Frequency-selective Multiple-input Multiple-output Channels Research Articles

On the BER Performance of Constant Envelope OFDM in Frequency Selective MIMO Channels With ML Detection

In this contribution, we investigate the issue of constant envelope orthogonal frequency-division multiplexing (CE-OFDM) transmission in multipath fading channels, by quantifying its bit-error rate (BER) performance with the aid of maximum likelihood (ML) detection in multiple-input multipleoutput (MIMO) configurations. Through theoretical derivation, we demonstrate the advantage of CE-OFDM over its traditional counterparts as original OFDM and discrete Fourier transformspread-OFDM (DFT-s-OFDM) in terms of BER performance, which is ultimately supported by the simulation results.

B-Spline Neural Network Assisted Space-Time Equalization for Single-Carrier Multiuser Nonlinear Frequency-Selective MIMO Uplink

This paper designs a nonlinear space-time equalizer based on B-spline neural network (BSNN) for the singlecarrier high-throughput multiuser frequency-selective multipleinput multiple-output (MIMO) nonlinear uplink. Specifically, based on a BSNN parametrization of the nonlinear high power amplifiers (NHPAs) at mobile terminals’ transmitters, a novel nonlinear identification scheme is developed to estimate the nonlinear dispersive MIMO uplink channel, which includes the BSNN models for the NHPAs at transmitters as well as the frequency-selective MIMO channel impulse response (CIR) matrix. Furthermore, the BSNN inverse models of the NHPAs are also estimated in closed-form. This allows the base station to implement nonlinear multiuser detection effectively using the space-time equalization (STE) based on the estimated frequencyselective MIMO CIR matrix and followed by compensating for the nonlinear distortion of the transmitters’ NHPAs based on the estimated BSNN inverse models. Simulation results are utilized to demonstrate the superior bit error rate performance of our nonlinear STE approach for single-carrier highthroughput multiuser nonlinear frequency-selective MIMO uplink.

Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

In this paper, we propose a generalized singular value decomposition (GSVD) for polynomial matrices, or polynomial GSVD (PGSVD). We then consider PGSVD-based beamforming for two-user, frequency-selective, multiple-input multiple-output (MIMO) multicasting. The PGSVD can jointly factorize two frequency-selective MIMO channels, producing a set of virtual channels (VCs), split into: private channels (PCs) and common channels (CCs). An important advantage of the proposed PGSVD-based beamformer, over the application of GSVD independently to each frequency bin of the orthogonal frequency division multiplexing (OFDM) scheme, is that it can facilitate different modulation and/or access schemes to various users. Using computer simulations, we characterize the bit error rate performance of our two-user MIMO multicasting system for different PCs/CCs configurations. Here, we also propose an OFDM-GSVD benchmark system, and show that our PGSVD-based beamformer compares favorably to this benchmark under erroneous and uncertain MIMO channel conditions, in addition to its advantage of facilitating heterogeneous modulation and access for various users.

Optimized Precoded Spatio-Temporal Partial-Response Signaling Over Frequency-Selective MIMO Channels

Due to the continuous demand for higher bit rates, the management of the spatio-temporal intersymbol interference in frequency-selective multiple-input multiple-output (MIMO) channels becomes increasingly important. For single-input single-output channels, equalized precoded partial-response signaling is capable of handling a large amount of intersymbol interference, but, to date, no equalization scheme with general partial-response signaling has been presented for the frequency-selective MIMO channel. Not only does this contribution extend partial-response signaling to the MIMO channel by proposing a general spatio-temporal partial-response precoder, but it also develops a minimum mean-squared-error optimization framework in which the equalization coefficients and the spatio-temporal target response are jointly optimized. Three iterative optimization algorithms are discussed, which update (part of) a row of the target impulse response matrix in each iteration. In particular, the third algorithm reformulates this row optimization as a lattice decoding problem. Numerical simulations confirm that the general partial-response signaling clearly outperforms the traditional full-response signaling in terms of the mean squared error and the bit error rate. The third optimization algorithm has a better performance but a higher complexity, compared to the first and the second algorithm.

New OSTBC for Blind Channel Estimation and Tracking in MIMO-OFDM Systems

Applying orthogonal space time block coding (OSTBC) to multiple-input multiple-output (MIMO) systems helps reduce receiver complexity. However, this approach has been applied only to flat fading channels, as when the channel is a frequency selective fading MIMO channel, OSTBC cannot be used directly since its orthogonal propriety may be lost. Furthermore, the MIMO channel is not always known. To deal with this problem, many techniques were proposed to estimate the channel using a training sequence. Unfortunately, these techniques reduce the useful spectral bandwidth. This paper proposes OSTBC for blind channel estimation and data detection in the case of a MIMO frequency selective channel. The aim of this new OSTBC is twofold: to solve the ambiguity of channel estimation and to reduce the complexity of the detector. By exploiting the well-known technique of orthogonal frequency division multiplexing (OFDM), the frequency selective fading MIMO channel is split into a set of flat fading subchannels. Moreover, to accommodate the fact that a MIMO channel can be time varying, the steady state Kalman channel estimator (SS-KCE) is extended to track the channel’s fast variations. The performance of the proposed blind algorithm is related by the adequate choice of the number of subcarriers and it is compared with other existing approaches by means of Monte Carlo simulations.

Secure Sum-Rate-Optimal MIMO Multicasting Over Medium-Voltage NB-PLC Networks

We propose a multiple-input multiple-output orthogonal frequency-division multiplexing transceiver for narrowband power-line communication applications in multi-user medium-voltage multicasting networks. The 3-phase medium-voltage multicasting network is modeled as a 2-input/3-output multiple-input multiple-output frequency-selective channel over the 3–500 kHz frequency band. We design the optimal spatial precoder, spatial power allocation, and frequency bit loading profile which maximize the sum-rate of the multicasting groups. In addition, we propose two schemes to secure data transmission through the two-group multicasting network. The first scheme secures the network when the eavesdropper is a user in one of the two multicasting groups and, hence, its channel state information is known at the transmitter. The second scheme secures the multicasting network from external passive eavesdroppers and, hence, the channels between the transmitter and the eavesdroppers are assumed to be unknown at the transmitter. The secrecy rate is evaluated for both scenarios.

Multi-User Millimeter Wave MIMO With Full-Dimensional Lens Antenna Array

Millimeter wave (mmWave) communication by utilizing lens antenna arrays is a promising technique for realizing cost-effective 5G wireless systems with large MIMO (multiple-input multiple-output) but only limited radio frequency (RF) chains. This paper studies an uplink multi-user mmWave single-sided lens MIMO system, where only the base station (BS) is equipped with a full-dimensional (FD) lens antenna array with both elevation and azimuth angle resolution capabilities, and each mobile station (MS) employs the conventional uniform planar array (UPA) without the lens. By exploiting the angle-dependent energy focusing property of the lens antenna array at the BS as well as the multi-path sparsity of mmWave channels, we propose a low-complexity path division multiple access (PDMA) scheme, which enables virtually interference-free multi-user communications when the angle of arrivals (AoAs) of all MS multi-path signals are sufficiently separable at the BS. To this end, a new technique called path delay compensation is proposed at the BS to effectively transform the multi-user frequency-selective MIMO channels to parallel frequency-flat small-size MIMO channels for different MSs, for each of which the low-complexity single-carrier(SC) transmission is applied. For general scenarios with insufficient AoA separations, analog beamforming at the MSs and digital combining at the BS are jointly designed to maximize the achievable sum-rate of the MSs based on their effective MIMO channels resulting from path delay compensation. In addition, we propose a new and efficient channel estimation scheme tailored for PDMA, which requires negligible training overhead in practical mmWave systems and yet leads to comparable performance as that based on perfect channel state information (CSI).

MIMO Detector for LTE/LTE-A Uplink Receiver

We propose a carefully selected receiver structure, detector and detector implementation architecture for multiple-input multiple-output (MIMO) uplink base station receiver for fourth generation (4G) wireless cellular systems. First, we compare different receiver algorithms and structures for single-carrier frequency-division multiple access (SC-FDMA) uplink transmission to get a good understanding of the performance and complexity of these algorithms and their suitability for practical realization. One of those structures, namely the frequency domain MMSE equalization with sphere detection (SD), is proposed for implementation. The receiver consists of separate stages for inter-symbol interference (ISI) and inter-antenna interference (IAI) mitigation in frequency selective MIMO channels. Frame error rate (FER) performance is studied via simulations in realistic wireless channels and practical system parameters. K-best SD is selected as a detector algorithm for this receiver. There are several publications proposing a sort-free architecture for tree search type of detectors. Both a conventional K-best architecture and a sort-free architecture are implemented on a Xilinx Virtex-6 field-programmable gate array (FPGA) using High Level Synthesis (HLS) tool. Both architectures support 4 × 4 MIMO with 64-level modulation (64-QAM). Complexity results confirm that avoiding the sorter is not always recommended. The benefit of sort-free architecture depends on the system parameters.

Performance analysis of adaptive DFE using set-membership binormalized data-reusing LMS algorithm for frequency selective MIMO channels

This paper addresses the concern of complexity involved with adaptive equalization in wireless systems operating over time-varying and frequency selective multiple-input multiple-output (MIMO) channels. Here, we propose a decision feedback equalizer using binormalized data-reusing least mean square (BNLMS) algorithm with set-membership filtering for MIMO channels. The performance of the equalizer is investigated for a MIMO receiver in a multi-path fading environment as experienced in the indoor and pedestrian environment. The equalizer performance is also studied for channels having higher delay and Doppler spread. The convergence issues, BER performance and tracking capabilities are examined through computer simulations. Moreover, the computational complexity issue for this MIMO equalizer is compared with other existing data-selective algorithm based techniques.

A Low Complexity Diversity Achieving Decoder Based on a Two-Stage Lattice Reduction in Frequency-Selective MIMO Channels

Based on the V-BLAST zero-padded block transmission scheme in the frequency-selective multiple-input multiple-output channels, we propose a two-stage lattice-reduction (LR)-aided decoder and prove analytically that it can achieve the maximum diversity gain, which is equal to the product of the number of receive-antennas and the number of multipath channel taps. In the proposed decoding method, at first, we decouple the detection problem into several reduced-size detection problems and perform the lattice reduction algorithm for the decoupled blocks. Then, by choosing a proper threshold, a clustering algorithm divides the blocks into the maximum two clusters. We prove that the corresponding blocks of the first cluster achieve the full diversity through their linear equalization. For the remainder of the blocks, based on the entire observations of the second cluster, we propose an LR-aided detection method, which decodes the information symbols in this cluster with full diversity. Our proposed two-stage LR-aided algorithm performs better than the conventional LR-aided detection in terms of both the decoding computational complexity and the error probability. Additionally, we prove analytically that at high signal-to-noise ratio, the decoding complexity of the proposed decoder is equal to that of decoding the first cluster.

Analysis of MIMO-OFDM system impaired by nonlinear dual-band power amplifiers

This paper presents a theoretical analysis of multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing in the presence of nonlinear dual-band power amplifiers. A two-dimensional memory polynomial model is used to describe the dual-band power amplifier. It is analytically shown that the effect of nonlinearity impairment in the transmitter can be modeled by a complex coefficient and a nonlinear additive noise. An analytical formulation is provided for symbol error rate (SER) of this system considering a frequency selective MIMO channel. The experimental results have been deployed to extract a realistic model for a dual-band amplifier. Also, the model of the linearized power amplifier has been extracted after applying digital pre-distortion (DPD). The proposed model is validated by simulation for 2 × 2 and 2 × 4 MIMO systems. The results show that the analytical model maps well onto the simulation. Also, it is shown that the DPD is able to compensate for the nonlinearity effect of the dual-band power amplifier as the SER is improved.

Modulation-Mode and Power Assignment in SVD-Assisted Broadband MIMO Systems using Polynomial Matrix Factorization

Singular-value decomposition (SVD)-based multiple-input multiple-output (MIMO) systems have attracted a lot of attention in the wireless community. However, applying SVD to frequency-selective MIMO channels results in unequally weighted single-input single-output (SISO) channels requiring complex resource allocation techniques for optimizing the channel performance. Therefore, a different approach utilizing polynomial matrix factorization for removing the MIMO interference is analyzed, outperforming conventional SVD-based MIMO systems in the analyzed channel scenario.

PAPR Reduction in STBC MIMO OFDM System using AMS and PTS Schemes

data rates and reliability are the two key factors required to support emerging multimedia applications and new communications technologies. The two techniques used in high data rate transmission are orthogonal frequency division multiplexing (OFDM) and multiple-input multiple- output (MIMO) scheme. The OFDM is used to mitigate the problem of inter symbol interference (ISI) and provides good protection against co-channel interference and noise. MIMO system helps to reduce fading and can be used for decreasing bit error rate that is spatial diversity or to increase the data rate that is spatial multiplexing. The combination of MIMO and OFDM is MIMO OFDM system. MIMO-OFDM system converts frequency selective MIMO channel into multiple parallel flat fading channels. One of the major drawbacks of in MIMO-OFDM systems is that the transmitted signal exhibits a high PAPR when the input sequences are correlated. In this paper, AMS and PTS schemes have been used to reduce peak to average power ratio (PAPR) in multiple input multiple output orthogonal frequency division multiplexing (MIMO OFDM) system with Alamouti's space time block coding (STBC). The AMS scheme reduces the computational complexity and when AMS scheme is used with quadrature amplitude modulation (QAM). Simulation and results show that the AMS scheme reduces PAPR more efficiently than the PTS scheme.

Block Diagonal GMD for Zero-Padded MIMO Frequency Selective Channels

In the class of systems with linear precoder and decision feedback equalizers (DFE) for zero-padded (ZP) multiple-input multiple-output (MIMO) frequency selective channels, existing optimal transceiver designs present two drawbacks. First, the optimal systems require a large number of feedback bits from the receiver to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as the bandwidth (BW) efficiency increases. In this paper, we propose using block diagonal geometric mean decomposition (BD-GMD) to design the transceiver. Two new BD-GMD transceivers are proposed: the ZF-BD-GMD system, where the receiver is a zero-forcing DFE (ZF-DFE), and the MMSE-BD-GMD system, where the receiver is a minimum- mean-square-error DFE (MMSE-DFE). The BD-GMD systems introduced here have the following four properties: a) They use the block diagonal unitary precoding technique to reduce the required number of encoding bits and simplify the computation. b) For any block size, the BD-GMD systems are optimal within the family of systems using block diagonal unitary precoders and DFEs. As block size gets larger, the BD-GMD systems produce uncoded bit error rate (BER) performance similar to the optimal systems using unitary precoders and DFEs. c) For the two ZF transceivers (ZF-Optimal and ZF-BD-GMD) and the two MMSE transceivers (MMSE-Optimal and MMSE-BD-GMD), the average BER degrades as the BW efficiency increases. d) In the case of single-input single-output (SISO) channels, the BD-GMD systems have the same performance as those of the lazy precoder transceivers. These properties make the proposed BD-GMD systems more favorable designs in practical implementation than the optimal systems.

Appropriate Algorithms for Estimating Frequency-Selective Rician Fading MIMO Channels and Channel Rice Factor: Substantial Benefits of Rician Model and Estimator Tradeoffs

The training-based channel estimation (TBCE) scheme in multiple-input multiple-output (MIMO) frequency-selective Rician fading channels is investigated. We propose the new technique of shifted scaled least squares (SSLS) and the minimum mean square error (MMSE) estimator that are suitable to estimate the above-mentioned channel model. Analytical results show that the proposed estimators achieve much better minimum possible Bayesian Cramér-Rao lower bounds (CRLBs) in the frequency-selective Rician MIMO channels compared with those of Rayleigh one. It is seen that the SSLS channel estimator requires less knowledge about the channel and/or has better performance than the conventional least squares (LS) and MMSE estimators. Simulation results confirm the superiority of the proposed channel estimators. Finally, to estimate the channel Rice factor, an algorithm is proposed, and its efficiency is verified using the result in the SSLS and MMSE channel estimators.

Pilot Designs for Channel Estimation of MIMO OFDM Systems with Frequency-Dependent I/Q Imbalances

Multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems facilitate high data rate wireless communications, and require reliable channel estimates to fully materialize their advantages. The semiconductor downscaling trend has exacerbated device impairments such as inphase and quadrature (I/Q) imbalances which cause inter-carrier interferences in OFDM systems which cannot be remedied by increasing signal power. Different RF chains of MIMO branches can cause different I/Q imbalances which further complicates MIMO OFDM channel estimation. This paper proposes several pilot designs for the estimation of the combined responses of MIMO frequency-selective channels and frequency-dependent I/Q imbalances. The proposed designs require much smaller pilot overhead than the existing designs, and also provide estimation mean-squares error optimality (under white noise) and general applicability to preamble as well as pilot-data-multiplexed symbols in MIMO systems with or without null guard tones. Performance analyses and simulation results corroborate advantages of the proposed designs.

Unifying eigen-mode MIMO transmission

Multiple-input multiple-output (MIMO) technique plays a key role in improving the spectrum and power efficiency in future mobile communication systems. Exploiting a unified MIMO transmission scheme that can adapt with various channel conditions is well motivated both in theory and practical applications. An eigen-mode based closed-loop MIMO transmission over frequency selective fading MIMO channels, which considers receive correlation, transmit correlation and line of sight (LOS) components, is investigated by maximizing the upper bound of channel capacity under the assumption that the channel is partially known at the transmitter and perfectly known at the receiver. Based on the eigen-mode transmission, several key techniques including linear precoding, stream selection, virtual spatial hopping and online capacity estimation are proposed, and a unified MIMO transmission scheme is established. Both computer simulation and field test results show that the proposed scheme can significantly improve the spectral efficiency and link reliability under various channel conditions.

Zero-forcing precoding for frequency selective MIMO channels with [formula omitted] criterion and causality constraint

We consider zero-forcing equalization of frequency selective multiple-input multiple-output (MIMO) channels by causal and linear time-invariant precoders in the presence of intersymbol interference. Our motivation is twofold. First, we are concerned with the optimal performance of causal precoders from a worst case point of view. Therefore we construct an optimal causal precoder, where contrary to other works our construction is not limited to finite or rational impulse responses. Moreover, we derive a novel numerical approach to computation of the optimal performance index achievable by causal precoders. This quantity is important in the numerical determination of optimal precoders.

A new framework for soft decision equalization in frequency selective MIMO channels

We introduce a novel framework for soft-input, soft-output (SISO) equalization in frequency selective multipleinput multiple-output (MIMO) channels based on the well-known belief propagation (BP) algorithm. As in the BP equalizer, we model the multipath channels using factor graphs (FGs) where the transmitted and received signals are represented by the function and variable nodes respectively. The edges connecting the function and variable nodes illustrate the dependencies of the multipath channel and soft decisions are developed by exchanging information on these edges iteratively. We incorporate powerful techniques such as groupwise iterative multiuser detection (IMUD), probabilistic data association (PDA) and sphere decoding (SD) in order to reduce the computational complexity of BP equalizer with relatively small degradation in performance. The computational complexity of this new reduced-complexity BP (RCBP) equalizer grows linearly with block size and memory length of the channel. The proposed framework has a flexible structure that allows for parallel as well as serial detection. We will illustrate through simulations that the RCBP equalizer can even handle overloaded scenarios where the channel matrix is rank deficient, and it can achieve excellent performance by applying iterative equalization using the low-density parity check codes (LDPC).

Frequency-selective multiple-input multiple-output channel estimation with transmitter non-linearities

The authors propose an algorithm based on the knowledge of training sequences to obtain an asymptotically unbiased estimator of non-linear multiple-input multiple-output (MIMO) channels, which involves the radio frequency front-end non-linearity and linear frequency selective MIMO channels. Although the impact of non-linearity in the transmitter side has been widely studied, most work on the channel estimation assumes linear channel models and ignores the non-linear effects. In this study, we develop a non-linear channel estimator that can simultaneously estimate the linear MIMO channel model and non-linearity of the transmitter is developed. With these two sets of parameters, the non-linear channel model can be fully described. This channel estimation algorithm is implemented over an empirical MIMO channel model using an orthogonal frequency division multiplexing system.