Near-optimum soft decision equalization for frequency selective MIMO channels

In this paper, we develop soft decision equalization (SDE) techniques for frequency selective multiple-input multiple-output (MIMO) channels in the quest for low-complexity equalizers with error performance competitive to that of maximum likelihood (ML) sequence detection. We demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered and linear in the signal constellation size. Building on the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. The first SDE algorithm adopts a zero-padded transmission structure to convert the challenging sequence detection problem into a block-by-block least-square formulation. It introduces key enhancement to the original PDA to enable applications in rank-deficient channels and for higher level modulations. The second SDE algorithm takes advantage of the Toeplitz channel matrix structure embodied in an equalization problem. It processes the data samples through a series of overlapping sliding windows to reduce complexity and, at the same time, performs implicit noise tracking to maintain near-optimum performance. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Simulation comparisons of our SDE methods with minimum-mean-square error (MMSE)-based MIMO DFE and sphere decoded quasi-ML detection are presented.     

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).     

CRC-aided turbo equalization for MIMO frequency selective fading channels

This paper presents a CRC （Cyclic Redundancy Check）-aided turbo equalization approach to reduce the computational complexity. In this approach, CRC code bits are padded to the end of each transmit block, and a cyclic redundancy check is performed after decoding each block at the receiver en.d. If the check sum is zero, which means the receive block is correct, the corresponding LLRs （Log Likelihood Ratios） of this block are set high reliable values, and all the computations corresponding to this block can be cancelled for the subsequent outer iterations. With a lower computational complexity the proposed approach can achieve the same as or even better performance than the conventional non-CRC method.     

Sampling-based soft equalization for frequency-selective MIMO channels

We consider the problem of channel equalization in broadband wireless multiple-input multiple-output (MIMO) systems over frequency-selective fading channels, based on the sequential Monte Carlo (SMC) sampling techniques for Bayesian inference. Built on the technique of importance sampling, the stochastic sampler generates weighted random MIMO symbol samples and uses resampling to rejuvenate the sample streams; whereas the deterministic sampler, a heuristic modification of the stochastic counterpart, recursively performs exploration and selection steps in a greedy manner in both space and time domains. Such a space-time sampling scheme is very effective in combating both intersymbol interference and cochannel interference caused by frequency-selective channel and multiple transmit and receiver antennas. The proposed sampling-based MIMO equalizers significantly outperform the decision-feedback MIMO equalizers with comparable computational complexity. More importantly, being soft-input soft-output in nature, these sampling-based MIMO equalizers can be employed as the first-stage soft demodulator in a turbo receiver for coded broadband MIMO systems. Such a turbo receiver successively improves the receiver performance through iterative equalization, channel re-estimation, and channel decoding. Finally, computer simulation results are provided to demonstrate the performance of the proposed sampling-based soft MIMO equalizers in both uncoded and turbo coded systems.     

Adaptive modulation and decision feedback equalization for frequency‐selective MIMO channels

In this paper, an adaptive modulation scheme for the multiple‐input multiple‐output (MIMO) frequency‐selective channels is investigated. We consider a scenario with precoded block‐based transceivers over spatially correlated Rayleigh multipath MIMO channels. To eliminate the inter‐block interference, the zero‐padding is used. The receiver is equipped with a MIMO minimum‐mean‐squared‐error decision feedback equalizer. The precoder aims to force each subchannel to have an identical signal‐to‐interference‐plus‐noise ratio (SINR). To adjust the constellation size, the unbiased mean square error at the equalizer output is sent back to the transmitter. To simplify our analysis, the feedback channel is considered as instantaneous and error free. We first derive the probability density function of the overall SINR for flat fading and frequency‐selective channels. On the basis of the probability density function of the upper bound of the SINR, we evaluate the system performance. We present accurate closed‐form expressions of the average spectral efficiency, the average bit error rate and the outage probability. The derived expressions are compared with Monte Carlo simulation results. Furthermore, we analyze the effect of the channel spatial correlation. Copyright © 2013 John Wiley & Sons, Ltd.     

Soft input soft output Kalman equalizer for MIMO frequency selective fading channels

We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas. Each substream is modulated into M-ary symbols before being transmitted over a frequency selective channel. At the receiver, we propose to use the Kalman filter as a low complexity MIMO equalizer, as opposed to the trellis based maximum a-posteriori (MAP) equalizer whose computational complexity grows exponentially with the channel memory, the number of transmit antennas and the spectral efficiency (bits/s/Hz) of the system. We modify the structure of the Kalman filter and enable it to process the a-priori (soft) information provided by the channel decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The iterative equalizer structure is designed for general M-ary constellations. We also propose a low complexity version of the above algorithm whose performance is comparable to its full complexity counterpart, but which achieves a significant complexity reduction. We demonstrate via simulations that for higher order constellations, when sufficient number of receive antennas are available (e.g. for a 2 transmitter, 3 receiver system, QPSK), the performance of the proposed algorithms after 4 iterations is within 1.5 dB of the non-iterative MAP algorithm with close to an order of magnitude complexity reduction. By objectively quantifying the complexity of all the considered algorithms we show that the complexity reduction for the proposed schemes becomes increasingly significant for practical systems with moderate to large constellation sizes and a large number of transmit antennas     

Adaptive MIMO decision feedback equalization for receivers with time-varying channels

In an attempt to reduce the computational complexity of vertical Bell Labs layered space time (V-BLAST) processing with time-varying channels, an efficient adaptive receiver is developed based on the generalized decision feedback equalizer (GDFE) architecture. The proposed receiver updates the filter weight vectors and detection order using a recursive least squares (RLS)-based time- and order-update algorithm. The convergence of the algorithm is examined by analysis and simulation, and it is shown that the proposed adaptive technique is considerably simpler to implement than a V-BLAST processor with channel tracking, yet the performances are almost comparable.     

Layered maximum likelihood detection for MIMO systems in frequency selective fading channels

By transmitting different substreams in different antennas simultaneously, a multiple element antenna array system provides increased capacity that grows linearly with the number of transmit antennas. Layered space-time processing that performs ing, detection and cancellation for each substream can be used for reception, with a linear growth in receiver complexity. This paper considers this multi-input multi-output system over a slow time-varying frequency selective Rayleigh fading channel environment. With the equivalent channel tap delay line model, each delayed tap in every transmit-receive antenna pair can be considered as an imaginary antenna transmitting a delayed version of the substreams. Based on this idea, we propose a layered maximum likelihood detection (L-MLD) scheme which performs layered processing and maximum likelihood detection for each substream and its delayed elements. To further improve the performance, a group maximum likelihood detection (G-MLD) scheme is also proposed by grouping the substreams and performing layered processing in groups and maximum likelihood detection within the group. However, both schemes increase the required number of receiving antennas, which increases hardware cost and size. To reduce this requirement, we propose the use of oversampling technique to increase the dimension of the received signal. Simulation results show that the L-MLD scheme achieves frequency diversity and outperforms existing schemes such as the V-BLAST system with OFDM and multi-input multi-output decision feedback equalizers (MIMO-DFE). Moreover, the G-MLD scheme performs better than L-MLD with an increased detection complexity. In addition, it was showed that further increasing the oversampling rate beyond the minimum requirement does not improve the performance.     

Bayesian techniques for equalization of rapidly fading frequency selective channels

This paper applies the Bayesian conditional decision feedback estimator (BCDFE) to rapidly fading frequency selective channels. The BCDFE is a model-based deconvolution algorithm which jointly estimates the transmitted data and channel parameters. The BCDFE smoothly transitions between trained and blind operation and consequently provides robust performance in rapidly fading channels. We provide a brief derivation of the BCDFE and characterize the performance on the land mobile radio channel. We assess the BCDFE's principle design characteristics and the resulting performance in both transient and steady-state operation. The effects of delay spread, Doppler spread, and cochannel interference on the bit error probability performance are also presented. The BCDFE demonstrates many of the desirable characteristics of an equalizer for mobile radio.     

Adaptive turbo reduced-rank equalization for MIMO channels

An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE.     

Receiver with iterative soft decision for frequency selectivefading channels

The authors propose a novel receiver which makes an iterative soft decision based on an a posteriori probability criterion with forward-error-corrected data. The proposed receiver significantly improves the bit error rate after forward-error-correction in selective fading channels     

一种应用于802.11n系统的自适应树查找算法的VLSI实现

A 4×4 64-QAM multiple-input multiple-output(MIMO) detector is presented for the application of an IEEE 802.11n wireless local area network.The detector is the implementation of a novel adaptive tree search(ATS) algorithm,and multiple ATS cores need to be instantiated to achieve the wideband requirement in the 802.11n standard.Both the ATS algorithm and the architectural considerations are explained.The latency of the detector is 0.75 μs,and the detector has a gate count of 848 k with a total of 19 parallel ATS cores.Each ATS core runs at 67 MHz.Measurement results show that compared with the floating-point ATS algorithm,the fixed-point implementation achieves a loss of 0.9 dB at a BER of 10-3.     

Per-tone equalization for MIMO OFDM systems

This paper focuses on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with channel order larger than the cyclic prefix (CP) length. Writing the demodulating fast Fourier transform (FFT) as a sliding FFT followed by a downsampling operation, we show in this paper that by swapping the filtering operations of the MIMO channel and the sliding FFT, the data model for the temporally smoothened received signal of each individual tone of the MIMO OFDM system is very similar to the data model for the temporally smoothened received signal of a MIMO single-carrier (SC) system. As a result, to recover the data symbol vectors, the conventional equalization approach for MIMO SC systems can be applied to each individual tone of the MIMO OFDM system. This so-called per-tone equalization (PTEQ) approach for MIMO OFDM systems is an attractive alternative to the recently developed time-domain equalization (TEQ) approach for MIMO OFDM systems. In the second part of this paper, we focus on direct per-tone equalizer design and adapt an existing semi-blind equalizer design method for space-time block coding (STBC) SC systems to the corresponding semi-blind per-tone equalizer design method for STBC OFDM systems.     

A transmit MIMO scheme with frequency domain pre-equalization for wireless frequency selective channels

In this paper, we introduce a transmit multiple-input multiple-output (MIMO) scheme with frequency domain pre-equalization for a multipath or frequency selective channel. In this scheme, MIMO processing in the frequency domain is performed at the transmitter or base station so that the receiver or mobile station only requires limited processing. This scheme provides high data rates and also inherits from the frequency domain equalization the property of relatively low complexity in severe multipath environments. The MIMO transmit processing is derived by minimizing the minimum mean square errors (MMSE), and expressions for the signal-to-interference-plus-noise ratio and error probability based on the Gaussian approximation of the interference term are provided. Some important associated issues, such as channel errors and computational complexity, are also investigated. Numerical simulations are also provided and these demonstrate the improved performance of our proposed scheme compared to other transmit MIMO schemes. In particular, they show that the proposed system can attain multipath or frequency diversity of the channel.     

频率选择性信道下的MIMO收发机联合设计

研究了频率选择性信道下非块传输多天线系统的线性空间收发机联合设计问题,提出了基于最小均方误差准则(MMSE)的联合最优收发算法.为了避免MMSE算法所需要的收发机迭代计算,还给定MMSE接收机、提出了一种低复杂度的串行搜索迫零(ZF-SS)发射预编码,它能够采用多天线提供的空间资源减小或消除多径信道带来的符号间干扰.仿真分析表明,MMSE算法和ZF-SS算法在高信噪比下的性能明显优于现有的基于特征值的波束形成算法.     

An equalization technique for orthogonal frequency-divisionmultiplexing systems in time-variant multipath channels

A loss of subchannel orthogonality due to time-variant multipath channels in orthogonal frequency division multiplexing (OFDM) systems leads to interchannel interference (ICI) which increases the error floor in proportion to the Doppler frequency. A simple frequency-domain equalization technique which can compensate for the effect of ICI in a multipath fading channel is proposed. In this technique, the equalization of the received OFDM signal is achieved by using the assumption that the channel impulse response (CIR) varies in a linear fashion during a block period and by compensating for the ICI terms that significantly affect the bit-error rate (BER) performance     

Space-time turbo equalization in frequency-selective MIMO channels

A computationally efficient space-time turbo equalization algorithm is derived for frequency-selective multiple-input-multiple-output (MIMO) channels. The algorithm is an extension of the iterative equalization algorithm by Reynolds and Wang (see Signal Processing, vol.81, no.5, p.989-995, 2001) for frequency-selective fading channels and of iterative multiuser detection for code-division multiple-access (CDMA) systems by Wang and Poor (see IEEE Trans. Commun., vol.47, p.1046-1061, 1999). The proposed algorithm is implemented as a MIMO detector consisting of a soft-input-soft-output (SISO) linear MMSE detector followed by SISO channel decoders for the multiple users. The detector first forms a soft replica of each composite interfering signal using the log likelihood ratio (LLR), fed back from the SISO channel decoders, of the transmitted coded symbols and subtracts it from the received signal vector. Linear adaptive filtering then takes place to suppress the interference residuals: filter taps are adjusted based on the minimum mean square error (MMSE) criterion. The LLR is then calculated for adaptive filter output. This process is repeated in an iterative fashion to enhance signal-detection performance. This paper also discusses the performance sensitivity of the proposed algorithm to channel-estimation error. A channel-estimation scheme is introduced that works with the iterative MIMO equalization process to reduce estimation errors.     

Layered space-time equalization for wireless MIMO systems

We investigate layered space-time equalization (LSTE) architectures for multiple-input multiple-output (MIMO) frequency-selective channels. At each stage or layer of detection, a MIMO delayed decision feedback sequence estimator (MIMO-DDFSE) is used to tentatively detect a group of selected data streams, among which a subgroup of data streams are output and are canceled from the received signals. With the proposed architectures, the numbers of the tentatively detected data streams and output data streams can be different at different LSTE stages, while the MIMO-DDFSE can also reduce to the special cases of multiple-input single-output decision feedback equalizer (MISO-DFE), MISO-DDFSE, and MIMO-DFE, allowing tradeoffs between performance and complexity. We also derive the equalizer coefficients, discuss timing recovery, and consider channel estimation. Simulation results demonstrate the performance of the proposed LSTE structures and the tradeoffs between performance and complexity of the multistage structure and the single-stage version. We also demonstrate the impact of imperfect channel estimation, imperfect interference cancellation, the number of receive antennas, filter length, and oversampling on performance.     

频率选择MIMO信道多用户块传输SCFDE系统的联合波束赋形

对频率选择多入多出信道多用户场景下块传输单载波频域均衡系统联合波束成形的问题进行了研究。首先将频域波束成形转化为时域成形滤波。在时域模型中给出了频域最小均方误差均衡后各接收节点判决处的信干噪比;在使每个接收节点都满足给定服务质量要求的约束下,将非凸的二阶约束二次优化问题通过松弛约束条件转化为凸半正定优化问题求解,从而得到一组最佳波束成形系数,使所有发射节点的发射功率最小化。仿真表明所有发射节点的总发射功率随模型不同设置表现有规律地变化。     

Low-complexity adaptive decision-feedback equalization of MIMO channels

A new adaptive MIMO channel equalizer is proposed based on adaptive generalized decision-feedback equalization and ordered-successive interference cancellation. The proposed equalizer comprises equal-length subequalizers, enabling any adaptive filtering algorithm to be employed for coefficient updates. A recently proposed computationally efficient recursive least squares algorithm based on dichotomous coordinate descents is utilized to solve the normal equations associated with the adaptation of the new equalizer. Convergence of the proposed algorithm is examined analytically and simulations show that the proposed equalizer is superior to the previously proposed adaptive MIMO channel equalizers by providing both enhanced bit error rate performance and reduced computational complexity. Furthermore, the proposed algorithm exhibits stable numerical behavior and can deliver a trade-off between performance and complexity.