Exploiting non-Gaussianity in blind identification and equalisation of MIMO FIR channels

The problem of blind identification and equalisation (BIE) of finite impulse response (FIR) channels in multiuser digital communications is investigated. The non-Gaussian nature and statistical independence of the users' data streams is exploited by resorting to blind signal separation (BSS) based on higher-order statistics (HOS). Two such techniques are put forward. The first technique is composed of an extension to the multiuser case of a second-order BIE method, followed by a BSS-based space-equalisation step. The second technique achieves joint space-time equalisation through the direct application of a HOS-based BSS method followed by a blind identification algorithm. In a number of numerical experiments, the first procedure proves less costly and more effective for short data records. Despite their computational complexity, interesting features such as constellation-independent channel identification and symbol recovery, and robustness to ill-conditioned channels in high SNR environments render HOS-BSS based BIE methods an effective alternative to BIE techniques exploiting other spatio-temporal structures.     

Precoder Partitioning in Closed-loop MIMO Systems

We study unitary precoding for multistream MIMO systems with partial channel state information at the transmitter. We introduce a quantization scheme in which the full space of non-equivalent precoding matrices is partitioned into Grassmannian and orthogonalization parts. The Grassmannian part is used for maximizing the power after precoding and the orthogonalization part is used for removing cross talk between the data streams. We show that orthogonalization improves the attainable capacity when the receiver is linear. We give a parametrization for the non-equivalent orhogonalization matrices and a metric which measures the orthogonality of the transmission. Optimal orthogonalization codebooks for two-stream transmission are presented. When feedback is limited, the optimal partitioning of feedback bits between Grassmannian and orthogonalization parts becomes an issue. In correlated scenarios, the number of feedback bits may be significantly reduced by investing bits into the orthogonalization part.     

适合频率选择性MIMO信道的FIR预编码器

改善频率选择性多输入多输出(MIMO)系统的信道容量,具有重要的理论和现实意义。基于最大信道容量准则,提出一种适合MIMO频率选择性衰落信道的预编码新方法。该方法将预编码器建模为一个有限冲击响应(FIR)滤波器,利用秩松弛将原非凸优化问题转换成为半定规划(SDP)问题,并结合特征值分解设计预编码器。仿真实验结果和分析表明,相对于扩展均匀信道分解(EUCD)等其它现有算法,该算法仅需较少的滤波器阶数即可显著提升系统的信道容量,具有较低的实现复杂度。     

Precoder Design for Non-Regenerative MIMO Relay Systems

This paper studies the precoder design for a 3-node non-generative MIMO relay channel, taking the direct link transmission into consideration. We first look into the scenario where precoding is only performed at the relay. Our analytical approach enables a relay precoding design to achieve better ergodic capacity than the precoding design to achieve a lower bound of the capacity reported in earlier works. We next propose an iterative algorithm to perform joint precoding design at both the source and the relay. To reduce the computation complexity of the iterative algorithm, a two-step algorithm is then developed. Our numerical results show that under some circumstances, capacity gain can be achieved by performing precoding at both the source and the relay compared to the case where precoding is performed at the relay only. The efficiency of the proposed two-step algorithm is verified since it achieves roughly identical capacity as the iterative joint precoding scheme.     

EM-based blind LDPC identification in multipath channels

As the advent of cognitive radios,blind encoder identification has attracted increasingly attentions since it plays an important role.The existing works mainly focus on additive white Gaussian noise (AWGN) channel,while the blind identification in multipath scenarios has not been sufficiently investigated.Considering the blind low density parity-check (LDPC) codes identification in the presence of unknown multipath fading channel,a likelihood-based classifier was proposed using the expectation maximization (EM) algorithm to obtain the maximum likelihood estimates of the unknown parameters.Then,an average log-likelihood ratio (LLR) estimator was adopted to classify the unknown encoder.Numerical results show that the proposed algorithm provides promising identification performance in multipath channels,especially in the low signal-to-noise ratio region.     

MIMO channel blind identification in the presence of spatiallycorrelated noise

We address the problem of the second-order blind identification of a multiple-input multiple-output (MIMO) transfer function in the presence of additive noise. The additive noise is assumed to be (temporally) white, i.e., uncorrelated in time, but we do not make any assumption on its spatial correlation. This problem is thus equivalent to the second-order blind identification of a MIMO transfer function in the noiseless case but from a partial auto-covariance function {R_n }_n≠0. Our approach consists of computing the missing central covariance coefficient R₀ from this partial auto-covariance sequence. It can be described simply within the algebraic framework of rational subspaces. We propose an identifiability result that requires very mild assumptions on the transfer function to be estimated. Practical subspace-based identification algorithms are deduced and tested via simulations     

Blind identification of FIR MIMO channels by decorrelating subchannels

We study blind identification and equalization of finite impulse response (FIR) and multi-input and multi-output (MIMO) channels driven by colored signals. We first show a sufficient condition for an FIR MIMO channel to be identifiable up to a scaling and permutation using the second-order statistics of the channel output. This condition is that the channel matrix is irreducible (but not necessarily column-reduced), and the input signals are mutually uncorrelated and of distinct power spectra. We also show that this condition is necessary in the sense that no single part of the condition can be further weakened without another part being strengthened. While the above condition is a strong result that sets a fundamental limit of blind identification, there does not yet exist a working algorithm under that condition. In the second part of this paper, we show that a method called blind identification via decorrelating subchannels (BIDS) can uniquely identify an FIR MIMO channel if a) the channel matrix is nonsingular (almost everywhere) and column-wise coprime and b) the input signals are mutually uncorrelated and of sufficiently diverse power spectra. The BIDS method requires a weaker condition on the channel matrix than that required by most existing methods for the same problem.     

SUBSPACE METHOD FOR BLIND IDENTIFICATION OF CDMA TIME—VARYING CHANNELS

A new blind method is proposed for identification of CDMA Time-Varyin(TV) channels in this paper.By representing the TV channel‘s impulse responses in the delay-Doppler spread domain, the discrete-time canonical model of CDMA-TV systems is developed and a subspace method to identify blindly the Time-Invariant(TI) coordingates is proposed.Unlike existing basis expansion methods, this new algorithm does not require estimation of the base frequencies, neither need the assumption of linearly varying delays across symbols.The algorithm offers definite explanation of the expansion coordinates.Simulation demonstrates the effectiveness of the algorithm.     

A moment-based blind method for identification of FIR down-linkDS-CDMA channels

In order to achieve lower bit error rates (BERs), multiuser detection techniques have been proposed. Generally, multiuser detectors can provide excellent performance only when channel parameters are precisely known. In this paper, we propose a moment-based blind method to estimate down-link channels precisely. The mean square error (MSE) expression of the channel vector estimate has been derived. Through simulations, we show the effect of the channel estimation error on the performance of a multiuser detector. In this paper, we also show that finite impulse response (FIR) channels can be blindly identified by using the proposed method and the spreading operation. Since the spreading operation of the code division multiple access (CDMA) can induce cyclostationarity, any FIR channel can be identified by the proposed method. Of course, in order to guarantee identifiability, some conditions on the spreading codes will be satisfied. In this paper, these conditions are also found     

Multistep linear predictors-based blind identification andequalization of multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider the estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. We extend the multistep linear prediction approach to MIMO channels where the multichannel transfer function need not be column reduced. Moreover, we allow infinite impulse response (IIR) channels as well as the case where the “subchannel” transfer functions have common zeros. In the past, this approach has been confined to SIMO finite impulse response (FIR) channels with no common subchannel zeros. A related existing approach applicable to MIMO channels is restricted to FIR column-reduced systems with equal length subchannels. In our approach, the knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the “subchannel” transfer functions have common zeros, as long as the common zeros are minimum-phase zeros. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. Illustrative computer simulation examples are provided     

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.     

Robust Precoder Adaptation for MIMO Links With Noisy Limited Feedback

In this paper, we propose two robust limited feedback designs for multiple-input multiple-output (MIMO) adaptation. The first scheme, namely, the combined design jointly optimizes the adaptation, CSIT (channel state information at the transmitter) feedback as well as index assignment strategies. The second scheme, namely, the decoupled design, focuses on the index assignment problem given an error-free limited feedback design. Simulation results show that the proposed framework has significant capacity gain compared to the naive design (designed assuming there is no feedback error). Furthermore, for large number of feedback bits $C_{rm fb}$, we show that under two-nearest constellation feedback channel assumption, the MIMO capacity loss (due to noisy feedback) of the proposed robust design scales like ${cal O}(P_e2^{-{{C_{rm fb}}over{t+1}}})$ for some positive integer $t$. Hence, the penalty due to noisy limited feedback in the proposed robust design approaches zero as $C_{rm fb}$ increases.      

OFDM MIMO radar waveform design for targets identification

In order to obtain better target identification performance, an efficient waveform design method with high range resolution and low sidelobe level for orthogonal frequency division multiplexing (OFDM) multiple-input multiple-output (MIMO) radar is proposed in this paper. First, the wideband CP-based OFDM signal is transmitted on each antenna to guarantee large bandwidth and high range resolution. Next, a complex orthogonal design (COD) is utilized to achieve code domain orthogonality among antennas, so that the spatial diversity can be obtained in MIMO radar, and only the range sidelobe on the first antenna needs suppressing. Furthermore, sidelobe suppression is expressed as an optimization problem. The integrated sidelobe level (ISL) is adopted to construct the objective function, which is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The numerical results demonstrate the superiority in performance (high resolution, strict orthogonality, and low sidelobe level) of the proposed method compared to existing algorithms.     

Frequency domain blind MIMO system identification based on second and higher order statistics

We present a novel frequency-domain framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent, unobservable inputs. The system frequency response is obtained based on singular value decomposition (SVD) of a matrix constructed based on the power-spectrum and slices of polyspectra of the system output. By appropriately selecting the polyspectra slices, we can create a set of such matrices, each of which could independently yield the solution, of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance. The freedom to select the polyspectra slices allows us to bypass the frequency-dependent permutation ambiguity that is usually associated with frequency domain SVD, while at the same time allows us compute and cancel the phase ambiguity. An asymptotic consistency analysis of the system magnitude response estimate is performed     

CDMA时变色散信道的两级盲辨识算法

本文通过对时变信道的扩展函数在时频域进行正则采样，得到了CDMA时变系统的离散正则模型。针对该模型提出了一种具有较低运算量的两级盲辨识算法。为避免两级算法产生的误差传播效应，文章将理想SIMO模型等效为加性噪声模型来处理。与基展开模型方法相比，该算法具有不需利用观测数据的高阶统计量估计展开基频率的优点。文章通过仿真验证了该算法是可行的。     

Transmit signal design for optimal estimation of correlated MIMO channels

We address optimal estimation of correlated multiple-input multiple-output (MIMO) channels using pilot signals, assuming knowledge of the second-order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the recently proposed virtual channel representation, which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in the correlated channel. However, our design framework is applicable to more general channel models, which include known channel models, such as the transmit and receive correlated model, as special cases. We show that optimal signaling is in a block form, where the block length depends on the signal-to-noise ratio (SNR) as well as the channel correlation matrix. The block signal corresponds to transmitting beams in successive symbol intervals along fixed virtual transmit angles, whose powers are determined by (nonidentical) water filling solutions based on the optimization criteria. Our analysis shows that these water filling solutions identify exactly which virtual transmit angles are important for channel estimation. In particular, at low SNR, the block length reduces to one, and all the power is transmitted on the beam corresponding to the strongest transmit angle, whereas at high SNR, the block length has a maximum length equal to the number of active virtual transmit angles, and the power is assigned equally to all active transmit angles. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.     

MIMO Precoder Designs for Frequency-Selective Fading Channels Using Spatial and Path Correlation

Multiple-input–multiple-output (MIMO) precoder design for frequency-selective fading channels using partial channel information based on the spatial and path correlation matrices is presented. By representing a frequency-selective fading channel as a multipath model with $L$ effective paths, a general precoding structure is proposed and used to derive optimum precoding designs that maximize Jensen's upper bound on the channel ergodic capacity under the transmitted power constraint for two cases, i.e., uncorrelated and correlated channel paths. Analytical results show that, in the uncorrelated case, the precoder structure consists of a number of parallel precoders for frequency-flat fading channels. The power assignment to each precoder and the power allocation over the eigenmodes of each precoder are calculated based on the power of channel paths and the eigenvalues of the transmit correlation matrix. In the correlated case, the precoder structure is an eigenbeamformer with the beams referred to a function of eigenvectors of the Kronecker product of path and transmit correlation matrices. Furthermore, the power allocated to each eigenmode can be obtained from a statistical water-pouring policy that is specified by the product of eigenvalues of the transmit antenna and path correlation matrices. Simulation results for different scenarios indicate that the proposed precoder can increase the ergodic capacity of MIMO systems in a frequency-selective fading environment with spatial and path correlations, and its offered capacity gain is increased with the level of correlation and numbers of antennas and channel paths.      

Linear prediction error method for blind identification of periodically time-varying channels

Blind channel estimation for single-input multiple-output (SIMO) periodically time-varying channels is considered using only the second-order statistics of the data. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). The linear prediction error method for blind identification of time-invariant channels is extended to time-varying channels represented by a CE-BEM. Sufficient conditions for identifiability are investigated. The cyclostationary nature of the received signal is exploited to consistently estimate the time-varying correlation function of the data from a single observation record. The proposed method requires the knowledge of the active basis functions but not the channel length (an upper bound suffices). Several existing methods require precise knowledge of the channel length. Equalization of the time-varying channel, given the estimated channel, is investigated. Computer simulation examples are presented to illustrate the approach and to compare it with two existing approaches.     

A multidelay whitening approach to blind identification andequalization of SIMO channels

Blind channel estimation and blind equalization of single-input multiple-output communications channels is considered using only the second-order statistics of the data. Estimation of (partial) channel impulse response and design of finite-length minimum mean-square error blind equalizers is investigated. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. Infinite-impulse response channels are allowed. The proposed approach also works when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. Three illustrative simulation examples using 4-QAM and 16-QAM signals are provided where the proposed approach is compared with several existing approaches     

Minimum-phase fir precoder design for multicasting over MIMO frequency-selective channels

To maximize the throughput of frequency-selective multicast channel, the minimum-phase Finite Impulse Response (FIR) precoder design is investigated in this paper. This problem can be solved in two steps. Firstly, we focus on designing a nonminimum-phase FIR precoder under the criterion of maximizing the throughput, and develop two efficient algorithms for the FIR precoder design from perspectives of frequency domain and time domain. In the second step, based on the theory of spectral factorization, the nonminimum-phase FIR precoder is transformed into the corresponding minimum-phase FIR precoder by a classic iterative algorithm without affecting the throughput. Numerical results indicate that the achievable rate of the proposed design has remarkable improvement over that of existing schemes, moreover, the group delay introduced by the FIR precoder is minimized.