Blind Channel Estimation Scheme Research Articles

Blind Channel Estimation and Symbol Detection for Multi-Cell Massive MIMO Systems by Expectation Propagation

Massive MIMO systems exploit the favorable propagation condition of the radio channel, whereby the vector-valued channels between the base station (BS) and the terminals become mutually orthogonal. This property is used in a recently-proposed channel estimation method for multi-cell massive MIMO systems based on the eigenvalue decomposition (EVD) of the correlation matrix of the received vectors. In this paper, we present a blind channel estimation and symbol detection scheme for multi-cell massive MIMO systems based on expectation propagation (EP). The proposed algorithm is initialized with the channel estimation result from the EVD-based method. It is shown that in our EP formulation, channel estimation and symbol detection are “decoupled” in that EP iterations for channel estimation can be performed without the knowledge of the specific transmitted symbols. Therefore, channel estimation can be performed first followed by symbol detection. In particular, a liner symbol detection scheme such as zero-forcing (ZF) or minimum mean-squared error (MMSE) algorithm may be employed. Simulation results show that after a few iterations, the EP-based algorithm significantly improves the performance of the EVD-based method in both channel estimation and symbol error rate. Comparisons are also made with the results from a recently proposed blind detection scheme and it is shown that the proposed algorithm has better performance.

Distributed Cophasing With Autonomous Constellation Selection

In this paper, we consider a distributed cophasing (DCP) technique in which multiple sensor nodes (SNs) communicating their observations to a fusion center (FC) need to transmit different classes of data requiring different levels of error protection. To achieve this, we propose a variant of the DCP technique with autonomous constellation selection at the different SNs. In the first stage of the two-stage time division duplexed cophasing scheme, the SNs obtain estimates of the channels to the FC using pilot symbols transmitted by the latter. Following this, the SNs simultaneously transmit their data symbols prerotated according to the estimated channel phases to combine coherently at the FC. The symbols transmitted by different SNs are drawn from possibly different constellations selected based on the estimated instantaneous channel gains. We show that this scheme is equivalent to transmitting symbols from hierarchical constellations. Based on the properties of hierarchical constellations, we develop recursive expressions for the BER of the proposed system. Following this, we use the properties of the effective channel coefficients to show that it is possible to recover the transmitted data bits from the signal received at the FC blindly, without requiring explicit pilot symbols to be sent by the power-starved SNs. We develop three blind channel estimation and data detection schemes for the presented system model. Using Monte Carlo simulations, we show that the proposed blind channel estimation algorithm achieves a probability of error performance close to that with genie aided perfect channel state information (CSI) at the FC, while using only a moderate number of unknown data symbols for channel estimation.

Semi-blind simplified mean value channel estimator for MC-IDMA systems

The Multi-Carrier Interleave Division Multiple Access (MC-IDMA) scheme combines Orthogonal Frequency Division Multiplexing and IDMA. The scheme combats both Inter-Symbol Interference (ISI) and Multiple Access Interference (MAI). For coherent detection of the transmitted signals at the receiver, Channel State Information (CSI) is crucial. There are several schemes that can be used to obtain CSI at the receiver, such as pilot-based schemes and decision directed scheme, semi-blind and as blind channel estimation schemes. This paper focuses on developing semi-blind channel estimation scheme for the MC-IDMA systems. The developed scheme is based on Minimum Mean Square Error (MMSE) algorithm. The estimator employs applications of the eigenvalue and eigenvector decomposition (EVD) techniques to simplify the MMSE algorithm, and is named Simplified Mean Value Estimator (SMVE). Simulation results show that the proposed SMVE-based estimator outperforms Least Mean Square (LMS) algorithm-based estimator, Modified Minimized Mean Value Estimator (MMMVE), and the Minimized Mean Value-MMSE Estimator (MMVE).

A New Precoder Design for Blind Channel Estimation in MIMO-OFDM Systems

A new precoder for precoding-based blind channel estimation for MIMO-OFDM systems is proposed. In the proposed scheme, only a small number of data symbols, commensurate with the channel length, are linearly precoded prior to transmission to induce the signal correlation needed for the scheme to blindly estimate the channels. Similar to how pilot symbols are transmitted, the subcarriers carrying these linearly precoded data symbols are equi-spaced across the frequency band. The other subcarriers carry data symbols in the standard way, enabling MLD per subcarrier and also allowing for MIMO linear precoding across antennas at each subcarrier. This is in contrast to previous precoding-based blind channel estimation schemes which precode all of the data symbols so that every subcarrier carries a linear combination of symbols, aking the resulting joint MLD problem infeasible. In addition, this also makes it infeasible to employ MIMO precoding per subcarrier across the transmit antennas. The proposed precoder is designed via a multi-stage optimization process that seeks to minimize both channel estimation error and symbol estimation error. For channel estimation purposes, the resulting optimal design offers low-cost features such as sign change and FFT while providing reasonable channel estimation performance for low mobility applications.

Performance Analysis of Downlink W-CDMA Systems in Weibull and Lognormal Fading Channels Using Chaotic Codes

In this paper, a subspace based blind channel estimation scheme for downlink W-CDMA systems using chaotic codes under Weibull and Lognormal fading channel conditions is proposed and compared with W-CDMA system using PN codes. The algorithm provides estimates of multiuser channels by exploiting the structural information of the data output. The subspace of the (data + noise) matrix contains sufficient information for unique determination of channels and, hence, the signature waveforms and signal constellations. The proposed channel estimation algorithm is also implemented for multiuser--orthogonal frequency division multiplexing (OFDM) system. Performance measures like bit error rate (BER) and root mean square error (RMSE) are plotted for Weibull and Lognormal fading channels. Signal constellations under Weibull and Lognormal channels are also plotted. Analytical and Simulation results for BER and RMSE are compared for W-CDMA system using PN codes and chaotic codes. Simulation results show that, chaos-based W-CDMA outperforms the PN-based W-CDMA in terms BER and RMSE. Simulation results of multiuser-OFDM system shows that performance is further improved when compared to the W-CDMA system.

Statistical covariance-matching based blind channel estimation for zero-padding MIMO–OFDM systems

We propose a statistical covariance-matching based blind channel estimation scheme for zero-padding (ZP) multiple-input multiple-output (MIMO)–orthogonal frequency division multiplexing (OFDM) systems. By exploiting the block Toeplitz channel matrix structure, it is shown that the linear equations relating the entries of the received covariance matrix and the outer product of the MIMO channel matrix taps can be rearranged into a set of decoupled groups. The decoupled nature reduces computations, and more importantly guarantees unique recovery of the channel matrix outer product under a quite mild condition. Then the channel impulse response matrix is identified, up to a Hermitian matrix ambiguity, through an eigen-decomposition of the outer product matrix. Simulation results are used to evidence the advantages of the proposed method over a recently reported subspace algorithm applicable to the ZP-based MIMO–OFDM scheme.

하향링크 MC-CMDMA 시스템을 위한 간단한 미상 채널 추정 방법

In multicarrier code-division multiple access (MC-CDMA) systems, conventional blind channel estimation schemes require the inverse matrix calculation or eigenvalue decomposition of the received signal covariance matrix. Therefore, computational complexity of the conventional schemes is too high and they cannot be employed in downlink systems. In this paper, we propose a simple blind channel estimation scheme with very low computational complexity. Simulation results show that the proposed scheme has better channel estimation and bit error rate (BER) performance than the conventional schemes.

OFDM 시스템에서 비중복 프리코딩을 이용한 미상 채널 추정 방법

직교 주파수 분할 다중화 시스템에서 비중복 프리코딩을 이용한 미상 채널 추정 방식을 제안한다. 제안한 방식에서는 수신 신호에 대한 공분산 행렬을 구하고, 그 행렬의 각 원소들을 프리코딩 행렬의 각 원소로 나눔으로써 변형된 공분산 행렬을 구한다. 이 행렬의 최대 고유값에 해당하는 고유벡터를 구함으로써 채널 계수들을 추정하게 된다. 이 때, 고유 벡터를 구하기 위하여 많은 계산량을 필요로 하는 고유치 분해 기법 대신에 간단한 파워 기법을 적용함으로써 계산량을 크게 줄이게 된다. 제안하는 채널 추정 방식의 평균 제곱 오차에 대한 이론적인 값을 유도하고, 모의실험 결과와 비교함으로써 유도한 값이 실험 결과와 일치한다는 것을 확인한다. 또한, 모의실험을 통해서, 제안한 방법이 기존 방법들보다 더 우수한 채널 추정 성능과 비트 오율 성능을 나타낸다는 것을 보인다. For orthogonal frequency-division multiplexing (OFDM) systems, we propose a blind channel estimation scheme based on non-redundant precoding. In the proposed scheme, a modified covariance matrix is first obtained by dividing the covariance matrix of the received signal vector by the precoding matrix element-by-element. Then, the channel vector is estimated as an eigenvector corresponding to the largest eigenvalue of the modified covariance matrix. The eigenvector can be obtained by power method with low computational complexity instead of the complicated eigenvalue decomposition. We analytically derive a mean square error (MSE) of the proposed channel estimation scheme and show that the analysis result coincides well with the simulation result. Also, simulation results show that the proposed scheme has better MSE and bit error rate (BER) performance than conventional channel estimation schemes.

Robust Design of Adaptive Equalizers

Although equalizers promise to improve the signal- to-noise energy ratio, zero forcing equalizers are derived classically in a deterministic setting minimizing intersymbol interference, while minimum mean square error (MMSE) equalizer solutions are derived in a stochastic context based on quadratic Wiener cost functions. In this paper, we show that it is possible-and in our opinion even simpler-to derive the classical results in a purely deterministic setup, interpreting both equalizer types as least squares solutions. This, in turn, allows the introduction of a simple linear reference model for equalizers, which supports the exact derivation of a family of iterative and recursive algorithms with robust behavior. The framework applies equally to multiuser transmissions and multiple-input multiple-output (MIMO) channels. A major contribution is that due to the reference approach the adaptive equalizer problem can equivalently be treated as an adaptive system identification problem for which very precise statements are possible with respect to convergence, robustness and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -stability. Robust adaptive equalizers are much more desirable as they guarantee a much stronger form of stability than conventional in the mean square sense convergence. Even some blind channel estimation schemes can now be included in the form of recursive algorithms and treated under this general framework.

Performance analysis of downlink W-CDMA systems in Weibull, Lognormal and Nakagami fading channels

Wideband Code Division Multiple Access (W-CDMA) is a third generation (3G) mobile wireless technology that promises much higher data speeds to mobile and portable wireless devices than those which are commonly offered in todayʼs market. In W-CDMA systems transmitting over multipath channels, both Inter Symbol Interference (ISI) as a result of Inter Chip interference (ICI) and Multiple Access Interference (MAI) cannot be easily eliminated. Although it is possible to design multiuser detectors that suppress MAI and ISI, these detectors often require explicit knowledge of at least the desired usersʼ signature waveform. Torlak and Xu proposed a blind estimation algorithm for Asynchronous CDMA (A-CDMA) systems to estimate the multiuser channels (Torlak and Xu, 1997 [1]). In our work, we study a similar blind channel estimation scheme for downlink W-CDMA systems that provides estimates of the multiuser channels by exploiting the structural information of the data output. In particular, we show that the subspace of the (data + noise) matrix contains sufficient information for unique determination of channels, and hence, the signature waveforms and signal constellations. Performance measures like Bit Error Rate (BER) and Root Mean Square Error (RMSE) are plotted for the Weibull and Lognormal fading channels. Estimated signal constellations under the Weibull, Lognormal and Nakagami fading channels are also plotted.

How Much Coherent Interval Should be Dedicated to Non-Redundant Diagonal Precoding for Blind Channel Estimation in Single-Carrier Block Transmission?

Transmit precoding is a key technique for facilitating blind channel estimation at the receiver but the impact due to precoding on the channel capacity is scarcely addressed in the literature. In this paper we consider the single-carrier block transmission with cyclic prefix, in which a recently proposed diagonal-precoding assisted blind channel estimation scheme via covariance matching is adopted to acquire the channel information. It is shown that, when perfect channel knowledge is available at the receiver, the optimal noise resistant precoder proposed in the literature incurs the worst-case capacity penalty. When the coherent interval is finite, channel mismatch occurs due to finite-sample covariance matrix estimation. Thus, we aim to determine how much of the coherent interval should be dedicated to precoding in order to trade channel estimation accuracy for the maximal capacity. Toward this end, we leverage the matrix perturbation theory to derive a closed-form capacity measure which explicitly takes account of the channel uncertainty in the considered blind estimation setup. Such a capacity metric is seen to be a complicated function of the precoding interval. To facilitate analysis, an approximate formula for the derived capacity measure is further given. This allows us to find a closed-form estimate of the capacity-maximizing precoding time fraction, and can also provide insights into the optimal tradeoff between channel estimation accuracy and achievable capacity. Numerical simulations are used for evidencing the proposed analytic study.

Blind Channel Estimation for Orthogonal STBC in MISO Systems

This paper presents a closed-form blind channel estimation scheme for orthogonal space-time block codes in multiple-input single-output (MISO) systems, with specific focus on Alamouti's code for two transmit antennas. The channel matrix is estimated from the eigenvalue decomposition of the fourth-order cumulant matrix of the received signal. Unlike previous blind estimation schemes for MISO systems, the proposed algorithm is tested with block and slowly fading channels. The proposed scheme performs very well in both cases. A single pilot tuple is required to correctly assign the estimated to the actual channels and to resolve the sign ambiguity common to all blind estimators. It is shown that this scheme outperforms the only other available blind channel estimation scheme for this scenario. To achieve good performance in terms of bit error rate, 100-300 sample points are sufficient to provide accurate channel estimates. The main disadvantage of the proposed scheme is the complexity associated with the estimation of fourth-order cumulants. This complexity is reduced by exploiting the symmetry inherent in the cumulant matrix.

Nonredundant Precoding-Assisted Blind Channel Estimation for Single-Carrier Space–Time Block-Coded Transmission With Frequency-Domain Equalization

Relying on nonredundant diagonal precoding and independent and identically distributed (i.i.d.) source assumption, this paper proposes a blind channel estimation scheme for single-carrier frequency-domain equalization-based space-time block coded systems. The proposed method exploits the precoding-induced linear signal structure in the conjugate cross correlation between the two temporal block received signals as well as the circulant channel matrix property and can yield exact solutions whenever the channel noise is circularly Gaussian and the receive data statistic is perfectly obtained. The channel estimation formulation builds on rearranging the set of linear equations relating the entries of conjugate cross-correlation matrix and products of channel impulse responses into one with a distinctive block-circulant with circulant-block (BCCB) structure. This allows a simple identifiability condition depending on precoder parameters alone and also provides a natural yet effective optimal precoder design framework for improving solution accuracy when imperfect data estimation occurs. We consider two models of data mismatch, from both deterministic and statistical points of view, and propose the associated design criteria. The optimization problems are formulated to take advantage of the BCCB system matrix property and are solved analytically. The proposed optimal precoder aims to optimize solution robustness against deterministic error perturbation and also minimize the mean-square error when the data mismatch is modeled as a white noise. Pairwise error probability analysis is conducted for investigating the equalization performance. Numerical examples are used to illustrate the performance of the proposed method

Blind channel estimation, equalisation and CRB for OFDM with unmodelled interference

A blind channel estimation and equalisation scheme is given for orthogonal frequency-division multiplexing systems with unmodelled interference. The approach uses a generalised multichannel minimum variance principle to design an equalising filterbank that preserves the desired signal components and suppresses the overall interference. A channel estimate is then obtained by deriving an asymptotically tight lower bound of the filterbank output power, which reduces the problem to a quadratic minimisation. By imposing a special structure on the received signal, the performance is shown to be significantly increased. To assess the performance of the proposed scheme, an unconditional Cramer–Rao bound (CRB) is derived which, similar to the proposed blind channel estimator, does not assume knowledge of the transmitted information symbols. The CRB serves as a lower bound for all unbiased blind channel estimation schemes. Numerical examples show that the proposed scheme approaches the CRB as the SNR increases. It also exhibits low sensitivity to unknown narrowband interference and compares favourably with a subspace blind channel estimator.

Constant Modulus Based Blind Channel Estimation for OFDM Systems

A novel blind channel estimation scheme is proposed for OFDM systems employing PSK modulation. This scheme minimizes the number of possible channels by exploiting the constant modulus property, chooses a best fit over the possible channels by exploiting the finite alphabet property of information signals, and achieves competitive performance with low computational complexity. Results comparing the new scheme with the finite-alphabet based channel estimation are presented.

Improved blind multipath estimation for long code DS-CDMA

This paper proposes a blind channel estimation scheme for long code direct sequence code division multiple access (DS-CDMA) systems with multipath fading channels. This scheme combines the advantages of Toeplitz displacement and correlation matching methods to achieve improved performance. The basic idea is to remove the effects of noise and interferences with Toeplitz displacement operation and then estimate the multipath channel parameters with the correlation matching method. Simulation results are presented to show that the proposed scheme provides better MSE performance and robustness against the near-far problem.

Joint blind channel estimation and interference suppression with efficient implementation for OFDM systems

A joint blind channel estimation and interference suppression scheme with efficient implementation for orthogonal frequency-division multiplexing (OFDM) systems is presented. In particular, an equalising filterbank is designed and the channel estimate from a lower bound of the filterbank output power is derived. The proposed scheme and exhibits low sensitivity to unknown narrowband interference. It compares favourably with a subspace blind channel estimator.

Totally Blind Channel Estimation for OFDM on Fast Varying Mobile Radio Channels

A new blind channel estimation scheme for orthogonal frequency division multiplexing systems is proposed based on the maximum likelihood principle. By avoiding the use of second- and higher-order statistics, a very fast convergence rate is achieved. A novel approach is also proposed for resolving the phase ambiguity of the blind channel estimate without the need for any reference symbols. The approach combines different modulation schemes on adjacent subcarriers, such as 3-phase shift keying (PSK) and quarternary PSK (QPSK), to resolve phase ambiguity. Simulations were performed for mobile radio environments with high Doppler frequencies and short-to-medium delay spreads. The achieved performance is comparable to that of pilot-based channel estimation for the case of QPSK-modulation.

Stochastic channel-adaptive rate control for wireless video transmission

In this paper, an empirically optimized channel-matched quantizer, and a joint stochastic-control based rate controller and channel estimator for H.261 based video transmission over a noisy channel is proposed. The rate controller adaptively learns to choose the correct channel matched quantizer using a stochastic learning algorithm. The stochastic automaton based learning algorithm aids in estimating the channel bit error rate based on a one bit feedback from the decoder. The algorithm is observed to converge to the optimal choice of the quantizer very quickly for various channel bit error probabilities and for different video sequences. When compared to traditional channel estimation schemes the proposed technique has several advantages. First, the proposed method results in a significant reduction in the delay and bandwidth requirement for channel estimation when compared to pilot symbol aided channel estimation schemes. Next, the stochastic learning algorithm used to estimate the channel bit error rate has simple computations. This makes it attractive for low power applications such as wireless video communications. This is in contrast to traditional blind channel estimation schemes that are computationally expensive, in general.

Totally blind APP channel estimation for mobile OFDM systems

A new two-dimensional blind channel estimation scheme for coherent detection of orthogonal frequency-division multiplexing (OFDM) signals in a mobile environment is presented. The channel estimation is based on the a posteriori probability (APP) calculation algorithm. The time-variant channel transfer function is completely recovered without phase ambiguity with no need for any pilot or reference symbols, thus maximizing the spectral efficiency of the underlying OFDM system. The phase ambiguity problem is solved by using a 4-QAM (quadrature amplitude modulation) scheme with asymmetrical arrangement. The results clearly indicate that totally blind channel estimation is possible for virtually any realistic time-variant mobile channel.