU-MIMO transmission with each receiver having knowledge of the MU-MIMO channel, however the modulation constellation of the co-scheduled user is unknown. We propose a joint maximum likelihood (ML) modulation classification of the co-scheduled user and data detection r…
We propose a joint channel estimation and data detection (JED) algorithm for densely-populated cell-free massive multiuser (MU) multiple-input multiple-output (MIMO) systems, which reduces the channel training overhead caused by the presence of hundreds of simultaneously transmitting user equipments (UEs). Our algorithm iteratively solves a relaxed version of a maximum a-posteriori JED problem and simultaneously exploits the sparsity of cell-free massive MU-MIMO channels as well as the boundedness of QAM constellations. In order to improve the performance and convergence of the algorithm, we p…
We investigate mismatched data detection for massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems in which the prior distribution of the transmit signal used in the data detector differs from the true prior. In order to minimize the performance loss caused by the prior mismatch, we include a tuning stage into the recently proposed large-MIMO approximate message passing (LAMA) algorithm, which enables the development of data detectors with optimal as well as sub-optimal parameter tuning. We show that carefully-selected priors enable the design of simpler and computatio…
A family of low-complexity detection schemes based on channel matrix puncturing targeted for large multiple-input multiple-output (MIMO) systems is proposed. It is well-known that the computational cost of MIMO detection based on QR decomposition is directly proportional to the number of non-zero entries involved in back-substitution and slicing operations in the triangularized channel matrix, which can be too high for low-latency applications involving large MIMO dimensions. By systematically puncturing the channel to have a specific structure, it is demonstrated that the detection process ca…
A neighborhood restricted Mixed Gibbs Sampling (MGS) based approach is proposed for low-complexity high-order modulation large-scale Multiple-Input Multiple-Output (LS-MIMO) detection. The proposed LS-MIMO detector applies a neighborhood limitation (NL) on the noisy solution from the MGS at a distance d - thus, named d-simplified MGS (d-sMGS) - in order to mitigate its impact, which can be harmful when a high order modulation is considered. Numerical simulation results considering 64-QAM demonstrated that the proposed detection method can substantially improve the MGS algorithm convergence, wh…
In this paper, we propose a new nonlinear detector with improved interference suppression in Multi-User Multiple Input, Multiple Output (MU-MIMO) system. The proposed detector is a combination of the following parts: QR decomposition (QRD), low complexity users sorting before QRD, sorting-reduced (SR) K-best method and minimum mean square error (MMSE) pre-processing. Our method outperforms a linear interference rejection combining (IRC, i.e. MMSE naturally) method significantly in both strong interference and additive white noise scenarios with both ideal and real channel estimations. This res…
This paper investigates the symbol error probability~(SEP) of point-to-point massive multiple-input multiple-output (MIMO) systems using equally likely PAM, PSK, and square QAM signallings in the presence of transmitter correlation. The receiver has perfect knowledge of the channel coefficients, while the transmitter only knows first- and second-order channel statistics. With a zero-forcing~(ZF) detector implemented at the receiver side, we design and derive closed-form expressions of the optimal precoders at the transmitter that minimizes the average SEP over channel statistics for various mo…
In this paper, we focus on 1-bit precoding approaches for downlink massive multiple-input multiple-output (MIMO) systems, where we exploit the concept of constructive interference (CI). For both PSK and QAM signaling, we firstly formulate the optimization problem that maximizes the CI effect subject to the requirement of the 1-bit transmit signals. We then mathematically prove that, when employing the CI formulation and relaxing the 1-bit constraint, the majority of the transmit signals already satisfy the 1-bit formulation. Building upon this important observation, we propose a 1-bit precodin…
Compared to the linear MIMO detectors, the Belief Propagation (BP) detector has shown greater capabilities in achieving near optimal performance and better nature to iteratively cooperate with channel decoders. Aiming at real applications, recent works mainly fall into the category of reducing the complexity by simplified calculations, at the expense of performance sacrifice. However, the complexity is still unsatisfactory with exponentially increasing complexity or required exponentiation operations. Furthermore, due to the inherent loopy structure, the existing BP detectors persistently enco…
We consider large MIMO systems, where by `{\em large}' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just $O(N_tN_r)$, where $N_t$ and $N_r$ denote the number of transmit and receive antennas, respe…
