Saeed Abdallah

Blind Channel Estimation for Amplify-and-Forward Two-Way Relay Networks Employing

We consider the problem of channel estimation for amplify-and-forward (AF) two-way relay networks (TWRNs). Most works on this problem focus on pilot-based approaches which impose a significant training overhead that reduces the spectral efficiency of the system. To avoid such losses, we propose blind channel estimation algorithms for AF TWRNs that employ constant-modulus (CM) signaling. Our main algorithm is based on the deterministic maximum likelihood (DML) approach. Assuming M -PSK modulation, we show that the resulting estimator is consistent and approaches the true channel with high probability at high SNR for modulation orders higher than 2. For BPSK, however, the DML algorithm performs poorly and we propose an alternative algorithm that yields much better performance by taking into account the BPSK structure of the data symbols. For comparative purposes, we also investigate the Gaussian maximum-likelihood (GML) approach which treats the data symbols as Gaussian-distributed nuisance parameters. We derive the Cramer-Rao bound and use Monte Carlo simulations to investigate the mean squared error (MSE) performance of the proposed algorithms. We also compare the symbol-error rate (SER) performance of the DML algorithm with that of the training-based least-squares (LS) algorithm and demonstrate that the DML offers a superior tradeoff between accuracy and spectral efficiency.

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We present two channel estimation algorithms for amplify-and-forward two-way relay networks that employ constant-modulus constellations. The proposed algorithms do not assume complete knowledge of the transmitted symbols: they only require the transmission of a very short training sequence in order to resolve the inevitable phase ambiguity in the channel estimate. We first derive the maximum-likelihood (ML) estimator which is shown to perform very well even for a relatively small number of samples when the signal-to-noise ratio is sufficiently high. To address the high computational complexity of the ML estimator we propose a second, simpler, algorithm that can be updated at run-time and performs well for a sufficiently large sample size. Theoretical and experimental studies demonstrate the performance of the proposed algorithms.

-PSK Modulation

We consider the problem of channel estimation for OFDM-based amplify-and-forward (AF) two-way relay networks (TWRNs). While previous works have adopted a pilot-based approach, we propose a semi-blind approach that exploits both the transmitted pilots as well as the received data samples to improve the estimation performance. Our proposed semi-blind estimator is based on the Gaussian maximum likelihood (GML) criterion which treats that data symbols as Gaussian-distributed nuisance parameters. The GML estimates are obtained using an iterative quasi-Newton method. To assist in the estimation of the individual channels, we adopt a superimposed training strategy at the relay. We design the pilot vectors of the terminals and the relay to optimize the estimation performance. Furthermore, we derive the semi-blind and pilot-based Cramer-Rao bounds (CRBs) to use as performance benchmarks. Finally, we use simulation studies to show that the proposed method provides substantial improvements in estimation accuracy over the conventional pilot-based estimation and that it approaches the semi-blind CRB as SNR increases. These improvements are possible using only a limited number of OFDM data blocks, which demonstrates the practicality of the semi-blind approach.

Semi-blind channel estimation for amplify-and-forward two-way relay networks employing constant-modulus constellations

We consider the problem of channel estimation for amplify-and-forward two-way relays assuming channel reciprocity and M-PSK modulation. In an earlier work, a partially-blind maximum-likelihood estimator was derived by treating the data as deterministic unknowns. We prove that this estimator approaches the true channel with high probability at high signal-to-noise ratio (SNR) but is not consistent. We then propose an alternative estimator which is consistent and has similarly favorable high SNR performance. We also derive the Cramer-Rao bound on the variance of unbiased estimators.

Semi-Blind Channel Estimation with Superimposed Training for OFDM-Based AF Two-Way Relaying

We analyze the mean squared error (MSE) performance of widely linear (WL) and conventional subspace-based channel estimation for single-input multiple-output (SIMO) flat-fading channels employing binary phase-shift-keying (BPSK) modulation when the covariance matrix is estimated using a finite number of samples. The conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the WL estimator. We derive accurate closed-form expressions for the MSE of the two estimators under four ambiguity resolution scenarios. In the first three scenarios, the receiver resolves the ambiguity using some clairvoyant knowledge about the channel. The first scenario, used as a reference, is the ideal case of optimal resolution. The second scenario assumes that one of the channel coefficients is known and the third assumes knowledge of the coefficient with the largest magnitude. The fourth scenario considers the more realistic case where pilot symbols are employed for ambiguity resolution. Our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of WL and conventional subspace-based estimators, showing that the WL estimator performs better when partial or inaccurate channel information is employed for ambiguity resolution.

Partially-Blind Estimation of Reciprocal Channels for AF Two-Way Relay Networks Employing M-PSK Modulation

In this letter, we propose an expectation maximization (EM)-based algorithm for semi-blind channel estimation of reciprocal channels in amplify-and-forward (AF) two-way relay networks (TWRNs). By utilizing data samples as well as pilots, the proposed algorithm provides substantially higher estimation accuracy than the conventional training-based least squares (LS) estimator without incurring a significant computational cost. Simulation results also show that it performs very close to the corresponding semi-blind Cramer-Rao bound.

Widely Linear versus Conventional Subspace-Based Estimation of SIMO Flat-Fading Channels: Mean Squared Error Analysis

Rate adaptation which adjusts the transmission rate based on channel quality, plays a key role in the performance of 802.11 networks and is critical for achieving high throughput. Traditional statistics-based methods for rate adaptation are unsuited for mobility scenarios because of the delay involved in statistics gathering. Methods based on channel state information (CSI) perform better but still fall short of optimal performance in high mobility. In this paper, we consider adaptive modulation based on Slepian channel prediction as a basis for rate adaptation in high mobility scenarios. Our proposed method utilizes low-complexity projection on a subspace spanned by discrete prolate spheroidal (DPS) sequences. These sequences are simultaneously bandlimited and highly energy concentrated, and they can be used to obtain a minimum energy bandlimited extension of a finite sequence. Using the predicted channel coefficients, we select the modulation scheme resulting in the highest expected throughput. Unlike Wiener prediction, the proposed method does not require detailed knowledge of the channel correlation, but only of the Doppler bandwidth. Our numerical results show that adaptive modulation based on the low-complexity Slepian prediction is substantially better than using outdated CSI and performs very close to Wiener prediction.

EM-Based Semi-Blind Channel Estimation in Amplify-and-Forward Two-Way Relay Networks

We consider the problem of channel estimation for amplify-and-forward (AF) two-way relay networks (TWRNs). The majority of works on this problem develop pilot-based algorithms that allocate significant resources for training. We will show in this work that such overhead is not necessary when the terminals employ M-ary phase-shift keying (M-PSK). Using the constant-modulus nature of the transmitted symbols, we develop a relaxed blind maximum-likelihood (ML) channel estimator. We study the performance of the ML estimator in the high SNR and large sample-size scenarios, demonstrating that it performs well in both cases. As a benchmark, we also present and analyze an intuitive low-complexity estimator based on sample-averaging. Simulation studies are used to compare the mean-squared error performance of the two algorithms.

Rate adaptation using long range channel prediction based on discrete prolate spheroidal sequences

In this paper, we derive the Cramer-Rao bound (CRB) for semiblind channel estimation in amplify-and-forward two-way relay networks employing square QAM, assuming flat-fading channel conditions. The derived bound is exact as it is based on the true likelihood function that takes into account the statistics of the transmitted data symbols. Using the new bound, we show that exploiting even a limited number of transmitted data symbols in addition to the pilot symbols leads to substantial estimation accuracy improvements over conventional pilot-based estimation. We also propose a semiblind expectation-maximization-based estimation algorithm that performs very close to the exact CRB at an affordable computational cost. The superior accuracy of the semiblind approach makes it possible to significantly reduce the training overhead for channel estimation, thus offering a higher throughput and a better tradeoff between accuracy and spectral efficiency. We also derive the modified CRB, which approximates the exact CRB at high SNR for low modulation orders.

Blind channel estimation for MPSK-based amplify-and-forward two-way relaying

We propose a novel widely linear (WL) minimum variance (MV) channel estimation algorithm for multicarrier code-division multiple access (MC-CDMA) systems. The presented algorithm outperforms the regular MV channel estimation algorithms when the modulation scheme is real-valued (such as BPSK). We build on the results of [1] to find a highly accurate closed form expression the asymptotic bias resulting from the additive noise. We show via simulations that the asymptotic bias and the MSE are significantly reduced when widely linear MV estimation is utilized.