Performance Analysis of Spatially Coded OFDM Wireless Systems Using Channel State Information

Abstract

With the dawn of next-generation technologies, the current as well as future wireless communication systems are driven by applications that are mostly multimedia-based. And, it requires a humongous exchange of data in terms of audio/video content, which poses a challenge to enable the high data-rate capable communication networks. The combination of spatial-coding techniques and multicarrier transmission has been found as an appropriate choice for supporting the high data-rate/capacity without compromising the performance of wireless systems. The orthogonal-frequency-division-multiplexing (OFDM) has been recognized as a promising candidate for the multicarrier communication technique. The exclusive feature of OFDM is its capability to divide the allocated bandwidth into a number of orthogonal narrowband subchannels (overlapping) that transforms a frequency-selective channel into a set of frequency-nonselective flat-fading subchannels. In addition, the deployment of multi-antennas for wireless transmission and reception introduces subchannels in the spatial-domain, by which, a set of subchannels are established over the same time and frequency parallely. Therefore, the high data-rate services can be catered to the wireless communication users by utilizing the spatially-coded OFDM systems without the requirement of extra bandwidth, by enhancing signal-to-noise-ratio (SNR) at the receiving end. Due to a crucial need for channel-state-information (CSI) in the spatially-coded OFDM systems, the channel estimation/prediction has emerged as an integral part of such systems, which provides an opportunity to combat the adverse effects of fading, interference and noise/disturbances. It also enhances the information symbol-detection rate at the wireless receiver. Therefore, the spatially-coded OFDM strategies stand as a promising choice also for the future high data-rate communication techniques. In order to enhance the spectral efficiency of the system, the incorporation of adaptive modulation techniques in OFDM systems (based on SNR criterion) has appeared as a lucrative option. It is beneficial to employ higher-order modulation modes on the subcarriers exhibiting relatively higher values of SNR, in the adaptive-orthogonal-frequency-division-multiplexing (AOFDM) systems. In uniform case, each subcarrier carries equal number of bits with equal power, but the order of modulation (on all subcarriers) can be switched according to the received SNR. Therefore, the AOFDM system relies on accurate channel-state-information (CSI) estimated/predicted at the receiver for its efficient working. We first present the channel estimation and long-range prediction technique for the AOFDM system. The efficient channel loading is accomplished by feeding the accurately predicted CSI back to the transmitter. The frequency selective wireless fading channel is modelled as a tapped-delay-line-filter governed by a first-order autoregressive (AR1) process; and an adaptive channel estimator based on the generalized variable-step-size least-mean-square (GVSS-LMS) algorithm is employed to track the AR1 correlation coefficient. To compensate for the signal fading due to channel state variations, a modified-Kalman-filter (MKF)-based channel estimator is utilized. In addition, channel tracking is also performed for predicting the future CSI at receiver, based on the numeric-variable forgetting-factor ecursive-least-squares (NVFF-RLS) algorithm. Subsequently, adaptive bit allocation for OFDM system is employed by using predicted CSI at transmitter. Here, the proposed combination of GVSS-LMS and MKF algorithms for robust channel estimation and the NVFF-RLS algorithm for efficient channel prediction is incorporated, which is validated by using different channel realizations through simulation, and also by comparing it with the fixed step-size LMS, MKF and fixed forgetting-factor RLS algorithm based conventional techniques. For appropriate prediction of CSI at the receiver, the wireless fading channel modelling plays a vital role. We also suggest an alternate approach for the simulation of basis-expansion-model (BEM) for channel fading, in which each time-varying BEM coefficient is considered to be governed by an AR1 process. To introduce a high degree of uncorrelation among the BEM coefficients, the Markov parameter of each AR1 process is also assumed to be time-varying according to another independent stationary ergodic AR1 process, which forms the base of BEM–AR1–AR1 paradigm. The simulation results manifest that the proposed BEM–AR1–AR1 scheme is in close agreement with the ideal BEM for slow as well as fast channel fading. However, the first-order Markov model (AR1-based) and second-order Markov-model (AR2-based), representing the wireless fading channels, have an edge due to their mathematical simplicity; and these models are the close approximation of Jakes’ model. Therefore, these paradigms may find applications in the time varying channel estimation due to its compatibility with model based adaptive algorithms. However, the utilization of training data (in terms of information symbol-blocks) in adaptive algorithms deployed for the channel estimation/prediction impose burden on the wireless OFDM communication system, which in turn leads to reduction in the bandwidth efficiency. Therefore to reduce this training data overhead, we present adaptive channel prediction techniques for wireless OFDM systems using cyclic-prefix (CP). The CP not only combats intersymbol-interference, but it also precludes requirement of additional training symbols. The proposed adaptive algorithms exploit the channel-state-information contained in CP of received OFDM symbol, under the time invariant and time-variant wireless multipath Rayleigh fading channels. For channel prediction, the convergence and tracking characteristics of conventional RLS algorithm, NVFF-RLS algorithm, Kalman-filtering (KF) algorithm and reduced Kalman least mean squares (RK-LMS) algorithm are compared. The simulation results are presented to demonstrate that KF algorithm is the best available technique as compared to RK-LMS, RLS and NVFF-RLS algorithms by providing low mean squared channel prediction error. But, RK-LMS and NVFF-RLS algorithms exhibit lower computational complexity than KF algorithm. Under typical conditions, the tracking performance of RK-LMS is comparable to RLS algorithm. However, RK-LMS algorithm fails to perform well in convergence-mode. For time-variant multipath fading channel prediction, the presented NVFF-RLS algorithm supersedes RLS algorithm in the channel tracking-mode under moderately high fade-rate conditions. This technique is further extended to the multiple transmitter-antenna systems along with spatial block-coding. The usage of CP can be helpful for both the space-time-block-coded OFDM (STBC-OFDM) systems as well as for the efficient channel estimation/prediction (when utilized as the training data). Under appropriate parameter setting in 2×1 STBC-OFDM system, the NVFF-RLS algorithm bestows enhanced channel tracking performance than RLS algorithm under the static as well as dynamic environment, which leads to significant reduction in the symbol-error-rate (SER). Moreover in frequency-domain, the multiple transmitter-antenna systems can also be employed with space-frequency-clock-codes (SFBC), in which the adjacent subcarriers are mapped onto the orthogonal/quasi-orthogonal codes, and that is analogous to STBC scheme in time-domain. But these have a common motive to improve the overall SNR. Therefore, we next present bit-error rate (BER) performance analysis of the space-frequency-block-coded OFDM (SFBC–OFDM) communication systems, working over wireless fading channels under the impulsive environment. The effects of imperfect channel-state-information on the BER performance are also investigated, while using the M-ary phase-shift keying and M-ary quadrature amplitude modulation for the digital data transmission over the fading channels corrupted by the impulse-noise and additive white-Gaussian-noise (AWGN). The imperfect CSI usually arises due to the noisy channel estimates at wireless receiver. The major focus is on the description of closed-form expressions for the BER performance of underlying SFBC–OFDM systems impaired by the impulse-noise, in which the noise bucket concept helps in quantifying its performance under the Rayleigh fading scenario. Simulation results are presented to connote the deterioration of BER performance of SFBC–OFDM systems due to the presence of impulse-noise, AWGN and noisy channel estimates at the receiver, under the different channel fading conditions exhibiting Rayleigh and Nakagami m probability distributions. For lower values of m in the range 0.5 ≤ m < 1, the adverse impact of impulse-noise can be reduced by increasing the number of subcarriers in an OFDM symbol-block period. With the advent of machine learning techniques, the CSI-estimation/prediction using artificial neural-network (ANN) based architectures have emerged as a viable strategy in the intelligence-based advanced wireless communication systems. Therefore, we further present an adaptive-slope squashing-function (ASF) based ANN for the efficient estimation of smoothly time-varying multipath fading channels, in a 4×1 SFBC-OFDM system using 64 subcarriers. The CSI estimated at the first-stage is further used for OFDM information symbol-detection (through minimum mean square error criterion based detection) at the second-stage. To combat the impact of smoothly time varying environment, we emphasize on the utilization of ASF-ANN using backpropagation (BP) algorithm for the estimation of channel tap-coefficients in the frequency-domain. The underlying ANN is modelled as feedforward multi-layered perceptron that updates the network weights. The major focus is on the gradient-descent algorithm based adaptation of the slope of squashing function (SF) along with other ANN parameters, which enhances the training efficiency of ASF ANN in terms of the lower mean squared channel estimation error in comparison to the traditional fixed-slope squashing-function (FSF) ANN technique. Simulation results corresponding to the underlying 4×1 SFBC-OFDM system are presented to depict that the ASF-ANN based approach outperforms the FSF-ANN technique by providing lower symbol error rate due to the usage of well-estimated CSI. At 15dB SNR and fade-rate = 0.001, the average BER reduces to 2.85×10^-4 for the ASF-ANN based approach, due to improved CSI-estimation; which accounts for approximately 5% improvement in the detection success-rate as compared to the FSF-ANN based approach. Furthermore, it has been observed that the squashing-function used for ANN deployment in many real-world applications is hyperbolic-tangent function. The usage of softsign squashing-function in an ANN based channel estimation (in the frequency-domain) for SFBC OFDM system is also considered. The softsign based approach outperforms the hyperbolic-tangent squashing-function by providing smoother asymptotes, while using feedforward neural networks for the estimation of slowly varying fading channels. By exploiting the lower saturation tendency of softsign-function, the efficiency of channel estimator can be enhanced, which in turn improves SER performance of SFBC-OFDM system. The intelligence-based signal processing using the ANN approach provides us an opportunity to recover/detect information symbols directly precluding the requirement of CSI at the receiver. Therefore, an intelligent receiver based on ANN for a 4×1 SFBC-OFDM system, working under slow time-varying frequency-selective fading channels, is also proposed that directly recovers the transmitted symbols from the received signal, without the explicit requirement of channel estimation. The ANN based equalizer is modelled by using the feedforward as well as the recurrent neural-network architectures, and is trained using the error backpropagation algorithms. The major focus is on efficiency and efficacy of three different strategies; namely, the gradient-descent with momentum (GDM), resilient-propagation (RProp), and Levenberg-Marquardt (LM) algorithms. The recurrent neural-network architecture based SFBC-OFDM system is found to be an appropriate choice in terms of the low bit-error-rate performance, while using the different quasi orthogonal space-time block-codes. Based on the aforementioned research work, which mainly addresses the spatially-coded OFDM systems (working under wireless fading environment) using CSI, it is apparent that channel estimation/prediction is the backbone of STBC-/SFBC-OFDM systems, which plays a pivotal role in the information symbol recovery. The upcoming advanced wireless communication systems are likely to utilize the STBC-/SFBC-OFDM system architectures along with the intelligent signal processing based channel estimation techniques, to combat the interference and noise. The future work includes the implementation of machine learning techniques to further improve the channel estimation/prediction and to enhance the symbol-detection/recovery in the spatially-coded OFDM systems.