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.     

Turbo equalization of doubly selective channels

In this paper, turbo equalization for transmission over doubly selective channels is proposed. The maximum a posteriori probability (MAP) algorithm is used for channel detection as well as for channel decoding. The detection/decoding constituents can exchange soft information in an iterative manner resulting in the so‐called turbo equalization. The time‐varying multi‐path fading channel is modeled using the basis expansion model (BEM). In this BEM, the time‐varying channel is viewed as a bank of time‐invariant finite impulse response filters, and the time variation is captured by means of time‐varying complex exponential basis functions. Therefore, the time‐varying transition tables that characterize the time‐varying channel can also follow a similar BEM. The complexity of the MAP channel detector is rather prohibitive for practical applications. This motivates the search for lower‐complexity soft‐output channel detectors. For this purpose, soft‐output linear minimum‐mean square error (LMMSE)‐based channel detectors are proposed for single carrier as well as for multi‐carrier systems. With the use of Gaussian approximation, expressions for the a posteriori and extrinsic log‐likelihood ratios have been derived. The performance of the proposed turbo equalization schemes are evaluated using numerical simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Turbo space-time processing to improve wireless channel capacity

By deriving a generalized Shannon capacity formula for multiple-input, multiple-output Rayleigh fading channels, and by suggesting a layered space-time architecture concept that attains a tight lower bound on the capacity achievable. Foschini (see Wireless Pers. Commun., vol.6, no.3, p.311-35, 1998) has shown a potential enormous increase in the information capacity of a wireless system employing multiple-element antenna arrays at both the transmitter and receiver. The layered space-time architecture allows signal processing complexity to grow linearly, rather than exponentially, with the promised capacity increase. This paper includes two important contributions. First, we show that Foschini's lower bound is, in fact, the Shannon bound when the output signal-to-noise ratio (SNR) of the space-time processing in each layer is represented by the corresponding "matched filter" bound. This proves the optimality of the layered space-time concept. Second, we present an embodiment of this concept for a coded system operating at a low average SNR and in the presence of possible intersymbol interference. This embodiment utilizes the already advanced space-time filtering, coding and turbo processing techniques to provide yet a practical solution to the processing needed. Performance results are provided for quasi-static Rayleigh fading channels with no channel estimation errors. We see for the first time that the Shannon capacity for wireless communications can be both increased by N times (where N is the number of the antenna elements at the transmitter and receiver) and achieved within about 3 dB in average SNR about 2 dB of which is a loss due to the practical coding scheme we assume-the layered space-time processing itself is nearly information-lossless.     

Soft-output equalization and TCM for wireless personalcommunication systems

This paper investigates the use of a maximum a posteriori probability (MAP) algorithm to realize soft-output equalization in a concatenated equalization and trellis-coded modulation (TCM) decoding-based wireless communication system. Specifically, we first begin with a general MAP algorithm and then focus on studying Bahl's (1974) MAP and Lee's (1974) MAP algorithms. We then propose a modified version of Lee's MAP algorithm which is much simpler than the original, in terms of complexity, and is more practical. In particular, a very simple channel estimation method which employs orthogonal training sequences is proposed. In order to improve the system performance, equal-gain combining and selection diversity are also considered. Finally, we compare the performance of the MAP algorithm-based equalization with our previously proposed equalization scheme, which combines decision feedback equalization and TCM     

Efficient decision feedback equalization for sparse wireless channels

A new efficient decision feedback equalizer (DFE) appropriate for channels with long and sparse impulse response (IR) is proposed. Such channels are encountered in many high-speed wireless communications applications. It is shown that, in cases of sparse channels, the feedforward and feedback (FB) filters of the DFE have a particular structure, which can be exploited to derive efficient implementations of the DFE, provided that the time delays of the channel IR multipath components are known. This latter task is accomplished by a novel technique, which estimates the time delays based on the form of the channel input-output cross-correlation sequence in the frequency domain. A distinct feature of the resulting DFE is that the involved FB filter consists of a reduced number of active taps. As a result, it exhibits considerable computational savings, faster convergence, and improved tracking capabilities as compared with the conventional DFE. Note that faster convergence implies that a shorter training sequence is required. Moreover, the new algorithm has a simple form and its steady-state performance is almost identical to that of the conventional DFE.     

On frequency-domain equalization and diversity combining for broadband wireless communications

This paper is concerned with the use of frequency-domain equalization (FDE) and space diversity within block transmission schemes for broadband wireless communications. The expected performance with both multicarrier (MC) and single-carrier (SC) modulations is emphasized, when a cyclic prefix, long enough to cope with the maximum relative channel delay, is appended to each transmitted block. A set of numerical results is presented and discussed, with the help of appropriate, analytical performance bounds which are conditional on a given channel realization. These bounds are used to explain the performance advantage of the SC/FDE option, the benefits of space diversity, and the impact of the criterion for computing the FDE parameters.     

Turbo equalization with sequential sequence estimation overmultipath fading channels

We investigate the performance of a turbo equalization scheme over frequency-selective fading channels, where a soft-output sequential algorithm is employed as the estimation algorithm. The advantage of this scheme comes from the low computational complexity of the sequential algorithm, which is only linearly dependent on the channel memory length. Simulation results of an 8-PSK trellis-coded modulation (TCM) system show that the performance of this scheme suffers approximately 2-dB loss compared with that of the turbo max-log maximum a posteriori (MAP) probability equalizer after 5 iterations     

Turbo equalization

Turbo equalization is an iterative equalization and decoding technique that can achieve equally impressive performance gains for communication systems that send digital data over channels that require equalization, i.e., those that suffer from intersymbol interference (ISI). In this article, we discuss the turbo equalization approach to coded data transmission over ISI channels, with emphasis on the basic ideas and some of the practical details. The original system introduced by Douillard et al. can be viewed as an extension of the turbo decoding algorithm by considering the effect of the ISI channel as another form of error protection, i.e., as a rate-1 convolutional code.     

Spatial and temporal equalization for broadband wireless indoornetworks at millimeter waves

The combined use of adaptive antennas and decision feedback equalization (DFE) is analyzed in a realistic propagation scenario at millimeter waves, taking the direction of arrivals (DOA's) of the received paths into account. The joint antennas and DFE scheme, with one forward filter for each antenna and a single feedback filter (FBF), can be viewed as a spatial and temporal DFE (ST-DFE). The performance of this solution is compared with the cascade of adaptive antenna used for beamforming and DFE. It is found that ST-DFE achieves better performance since it combines the beamforming capability of the antenna array with the equalization properties of the DFE, with great advantages especially when rays arrive from similar angles. The mean square error (MSE) is analytically derived for infinitely long filters in a quasi-static environment with multiple rays having different DOAs, and compared (for the two-path model) with simulation results assuming filters with a small number of taps. Finally, service availability through coverage evaluation is developed and compared with that of a coded-orthogonal frequency division multiplexing (C-OFDM) system     

Coding and equalization for PPM on wireless infrared channels

We analyze the performance of trellis-coded pulse-position modulation with block decision-feedback equalization (BDFE) and parallel decision-feedback decoding (PDFD) on indoor, wireless infrared channels. We show that the reduced complexities of BDFE and PDFD as compared to maximum-likelihood sequence detection allow for better codes whose increased coding gain more than compensates for the penalty due to suboptimal detection. We quantify these net gains in performance over a range of dispersive channels, indicating where BDFE and PDFD provide the best performance. Finally, we present Monte Carlo simulation results to verify our analysis     

双选择性信道条件下MIMO-OFDM系统中的ICI抑制及频域Turbo均衡

分析了双选择性信道条件下MIMO-OFDM系统的ICI产生原理,提出了一种以最大化缩短信干噪比(MSSINR,maximum shortening the signal to inter-carrier interference plus noise ratio)为目标的频域ICI抑制算法及其简化算法;在此基础上将Turbo均衡技术应用到MIMO-OFDM系统中,提出了一种基于MSSINR频域ICI抑制的频域Turbo均衡(FTE,frequency-domain Turbo equalization)算法,并进行了数值仿真和比较分析。     

Turbo equalization for GMSK signaling over multipath channels basedon the Gibbs sampler

We consider the problem of Bayesian data restoration for Gaussian minimum shift keying (GMSK) signals over unknown multipath channels. As an alternative to the linear approximation method employed in the conventional finite impulse response (FIR) model, we develop a nonlinear signal model for this system. A Bayesian equalizer based on the Gibbs sampler, a Markov chain Monte Carlo (MCMC) procedure, is developed for estimating the a posteriori symbol probability in the GMSK system without explicit channel estimation. The basic idea of this technique is to generate ergodic random samples from the joint posterior distribution of all unknowns, and then to average the appropriate samples to obtain the estimates of the unknown quantities. Being soft-input soft-output in nature, the proposed Bayesian equalization technique is well suited for iterative processing in a coded system, which allows the Bayesian equalizer to successively refine its processing based on the information from the decoding stage, and vice versa     

Blind equalization for an application of unitary space-time modulation in ISI channels

Transmit diversity schemes have gained attention due to the promise of increased capacity and improved performance. Among these schemes, unitary space-time modulation and differentially encoded unitary space-time modulation allow for simple noncoherent decoding for flat-fading channels. In this paper, a new blind equalization algorithm for these transmission schemes in intersymbol interference (ISI) channels is proposed. A matrix-type constant modulus algorithm that exploits the unitary structure of the space-time codes is developed. The equalizer is paired with a noncoherent decoder, resulting in a completely blind, low-complexity method for decoding in the presence of ISI. A noiseless convergence analysis is conducted and verified via simulation in both noiseless and noisy cases. The performance of the overall system is evaluated via simulation and semi-analytically, and the achieved performance is between that of the ideal zero-forcing and the minimum-mean squared-error equalizers.     

A canonical space-time characterization of mobile wireless channels

A canonical space-time characterization of mobile wireless channels is introduced in terms of a fixed basis that is independent of the true channel parameters. The basis captures the essential degrees of freedom in the received signal using discrete multipath delays, Doppler shifts, and directions of arrival. This provides a robust representation of the propagation dynamics and dramatically reduces the number of channel parameters to be estimated. The resulting canonical space-time receivers deliver optimal performance at substantially reduced complexity compared to existing designs     

Split soft-decision equalization for wireless channels with large delay spread

A novel split soft-decision equalizer (SSE) with near-optimum performance is proposed for wireless multipath channels with large delay spread. The concept of SSE is significantly different from the traditional notions of the Viterbi algorithm and decision-feedback equalizer. Instead of dealing with received sequence as a combined sequence, it splits the received sequence into its constituent paths. Using an iterative soft-decision algorithm, reliability of the soft decisions on each decomposed element is improved iteratively. The major advantage of SSE is the independence of computation complexity on channel time dispersion. Joint design of SSE with a soft-decision decoder is also considered in this paper. Performance analysis and simulation results show that performance of the proposed algorithm comes very close to that of the logarithmic maximum a posteriori decoder.     

Low-complexity channel-adapted space-time coding scheme for frequency-selective wireless MIMO channels

By exploiting the wireless multiple-input multiple-output (MIMO) channel structure, a brand new space-time code design criterion is derived. Based on the new criterion, we propose one low-complexity channel-adapted space-time (CAST) coding scheme, where trade-offs among codeword error rate, data throughput, and computational complexity are very flexible. Simulation results confirm that, in the frequency-selective MIMO channels, the CAST coding scheme can perform significantly better than the existing space-time codes, e.g., Alamouti space-time orthogonal code.     

A physical scattering model for MIMO macrocellular broadband wireless channels

This paper presents a physical scattering model that predicts multiple-input multiple-output (MIMO) channel characteristics conforming well to experimental observations in macrocells. Our approach is to start with a given single-input single-output power-delay profile (defined for specific range, bandwidth and antenna parameters) and fit a scattering model that characterizes the MIMO channel. From the derived scattering model and antenna array configurations, the MIMO channel is computed using a ray-based method. Simulations of several MIMO channels are shown to exhibit experimentally observed channel correlations, antenna beamwidth effect, range dependency, and frequency selectivity.     

Noncoherent space-time equalization

In this paper, noncoherent equalization is combined with multiple receive antennas. The resulting noncoherent space-time equalization (NSTE) schemes are analyzed and compared with the corresponding coherent receivers. In particular, noncoherent linear equalization (NLE), noncoherent decision-feedback equalization (NDFE), and noncoherent sequence estimation (NSE) are considered. For NLE and NDFE novel approximations for the signal-to-distortion ratio (SDR) are derived and verified by simulations. It is shown that NSTE can suppress interfering users and exploit diversity as efficiently as coherent STE. However, NSTE is more robust against channel phase variations than the combination of coherent STE and synchronization. Robust noncoherent recursive least squares (NC-RLS) algorithms, which compare favorably with the conventional RLS algorithm with additional carrier synchronization loop, are proposed for fast filter adaptation.     

Turbo编码MIMO/OFDM系统中的Turbo均衡

针对Turbo编码MIMO/OFDM系统,本文提出一种低复杂度的Turbo均衡算法,均衡器采用性能近于最优检测的概率数据辅助（Probabilistic Data Association）算法,与软输入软输出的Turbo信道解码器之间迭代交换外信息,实现信道均衡与信道解码的迭代更新,以充分利用已获得的信息,克服传统判决反馈均衡器误差传播的缺陷。仿真表明,该均衡算法性能要比MMSE＋MF线性检测算法提高约1dB,在Eb/No为4dB时误比特率达到10-6,且算法复杂度仅为O（N3）,经两次迭代就可获得较为满意的码间干扰消除效果。     

Blind equalization for broadband access

This article discusses the general principles of blind equalization and its use in emerging broadband access applications such as FTTC and xDSL. New results obtained for these applications are also presented