Semi-blind Channel Estimation Research Articles

Maximum-LikelihoodSemiblind Equalization of Doubly Selective Channels Using the EM Algorithm

Maximum-likelihood semi-blind joint channel estimation and equalization for doubly selective channels and single-carrier systems is proposed. We model the doubly selective channel as an FIR filter where each filter tap is modeled as a linear combination of basis functions. This channel description is then integrated in an iterative scheme based on the expectation-maximization (EM) principle that converges to the channel description vector estimation. We discuss the selection of the basis functions and compare various functions sets. To alleviate the problem of convergence to a local maximum, we propose an initialization scheme to the EM iterations based on a small number of pilot symbols. We further derive a pilot positioning scheme targeted to reduce the probability of convergence to a local maximum. Our pilot positioning analysis reveals that for high Doppler rates it is better to spread the pilots evenly throughout the data block (and not to group them) even for frequency-selective channels. The resulting equalization algorithm is shown to be superior over previously proposed equalization schemes and to perform in many cases close to the maximum-likelihood equalizer with perfect channel knowledge. Our proposed method is also suitable for coded systems and as a building block for Turbo equalization algorithms.

Simplified Semi-Blind Channel Estimation for Space–Time Coded MIMO-OFDM Systems

The combination of Space---Time Coded Multiple Input Multiple Output systems (STC-MIMO) with Orthogonal Frequency Division Multiplexing (OFDM) is recently being investigated as an effective means of providing high-speed data transmission over dispersive wireless channels. The strengths of the two techniques coalesce and render MIMO-OFDM systems robust to ISI and IBI. However, the decoding and demodulation of STC-OFDM needs reliable channel knowledge at the receiver, unless differential modulation techniques are used. Semi-blind methods for channel estimation are seen to provide the best trade-off in terms of bandwidth overhead, computational complexity and latency. The conventional Expectation-Maximization (EM) algorithm for semi-blind channel estimation improves a pilot-based estimate with a two step process; however, it is computationally complex to implement. In this paper, we propose a variant of the EM method, referred to as ML-EM, for semi-blind estimation of doubly dispersive channels in space---time coded MIMO-OFDM systems. Here, the conventional EM algorithm is coupled with the ML decoder for space time block codes (STBCs). The technique shows good performance, even in highly correlated antenna arrays, and is computationally simpler than conventional EM. The method incurs a training overhead of less than 1%, and performs close to exact CSI through iterative processing at the receiver.

Subspace-Based Semi-Blind Channel Estimation in Uplink OFDMA Systems

This paper presents a new approach for subspace-based semi-blind channel estimation in the uplink channel of orthogonal frequency division multiple access (OFDMA) systems. In the proposed approach, the orthogonality between the signal subspace and the noise subspace induced by the virtual carriers (VCs) is exploited to estimate the channel status of each user. The redundancy provided by the sub-carriers of the non-active users is then adopted to enhance the channel estimation performance. It is shown that while the proposed subspace-based channel estimation scheme is feasible for both sub-band and interleaved OFDMA systems, it is particularly effective for interleaved OFDMA systems due to their improved frequency diversity characteristic. In addition, a novel scheme, designated as the virtual carrier recovery (VCR) scheme, is proposed to further enhance the performance of the channel estimation process by recovering the VCs to zeros at the receiver end. The simulation results demonstrate that the VCR scheme yields a significant improvement in the channel estimation performance; particularly for the case of partially-loaded OFDMA systems. It is also shown that the proposed VCR scheme has a comparable bit error rate (BER) performance to that of the case when the receiver has perfect channel state information (CSI).

An Enhanced Embedded-Pilot Channel Estimation Architecture for MIMO MC-CDMA Systems

In this work an enhanced semi-blind channel estimator is presented for multicarrier CDMA systems with multiple transmit and receive antennas. The novel scheme is based on embedded pilots that are characterized as virtual users and their number is determined in a dynamic fashion according to the propagation channel conditions. The superimposed code-multiplexed pilots are used initially for channel estimation before the despreading operation, thus achieving per subcarrier estimation using the known unique multi-layer pattern of the virtual users. Afterwards, the estimation is enhanced by using the despread pilots. Furthermore, an iterative scheme is incorporated in channel estimation process minimizing the effect of multiuser interference and operates either in interference cancellation, or in virtual user mode. The proposed architecture is evaluated for spatial diversity systems (space- frequency block coded) with two transmit and up to four receive antennas operating in realistic propagation channels for various modulation and coding schemes. The results demonstrate a significant performance improvement especially as the channel is dominated by its time variant characteristics. The dynamic assignment of spreading codes in the payload and the pilots offers to the system realistic flexibility and adaptivity in demanding channels achieving concurrently maximization of the real overall system throughput, while maintaining low overhead and complexity burden.

Semiblind Channel Estimation for MIMO Single Carrier With Frequency-Domain Equalization Systems

We propose a semiblind channel-estimation method for multiple-input multiple-output (MIMO) single carrier with frequency-domain equalization systems. By taking advantage of periodic precoding and the block circulant channel model after cyclic prefix removal, we obtain the channel-product matrices by solving a series of decoupled linear systems, which is gained from the covariance matrix of the received data. Then, the channel-impulse-response matrix is obtained by computing the positive eigenvalues and eigenvectors of a Hermitian matrix formed from the channel-product matrices. We also propose an optimal design of the precoding sequence, which minimizes the noise effect and numerical error in covariance matrix estimation, and discuss the impact of the optimal sequence on channel equalization. With the proposed framework, the method is shown to be robust with respect to channel-order overestimation, and the identifiability condition is simply that the channel-impulse-response matrix has full column rank. Due to the identifiability condition, the method is applicable to MIMO channels with more transmitters or more receivers. Simulations are used to demonstrate the performance of the proposed method.

Linear prediction based semiblind channel estimation for multiuser OFDM with insufficient guard interval

To meet the demand of high data rate transmissions for multimedia wireless communications, orthogonal frequency division multiplexing (OFDM) systems in conjunction with multiple-input multiple-output (MIMO) signal processing have been considered one of the central techniques in advanced wireless communications. In the paper, two semiblind channel estimation algorithms are proposed for the uplink multiuser OFDM systems with insufficient guard interval, in contrast to sufficient guard interval assumed in most of the prior works. A zero-padding OFDM system, which zero-pads rather than cyclicly prefixing each block, is considered in this paper. By utilizing the relation between the linear prediction error filters (LPEFs) of the received signal with multiple prediction orders and the transmitted data sequence, the first proposed algorithm, namely the multistage LP (MLP) based algorithm, can estimate the MIMO channel coefficients, with only a single pilot OFDM block used. To reduce the sensitivity of the proposed algorithms to the channel order overestimation, it is proposed to implement the LPEFs with a QR-decomposition based approach. This QRdecomposition based approach alternatively computes the LPEFs without direct inversion of the received signal correlation matrix, thus exhibiting robustness against channel order overestimation. Some simulation results are presented to demonstrate the effectiveness and robustness of the proposed algorithms.

A Signal Perturbation Free Whitening-Rotation-Based Semiblind Approach for MIMO Channel Estimation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> It was shown in our previous work that, in the noise-free case, the whitening-rotation (WR)-based MIMO channel estimation algorithm is subject to a signal perturbation error, justifying that the WR-based method is efficient only in the low signal-to-noise ratio (SNR) case. In this paper, a very efficient signal-perturbation-free WR-based approach is proposed for semiblind channel estimation of MIMO systems. A novel transmit scheme is developed based on the eigenvalue decomposition of the correlation matrix of the transmitted signal. The new scheme is to send a small volume of data bearing the information of the correlation matrix to the receiver for the cancellation of the signal perturbation error so as to improve the performance of the WR-based method in the case of high SNRs. Then, a perturbation analysis of the proposed WR-based semiblind method with the new transmit scheme is conducted, leading to a closed-form expression for the mean square error (MSE) of the channel estimate. Computer simulations show that the proposed approach significantly outperforms the original WR-based method as well as some other channel estimation methods for all SNR levels. </para>

Wavelet-Based Semiblind Channel Estimation for Ultrawideband OFDM Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Ultrawideband (UWB) communications involve very sparse channels, because the bandwidth increase results in a better time resolution. This property is used in this paper to propose an efficient algorithm that jointly estimates the channel and the transmitted symbols. More precisely, this paper introduces an <emphasis emphasistype="boldital"> expectation-maximization</emphasis> (EM) algorithm within a wavelet-domain Bayesian framework for semiblind channel estimation of multiband orthogonal frequency division multiplexing based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response to model a sparseness property of the wavelet representation. This prior yields, in maximum <emphasis emphasistype="boldital">a posteriori</emphasis> estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding “insignificant” wavelet coefficients from the estimation process. Simulation results using UWB channels that were issued from both models and measurements show that, under sparseness conditions, the proposed algorithm outperforms pilot-based channel estimation in terms of the mean square error (MSE) and bit error rate (BER). Moreover, the estimation accuracy is improved, whereas the computational complexity is reduced compared with traditional semiblind methods. </para>

Semi-blind channel estimation for the uplink of multi-carrier code-division multiple access systems with timing offset

Timing offsets (TO) introduce misaligned interferences and phase errors, which degrade the performance of channel estimation. The authors propose a new semi-blind channel estimator that can cancel the TO effects on channel estimation and work well in the uplink of multi-carrier code-division multiple access systems in the presence of TO. The proposed channel estimator exploits the spreading sequence information instead of pilots to accomplish semi-blind estimation. Since the estimated channel coefficients are affected by the users' transmitted data, the effect of the users' data needs to be reduced. For this purpose, the authors also propose two smoothing algorithms, division smoothing and optimisation smoothing. In addition, to extend the new estimator to the system where the number of active users is too large, channel estimation over multiple symbols is discussed. The simulation results show that the proposed semi-blind estimator works better than a conventional estimator in the presence of TO, and its performance is very close to the conventional estimator in the absence of TO. Besides, the proposed estimator is compared with a sub-space estimator in simulation, and the results indicate that the new proposed estimator can achieve the same mean square error performance over the duration of a single symbol as the sub-space estimator over the duration of several symbols.

Signal processing advances for 3G WCDMA: From rake receivers to blind techniques

As already deployed and proven technology, code-division multiple access has evolved to support competitive high-data-rate low-latency multimedia services over wireless cellular networks. In this article we introduce advanced signal processing techniques to enhance CDMA receiver performance further. In particular, we consider the possibility of optimal joint multiuser detection for long code WCDMA using fast inversion based on a state-space approach with reasonable complexity, and semi-blind channel estimation techniques to realize rate-efficient transmission for the latest 3G standards.

Comments on "Semi-Blind Channel Estimation and Equalization for MIMO Space - Time Coded OFDM

For original paper see ibid., vol.53, no.2, p.363-374, Feb. 2006. A semiblind channel estimation scheme of the multiple-input-multiple-output space-time coded orthogonal frequency-division multiplexing system was proposed in the aforementioned paper for either real or complex with symmetric signals. We point out that this scheme cannot work correctly for complex signal scenario.

Non-Redundant Precoding-Based Blind and Semi-Blind Channel Estimation for MIMO Block Transmission With a Cyclic Prefix

By combining multiple-input-multiple-output (MIMO) communication with block transmission using a cyclic prefix (CP), MIMO block transmission systems can not only achieve high data rates but also simplify channel estimation and equalization. In this paper, to provide a bandwidth-efficient solution for channel estimation in MIMO block transmission systems with a CP, we present a framework for blind channel estimation based on a general non-redundant precoding. Using this framework, we propose a blind estimator exploiting a simplified non-redundant precoding that is robust against overestimates of a true MIMO channel order. Furthermore, in the case with the number of transmit antennas greater than that of receive antennas, we show under specific system conditions that the proposed blind algorithms can be used for estimation of the MIMO channel without oversampling the received signals. With the simplified precoding conditions established in this paper, the proposed method does not impose the strict identifiability conditions on the MIMO channel, which are required for the existing methods. Furthermore the proposed estimator achieves accurate channel estimation with a small number of symbol blocks. In addition, we derive a simplified precoder that is optimized in the sense of minimizing the impact of unknown additive noise. We discuss the tradeoff between channel estimation accuracy and bit error rate performance associated with the simplified precoder. Finally, we develop a technique for resolving the channel ambiguity in the proposed blind estimator to create a semi-blind channel estimator relying on only a few known symbols.

Semiblind Single-Carrier MIMO Channel Estimation Using Overlay Pilots

Semiblind (SB) channel estimation based on the expectation-maximization (EM) algorithm is studied for the case of single-carrier multiple-input-multiple-output (MIMO) systems using overlay pilots. Iterative channel estimation and data detection are performed at the receiver. We provide the formulation of the channel estimator and present numerical results on the iterative receiver performance. Presented results show an interesting performance improvement and a fast convergence using the SB scheme when enough transmit power is attributed to pilots. The proposed scheme is also compared to the classical case of time-multiplexed pilots, and the tradeoff between the channel-estimation quality and the data-transmission rate is discussed.

EM-based semi-blind channel estimation method for MIMO-OFDM communication systems

This paper presents a novel semi-blind method for channel estimation and symbol detection in multiple input multiple output–orthogonal frequency division multiplexing (MIMO-OFDM) digital communication systems over time-varying channels where the standard pilot-aided channel estimation (PACE) interpolation approaches are not directly applicable due to insufficient placement of pilot sequences over the frequency sub-channels. The presented channel estimation method utilizes the Expectation Maximization (EM) algorithm to exploit the information in the received signals and the statistical properties of the channel.

Joint Semiblind Frequency Offset and Channel Estimation for Multiuser MIMO-OFDM Uplink

A semiblind method is proposed for simultaneously estimating the carrier frequency offsets (CFOs) and channels of an uplink multiuser multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) system. By incorporating the CFOs into the transmitted symbols and channels, the MIMO-OFDM with CFO is remodeled into an MIMO-OFDM without CFO. The known blind method for channel estimation (Zeng and Ng in 2004) (Y. H. Zeng and T. S. Ng, ldquoA semi-blind channel estimation method for multi-user multi-antenna OFDM systems,rdquo IEEE Trans. Signal Process., vol. 52, no. 5, pp. 1419-1429, May 2004.) is then directly used for the remodeled system to obtain the shaped channels with an ambiguity matrix. A pilot OFDM block for each user is then exploited to resolve the CFOs and the ambiguity matrix. Two dedicated pilot designs, periodical and consecutive pilots, are discussed. Based on each pilot design and the estimated shaped channels, two methods are proposed to estimate the CFOs. As a result, based on the second-order statistics (SOS) of the received signal and one pilot OFDM block, the CFOs and channels are found simultaneously. Finally, a fast equalization method is given to recover the signals corrupted by the CFOs.

Semiblind Channel Estimation and Data Detection for OFDM Systems With Optimal Pilot Design

This paper considers semiblind channel estimation and data detection for orthogonal frequency-division multiplexing (OFDM) over frequency-selective fading channels. We show that the samples of an OFDM symbol are jointly complex Gaussian distributed, where the mean and covariance are determined by the locations and values of fixed pilot symbols. We exploit this distribution to derive a novel maximum-likelihood (ML) semiblind gradient-descent channel estimator. By exploiting the channel impulse response (CIR) statistics, we also derive a semiblind data detector for both Rayleigh and Ricean fading channels. Furthermore, we develop an enhanced data detector, which uses the estimator error statistics to mitigate the effect of channel estimation errors. Efficient implementation of both the semiblind and the improved data detectors is provided via sphere decoding and nulling-canceling detection. We also derive the Crameacuter-Rao bound (CRB) and design optimal pilots by minimizing the CRB. Our proposed channel estimator and data detector exhibit high bandwidth efficiency (requiring only a few pilot symbols), achieve the CRB, and also nearly reach the performance of an ideal reference receiver

Iterative receiver for OFDM systems based on semi-blind channel estimation

In this paper we propose two iterative algorithms of joint channel estimation and symbol detection for Orthogonal Frequency Division Multiplexing (OFDM) systems. In which, superimposed pilot scheme is adopted and an initial Channel State Information (CSI) is obtained by employing a first-order statistic. In each subsequent iteration, we propose two algorithms to update the CSI. The Mean Square Error (MSE) of channel estimation and Bit Error Rate (BER) performance are given and simulation results demonstrate that the iterative algorithm using method B has good performance approaching the ideal condition.

Joint semi-blind channel and timing estimation for generalized UWB transmitted reference systems

Synchronization is one of the most critical issues in ultra-wideband communications due to the short duration of the pulses. In this work, a semi-blind synchronization scheme based on maximum-likelihood techniques to recover both symbol and frame timing is developed. The proposed algorithm performs joint timing and channel estimation and is thus robust against moderate timing errors. The probability of acquisition is computed based on correlated Gaussian random variables and analytical results are shown to be accurate for moderate to high SNR values relative to simulated performance. The results reveal that the proposed algorithm achieves a significant performance gain in terms of mean-squared error and bit-error-rate in comparison to proposed frame rate (FR) based algorithms. The impact of a low resolution analog-to-digital converter is shown to be marginal

Blind Channel Identifiability for Generic Linear Space-Time Block Codes

Linear space-time block codes (STBCs) have proven their effectiveness in performance improvement of wireless multiple-input multiple-output communication systems. Their successful decoding, however, requires reliable channel knowledge at the receiver. In this paper, we present a semiblind channel estimation method for linear STBC without the usual code orthogonality condition. We provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration. We also present a simple channel estimation algorithm. Finally, we provide simulation results that illustrate the performance of the proposed scheme

Performance analysis of semiblind channel estimation in long-code DS-CDMA systems

The performance of second-order statistics (SOS)-based semiblind channel estimation in long-code direct-sequence code-division multiple-access systems is analyzed. The covariance matrix of second-order statistics estimates is obtained in the large system limit and is used to analyze the large-sample performance of two SOS-based semiblind channel estimation algorithms. A notion of blind estimation efficiency is also defined and is examined via simulation results.