New results on second-order statistics-based blind identification and equalization of SIMO channels

Channel estimation and blind equalization of MIMO (multiple-input multiple-output) communications channels is considered using primarily the second-order statistics of the data. We consider estimation of (partial) channel impulse response and design of finite-length MMSE (minimum mean-square error) blind equalizers. The basis of the approach is the design of a zero-forcing equalizer that whitens the noise-free data. We allow infinite impulse response (IIR) channels. Moreover, the multichannel transfer function need not be column-reduced. Our approaches also work 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. The sources are recovered up to a unitary mixing matrix and are further 'unmixed using higher-order statistics of the data. An illustrative simulation example is provided.

Blind channel estimation and blind minimum mean square error (MMSE) equalization of multiple-input multiple-output (MIMO) communications channels arising in multiuser systems is considered, using primarily the second-order statistics of the data. 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 (IIR) channels are allowed. Moreover, the multichannel transfer function need not be column-reduced. 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. Using second-order statistics, the sources are recovered up to a unitary mixing matrix, and are further "unmixed" using higher order statistics of the data. Two illustrative simulation examples are provided where the proposed method is compared with its predecessors and an existing method to show its efficacy.

The problem of blind equalization of single-input multiple-output (SIMO) communications channels is considered using only the second-order statistics of the data. Such models arise when a single receiver data is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We focus on direct design of finite-length minimum mean-square error (MMSE) blind equalizers. Unlike the past work on this problem, we allow infinite impulse response (IIR) channels. Our approaches also work when the "subchannel" transfer functions have common zeros as long as the common zeros are minimum-phase zeros. Illustrative simulation examples are provided.

ABSTRACTWhile inter-symbol interference is not of concern, inter-carrier interference that is caused by carrier frequency offset (CFO) is more concerned in orthogonal frequency division multiplexing (OFDM) systems. The estimation of channel impulse response (CIR) is another important parameter of interest in the system. Recently, a number of approaches for the joint estimation of CFO and CIR in OFDM systems have been proposed in the literature, and most of them are traditional maximum-likelihood-based approaches. In this paper, we propose a number of mixture cost-reference particle filtering (CRPF) approaches for joint estimation of CIR and CFO, and a couple of them can be applied without the knowledge of both state and measurement noise statistics. Conventional least mean squares algorithm or recursive least squares algorithm is jointly employed with recently developed CRPF for nonlinear and multiple parameters estimation in OFDM systems. The computer simulation results show that mixture CRPFs are more robust against particle impoverishment (PI) problem than standard mixture particle filtering (PF) and mixture regularized PF (RPF) approaches although RPF was particularly developed to tackle the PI problem. In this paper, we investigate a number of mixture PF approaches including ones that do not need the information of noise statistics for the joint estimation of CFO and channel in OFDM systems.

A computationally efficient ranging scheme that estimates time of arrival (TOA) by a low complexity minimum mean square error (MMSE) and a matrix pencil techniques is proposed for IEEE 802.15.4a chirp spread spectrum system. In TOA estimation, it is known that accurate channel delay can be estimated by the MMSE technique. However, the major drawback of the MMSE is its high computational complexity, which grows with number of signal samples. In this paper, thus, a computational efficient MMSE technique based on the chirp spectrum characteristic is proposed for a low complexity ranging algorithm. The proposed TOA estimation method consists of two-step signal processing: proposed low complexity MMSE-based channel impulse response (CIR) estimation and the channel delay tracking by matrix pencil algorithm. The proposed TOA estimation method not only has low computational complexity, but also achieves small ranging error. The effectiveness of the proposed algorithm is demonstrated by simulation results.

This paper introduces novel hybrid pilot-aided channel estimation with decision feedback equalizer(DFE) for OFDM systems and its corresponding hardware co-simulation platform. This pilot-aided channel estimation algorithm consists of two parts: coarse estimation and fine estimation. In the coarse estimation, the combined classical channel estimation methods including carrier frequency offset (CFO) and channel impulse response (CIR) estimation are used. Based on the received training sequence and pilot tones in the frequency domain, the major CFO, sampling clock frequency offset (SFO) and CIR effect coefficients are derived. In the fine estimation, the pilot-aided polynomial interpolation estimation combined with a new decision feedback equalizer scheme based on minimum mean squared error (MMSE) criteria is proposed to reduce the residual effect caused by imperfect CIR equalizer, SFO and CFO. At the same time, for the purpose of speeding up the whole development and verification process, a new architecture of co-simulation platform which combines software and hardware is introduced. The simulation results on the co-simulation platform indicate that the proposed hybrid channel estimation scheme can enhance the receiver performance by 6 dB in terms of error vector magnitude (EVM) over large ranges of CFO and SFO and BER performance by 7 dB for SNR range over 15 dB.

A family of new MMSE blind channel equalization algorithms based on second order statistics are proposed. Instead of estimating the channel impulse response, we directly estimate the cross-correlation function needed in Wiener-Hopf filters. We develop several different schemes to estimate the cross-correlation vector, with which different Wiener filters are derived according to minimum mean square error (MMSE). Unlike many known subspace methods, these equalization algorithms do not rely on signal and noise subspace separation and are consequently more robust to channel order estimation errors. Their implementation requires no adjustment for either single or multiple user systems. They can effectively equalize single-input multiple-output (SIMO) systems and can reduce the multiple-input multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. The implementations of these algorithms on SIMO system are given and simulation examples are provided to demonstrate their superior performance over some existing algorithms.

A novel efficient algorithm for the estimation of sparse channel impulse response (CIR) is addressed for OFDM systems. The innovation of this algorithm comes from the fact that it equivalently sees the CIR estimation problem as a decoding one. To do so, it exploits first the channel sparsity through the modelling of the sparse CIR as a Bernoulli-Gaussian process. Then, using the relationship between the Reed-Solomon codes and the OFDM modulator it efficiently estimates the sparse CIR using directly the decoding of the OFDM received signal. The obtained simulation results highlight that using the proposed algorithm gives good estimation performance in terms of mean squares error on the sparse CIR estimates.

Under highly mobile environments, the bit error rate (BER) performance of DFT spreading-orthogonal frequency division multiplexing (DFTS-OFDM) signal with a frequency domain equalization method would be degraded relatively due to the loss of orthogonality among subcarriers. To solve this problem, this paper proposes an iterative based time domain equalization (TDE) technique with a time domain channel impulse response (CIR) estimation method for the DFTS-OFDM signal. The salient features of proposed method are to employ a time domain training sequence (TS) in the estimation of CIR instead of using the conventional pilot subcarriers method and to employ the TDE technique with a maximum likelihood (ML) estimation method instead of using the conventional minimum mean square error frequency domain equalization (MMSE-FDE) method. This paper also proposes a low-complexity iterative method for the TDE method by using the preconditioned conjugate gradient squared (PCGS) algorithm for solving the simultaneous equations instead of using a direct calculation of inverse matrix. This paper presents various simulation results under highly mobile environments to demonstrate the effectiveness of proposed iterative based TDE with the CIR estimation method for the DFTS-OFDM signal as comparing with the conventional MMSE-FDE method.

Adaptive beamforming for binary phase shift keying communication systems

SSP based underwater CIR estimation with S-BiFPN

We introduce a new structured channel impulse response (CIR) estimation method for sparse multipath channels where we demonstrate a robust way of restoring the pulse shape into the composite CIR. We call this novel CIR estimation method time-of-arrival based blended least squares (TOA-BLS) which uses symbol rate sampled signals, and it is based on blending correlation processing followed by TOA estimation in the frequency domain by the least squares based channel estimation. TOA estimation in the frequency domain is accomplished by estimating the AR model parameters by solving the forward and forward-backward linear prediction equations in the least squares sense. Simulation examples are drawn from the ATSC digital TV 8-VSB system (ATSC Digital Television Standard, A/53, 1995). The delay spread for digital TV systems can be as long as several hundred times the symbol duration; however, digital TV channels are sparse where there are only a few dominant multipaths.

In orthogonal frequency division multiplexing (OFDM), Fourier Transform (FT) is used as a modulation technique. To avoid inter-symbol interference (ISI) in OFDM by a time dispersive channel, a cyclic prefix (CP) is used which also reduces its spectral efficiency. wavelet packet transform (WPT) as a modulation scheme has been proposed for wireless communication. In this paper, WPT based OFDM is presented and proposed using minimum mean square error (MMSE) equalizer. Equalization is a major factor in wavelets. MMSE is proposed for wavelet based OFDM (WOFDM) based on WPT and compared with zero forcing equalizer (ZFE). The performance is measured for arbitrary magnitude finite impulse response (FIR) channels in the presence of additive white Gaussian noise (AWGN) and impulse noise. Simulation results show a clear improvement in bit error rate (BER) for MMSE over ZFE equalization technique in the presence of noise.

To approach the potential MIMO capacity while optimizing the system bit error rate (BER) performance, the joint transmit and receive minimum mean squared error (MMSE) design has been proposed. It is the optimal linear scheme for spatial multiplexing MIMO systems, assuming a fixed number of spatial streams p as well as a fixed modulation and coding across these spatial streams. However, state-of-the-art designs arbitrarily choose and fix the value of the number of spatial streams p, which may lead to an inefficient power allocation strategy and a poor BER performance. We have previously proposed to relax the constraint of fixed number of streams p and to optimize this value under the constraints of fixed average total transmit power and fixed spectral efficiency, which we referred to as spatial-mode selection. Our previous selection criterion was the minimization of the system sum MMSE. In the present contribution, we introduce a new and better spatial-mode selection criterion that targets the minimization of the system BER. We also provide a detailed performance analysis, over flat-fading channels, that confirms that our proposed spatial-mode selection significantely outperforms state-of-the-art joint Tx/Rx MMSE designs for both uncoded and coded systems, thanks to its better exploitation of the MIMO spatial diversity and more efficient power allocation.

A method to estimate the channel impulse response using the received serial data in time-domain, without using DFT operations, is investigated. The processing required by the proposed method is substantially reduced when compared with LS-DFT channel estimation method, with no performance degradation. Furthermore, this method can incorporate the results of other published works that are DFT-based, at little or no added complexity, to improve the estimate of channel impulse response.