Habib Senol

Joint Channel Estimation, Equalization, and Data Detection for OFDM Systems in the Presence of Very High Mobility

This paper is concerned with the challenging and timely problem of joint channel estimation, equalization, and data detection for uplink orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The resulting algorithm is based on the space alternating generalized expectation maximization (SAGE) technique which is particularly well suited to multicarrier signal formats leading to a receiver structure that also incorporates interchannel interference (ICI) cancelation. In order to reduce the computational complexity of the algorithm, band-limited, discrete cosine orthogonal basis functions are employed to represent the rapidly time-varying fading channel by the discrete cosine serial expansion coefficients. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel perfectly and there is no need to know the correlation function of the input signal. In this way, the resulting reduced dimensional channel coefficients are estimated and the data symbols detected iteratively with tractable complexity. The proposed SAGE joint detection algorithm updates the data sequences serially and the channel parameters are updated in parallel, leading to a receiver structure that also incorporates ICI cancelation. Computer simulations show that the cosine transformation represents the time-varying channel very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance even with a very small number of channel expansion coefficients employed in the algorithm, resulting in substantial reduction of the computational complexity.

Performance of Distributed Estimation Over Unknown Parallel Fading Channels

We consider distributed estimation of a source in additive Gaussian noise, observed by sensors that are connected to a fusion center with unknown orthogonal (parallel) flat Rayleigh fading channels. We adopt a two-phase approach of i) channel estimation with training and ii) source estimation given the channel estimates and transmitted sensor observations, where the total power is fixed. In the second phase we consider both an equal power scheduling among sensors and an optimized choice of powers. We also optimize the percentage of total power that should be allotted for training. We prove that 50% training is optimal for equal power scheduling and at least 50% is needed for optimized power scheduling. For both equal and optimized cases, a power penalty of at least 6 dB is incurred compared to the perfect channel case to get the same mean squared error performance for the source estimator. However, the diversity order is shown to be unchanged in the presence of channel estimation error. In addition, we show that, unlike the perfect channel case, increasing the number of sensors will lead to an eventual degradation in performance. We approximate the optimum number of sensors as a function of the total power and noise statistics. Simulations corroborate our analytical findings.

Nondata-Aided Joint Channel Estimation and Equalization for OFDM Systems in Very Rapidly Varying Mobile Channels

This paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The resulting algorithm is based on the space alternating generalized expectation maximization-maximum a posteriori probability (SAGE-MAP) technique which is particularly well suited to multicarrier signal formats. The algorithm is implemented in the time-domain which enables one to use the Gaussian approximation of the transmitted OFDM samples. Consequently, the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate (SER) performance. Based on this Gaussian approximation the exact Bayesian Cramér Rao lower bound (CRLB) as well as the convergence rate of the algorithm are derived analytically. To reduce the computational complexity of the algorithm, discrete Legendre orthogonal basis functions are employed to represent the rapidly time-varying fading channel. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal. The computational complexity of the algorithm is shown to be ~O(NL) per detected data symbol and per SAGE-MAP algorithm cycle where is the number of OFDM subcarriers and is the number of multipath components.

Sparse Channel Estimation and Equalization for OFDM-Based Underwater Cooperative Systems With Amplify-and-Forward Relaying

This paper is concerned with a challenging problem of channel estimation and equalization for amplify-and-forward cooperative relay based orthogonal frequency division multiplexing (OFDM) systems in sparse underwater acoustic (UWA) channels. The sparseness of the channel impulse response and prior information for the non-Gaussian channel gains, modeled by an exact continuous Gaussian mixture (CGM), are exploited to improve the performance of the channel estimation algorithm. The resulting novel algorithm initially estimates the overall sparse complex-valued channel taps from the source to the destination as well as their locations using the matching pursuit (MP) approach. The effective time-domain non-Gaussian noise is approximated well as a Gaussian noise in the frequency-domain, where the estimation takes place. An efficient and low complexity algorithm is developed based on a combination of the MP and the maximum a posteriori probability (MAP) based space-alternating generalized expectation-maximization technique, to improve the estimates of the channel taps and their locations in an iterative manner. Computer simulations show that the UWA channel is estimated very effectively and the proposed algorithm exhibits excellent symbol error rate and channel estimation performance.

Outage Scaling Laws and Diversity for Distributed Estimation Over Parallel Fading Channels

We consider scaling laws of the outage for distributed estimation problems over fading channels with respect to the total power and the number of sensors. Using a definition of diversity which involves a fixed number of sensors, we find tight upper and lower bounds on diversity which are shown to depend on the sensing (measurement) signal-to-noise ratios (SNRs) of the sensors. Our results indicate that the diversity order can be smaller than the number of sensors, and adding new sensors might not add to the diversity order depending on the sensing SNR of the added sensor. We treat a large class of envelope distributions for the wireless channel including those appropriate for line of sight scenarios. Finally, we consider fixed power per sensor with an asymptotically large number of sensors and show that the outage decays faster than exponentially in the number of sensors.

Pilot-aided Bayesian MMSE channel estimation for OFDM systems: algorithm and performance analysis

The paper proposes a computationally efficient, pilot-aided, minimum mean square error (MMSE), channel estimation algorithm for OFDM systems. The proposed approach employs a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve (KL) orthogonal expansion and estimates uncorrelated series expansion coefficients. Moreover, optimal rank reduction is achieved in the proposed approach by exploiting the optimal truncation property of the KL expansion, resulting in a smaller computational load on the estimation algorithm. The performance of the proposed approach is studied through analytical and experimental results. We first consider the stochastic Cramer-Rao bound and derive the closed-form expression for the random KL coefficients. We then exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE.

Distributed estimation over parallel fading channels with channel estimation error

We consider distributed estimation of a source observed by sensors in additive Gaussian noise, where the sensors are connected to a fusion center with unknown orthogonal (parallel) flat Rayleigh fading channels. We adopt a two-phase approach of (i) channel estimation with training, and (ii) source estimation given the channel estimates, where the total power is fixed. We prove that allocating half the total power into training is optimal, and show that compared to the perfect channel case, a performance loss of at least 6 dB is incurred. In addition, we show that unlike the perfect channel case, increasing the number of sensors will lead to an eventual degradation in performance. We characterize the optimum number of sensors as a function of the total power and noise statistics. Simulations corroborate our analytical findings.

Distributed Estimation with Channel Estimation Error over Orthogonal Fading Channels

We study distributed estimation of a source corrupted by an additive Gaussian noise and observed by sensors which are connected to a fusion center with unknown orthogonal (parallel) flat Rayleigh fading channels. The fading communication channels are estimated with training. Subsequently, source estimation given the channel estimates and transmitted sensor observations is performed. We consider a setting where the estimated channels are fed-back to the sensors for optimal power allocation which leads to a threshold behavior of sensors with bad channels being unused (inactive). We also show that at least half of the total power should be used for training. Simulation results corroborate our analytical findings.

Information theoretical performance limits of single-carrier underwater acoustic systems

In this study, the authors investigate the information theoretical limits on the performance of point-to-point single-carrier acoustic systems over frequency-selective underwater channels with intersymbol interference. Under the assumptions of sparse and frequency-selective Rician fading channel and non-white correlated Gaussian ambient noise, the authors derive an expression for channel capacity and demonstrate the dependency on channel parameters such as the number, location and power delay profile of significant taps, as well as environmental parameters such as distance, temperature, salinity, pressure and depth. Then, the authors use this expression to determine the optimal carrier frequency, input signalling and bandwidth for capacity maximisation.

A low-complexity time-domain MMSE channel estimator for space-time/frequency block-coded OFDM systems

Focusing on transmit diversity orthogonal frequency-division multiplexing (OFDM) transmission through frequency-selective channels, this paper pursues a channel estimation approach in time domain for both space-frequency OFDM (SF-OFDM) and space-time OFDM (ST-OFDM) systems based on AR channel modelling. The paper proposes a computationally efficient, pilot-aided linear minimum mean-square-error (MMSE) time-domain channel estimation algorithm for OFDM systems with transmitter diversity in unknown wireless fading channels. The proposed approach employs a convenient representation of the channel impulse responses based on the Karhunen-Loeve (KL) orthogonal expansion and finds MMSE estimates of the uncorrelated KL series expansion coefficients. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Subsequently, optimal rank reduction is applied to obtain significant taps resulting in a smaller computational load on the proposed estimation algorithm. The performance of the proposed approach is studied through the analytical results and computer simulations. In order to explore the performance, the closed-form expression for the average symbol error rate (SER) probability is derived for the maximum ratio receive combiner (MRRC). We then consider the stochastic Cramer-Rao lower bound(CRLB) and derive the closed-form expression for the random KL coefficients, and consequently exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also analyze the effect of a modelling mismatch on the estimator performance. Simulation results confirm our theoretical analysis and illustrate that the proposed algorithms are capable of tracking fast fading and improving overall performance.