Wide-sense Stationary Uncorrelated Scattering Channel Research Articles

Multilevel/AES-LDPCC-CPFSK with channel equalization over WSSUS multipath environment

In this paper, in order to ensure secure and robust communication, a new type of data encryption and error correction mechanism called Multilevel/Advanced Encryption Standard-Low Density Parity Check Coded-Continuous Phase Frequency Shift Keying (Multilevel/AES-LDPCC-CPFSK) is carried out. Here, we have chosen AES for data encryption, LDPC codes for error correction and CPFSK for modulation. We have evaluated error performance of this scheme over Wide-Sense Stationary Uncorrelated Scattering (WSSUS) multipath channels with channel equalization. We have simulated 5-level AES, 2-level LDPC for 4CPFSK and 16CPFSK over WSSUS channels modeled by Cooperation in the field of Science & Technology, Project #207 (COST207). We have concluded that our proposed structure has promising results compared to Turbo Codes for all SNR values in WSSUS channels.

Equivalence of VSSO and VSVO Kalman Channel Estimators in Doubly-Selective OFDM Systems—A Theoretical Perspective

Vector state-vector observation (VSVO) , and vector state-scalar observation (VSSO) are two types of Kalman estimators that can be used for channel estimation in doubly-selective OFDM systems over wide-sense stationary uncorrelated-scattering (WSSUS) channels. It was shown in that the VSSO Kalman channel estimator resulted in over 90% complexity savings compared to the VSVO Kalman channel estimator and this was achieved without any loss of performance. This inevitably raises the question whether the VSSO and VSVO Kalman channel estimators are computationally equivalent? We attempt to answer this question in this letter and theoretically show the equivalence of the VSSO and VSVO Kalman channel estimator for WSSUS channels.

Optimal and Suboptimal Differentially Coherent Reception of MDPSK in Time-Spread WSSUS Channel

A model of the wide-sense stationary uncorrelated scattering (WSSUS) channel with time-spread and additive white Gaussian noise is considered. The general expression for the symbol-by-symbol reception algorithm of M-ary differential phase shift keying (MDPSK), which realizes implicit diversity, is obtained. Depending on the type of impulse response receiver filter (demodulator kernel), the partial cases that follow from this expression are considered: optimal demodulator, conventional differentially coherent demodulator, demodulator with iterative kernel and its special cases. Relations for assessing the bit error probability of the considered demodulators in the case when signals are transmitted with binary and quadrature differential phase shift keying without taking into account intersymbol interference are derived. The performance bounds for the optimized binary and quadrature systems are determined. The results of the calculation of the bit error probability are presented.

Optimized Paraunitary Filter Banks for Time-Frequency Channel Diagonalization

We adopt the concept of channel diagonalization to time-frequency signal expansions obtained by DFT filter banks. As a generalization of the frequency domain channel representation used by conventional orthogonal frequency-division multiplexing receivers, the time-frequency domain channel diagonalization can be applied to time-variant channels and aperiodic signals. An inherent error in the case of doubly dispersive channels can be limited by choosing adequate windows underlying the filter banks. We derive a formula for the mean-squared sample error in the case of wide-sense stationary uncorrelated scattering (WSSUS) channels, which serves as objective function in the window optimization. Furthermore, an enhanced scheme for the parameterization of tight Gabor frames enables us to constrain the window in order to define paraunitary filter banks. We show that the design of windows optimized for WSSUS channels with known statistical properties can be formulated as a convex optimization problem. The performance of the resulting windows is investigated under different channel conditions, for different oversampling factors, and compared against the performance of alternative windows. Finally, a generic matched filter receiver incorporating the proposed channel diagonalization is discussed which may be essential for future reconfigurable radio systems.

On the problems of symbol‐spaced tapped‐delay‐line models for WSSUS channels

AbstractThis paper analyzes the validity and statistical behavior of symbol‐spaced tapped‐delay‐line (SSTDL) models for wide‐sense stationary uncorrelated scattering (WSSUS) mobile radio channels. SSTDL models are obtained by sampling the channel impulse response (CIR) in delay domain at a rate equal to the reciprocal of the symbol duration. They were proposed more than four decades ago as canonical channel models for band‐limited time‐variant linear (TVL) systems, and are nowadays widely in use for assessing the performance of several wireless communication systems. The applicability of these tapped‐delay‐line (TDL) models seems to be unquestionable, as they were developed in the framework of the sampling theorem. Nonetheless, we show here that SSTDL models should be used with care to model WSSUS channels, because the channel's uncorrelated scattering (US) condition might easily be violated. Furthermore, we show that SSTDL models suffer from strong limitations in emulating the channel frequency correlation function (FCF). This drawback leads to an inaccurate performance evaluation of wireless communication systems sensitive to the FCF. To cope with this problem, we present a simple solution by doubling the channel's sampling rate. The benefits of this solution are demonstrated with some exemplary simulation results. Copyright © 2008 John Wiley & Sons, Ltd.

Soft-Output Demodulation on Frequency-Selective Rayleigh Fading Channels Using AR Channel Models

Optimal link adaption to the scattering function of wide-sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission, such link adaption is performed by pulse shaping, i.e., by properly adjusting the transmit and receive filters. For example, pulse-shaped offset-quadrature amplitude modulation (OQAM) systems have recently been shown to have superior performance over standard cyclic prefix orthogonal frequency-division multiplexing (OFDM) (while operating at higher spectral efficiency). In this paper, we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so-called Weyl-Heisenberg or Gabor signaling with respect to the scattering function of the WSSUS channel. In our framework, the pulse shape optimization problem is translated to an optimization problem over trace class operators which, in turn, is related to fidelity optimization in quantum information processing. By convexity relaxation, the problem is shown to be equivalent to a convex constraint quasi-convex maximization problem thereby revealing the nonconvex nature of the overall WSSUS pulse design problem. We present several iterative algorithms for optimization providing applicable results even for large-scale problem constellations. We show that with transmitter-side knowledge of the channel statistics a gain of 3-6 dB in signal-to-interference-and-noise-ratio (SINR) can be expected.

The WSSUS Pulse Design Problem in Multicarrier Transmission

Optimal link adaption to the scattering function of wide-sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission, such link adaption is performed by pulse shaping, i.e., by properly adjusting the transmit and receive filters. For example, pulse-shaped offset-quadrature amplitude modulation (OQAM) systems have recently been shown to have superior performance over standard cyclic prefix orthogonal frequency-division multiplexing (OFDM) (while operating at higher spectral efficiency). In this paper, we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so-called Weyl-Heisenberg or Gabor signaling with respect to the scattering function of the WSSUS channel. In our framework, the pulse shape optimization problem is translated to an optimization problem over trace class operators which, in turn, is related to fidelity optimization in quantum information processing. By convexity relaxation, the problem is shown to be equivalent to a convex constraint quasi-convex maximization problem thereby revealing the nonconvex nature of the overall WSSUS pulse design problem. We present several iterative algorithms for optimization providing applicable results even for large-scale problem constellations. We show that with transmitter-side knowledge of the channel statistics a gain of 3-6 dB in signal-to-interference-and-noise-ratio (SINR) can be expected.

Performance of multilevel‐turbo codes with blind/non‐blind equalization over WSSUS multipath channels

AbstractIn this paper, in order to improve error performance, we introduce a new type of turbo codes, called ‘multilevel‐turbo codes (ML‐TC)’ and we evaluate their performance over wide‐sense stationary uncorrelated scattering (WSSUS) multipath channels. The basic idea of ML‐TC scheme is to partition a signal set into several levels and to encode each level separately by a proper component of the turbo encoder. In the considered structure, the parallel input data sequences are encoded by our multilevel scheme and mapped to any modulation type such as MPSK, MQAM, etc. Since WSSUS channels are very severe fading environments, it is needed to pass the received noisy signals through non‐blind or blind equalizers before turbo decoders. In ML‐TC schemes, noisy WSSUS corrupted signal sequence is first processed in equalizer block, then fed into the first level of turbo decoder and the first sequence is estimated from this first Turbo decoder. Subsequently, the other following input sequences of the frame are computed by using the estimated input bit streams of previous levels. Here, as a ML‐TC example, 4PSK 2 level‐turbo codes (2L‐TC) is chosen and its error performance is evaluated in WSSUS channel modelled by COST 207 (Cooperation in the field of Science & Technology, Project #207). It is shown that 2L‐TC signals with equalizer blocks exhibit considerable performance gains even at lower SNR values compared to 8PSK‐turbo trellis coded modulation (TTCM). The simulation results of the proposed scheme have up to 5.5 dB coding gain compared to 8PSK‐TTCM for all cases. It is interesting that after a constant SNR value, 2L‐TC with blind equalizer has better error performance than non‐blind filtered schemes. We conclude that our proposed scheme has promising results compared to classical schemes for all SNR values in WSSUS channels. Copyright © 2005 John Wiley & Sons, Ltd.

Characterization of WSSUS channels: normalized mean square covariance

A set of second-order statistics collectively called normalized mean square covariance (NMSV) are defined to characterize the frequency and/or the time selectivity of wide-sense stationary uncorrelated scattering (WSSUS) channels. Normalized frequency mean square covariance (NFMSV) quantifies the frequency selectivity, while normalized time mean square covariance (NTMSV) characterizes the time selectivity. Normalized frequency-time mean square covariance is defined to characterize the combined effect of frequency and time selectivities. The NMSVs of a WSSUS channel can be computed easily from the scattering function. We show that there is a very close relationship between the NMSV of a WSSUS channel and the performance of various diversity combing schemes. Also we discuss, with practical system design problems, how useful the parameters are for efficient system design.

Rapid estimation of the range-doppler scattering function

Under wide sense stationary uncorrelated scattering (WSSUS) conditions, the signal spreading due to a random channel may be described by the scattering function (SF). In an active acoustic system, the received signal is modeled as the superposition of delayed and Doppler spread replicas of the transmitted waveform. The SF completely describes the second-order statistics of a WSSUS channel and can be considered a density function that characterizes the average spread in delay and Doppler experienced by an input signal as it passes through the channel. The SF and its measurement will be reviewed. An estimator is proposed based on a two-dimensional (2-D) autoregressive (AR) model for the scattering function. In order to implement this estimator, we derive the conditional minimum variance unbiased estimator of the time-varying frequency response of a linear channel. Unlike conventional Fourier methods, the AR approach does not suffer from the usual convolutional smoothing due to the signal ambiguity function. Simulation results are given.

On the correlation and scattering functions of the WSSUS channel for mobile communications

The wide-sense stationary-uncorrelated scattering (WSSUS) channel model is a commonly employed model for the multipath channel experienced in mobile communications. The second order statistics of these channels are described by the delay cross-power density /spl phi//sub h/(/spl tau/;/spl Delta/t) or by its /spl Delta/t-Fourier transform, the scattering function S/sub h/(/spl tau/;/spl lambda/). This paper presents an analysis of the delay cross-power density and scattering functions for mobile communications channels. We assume an arbitrary spatially uncorrelated scattering (US) field with arbitrary propagation-loss factors. Our first result is a general integral expression for /spl phi//sub h/(/spl tau/;/spl Delta/t) that holds with both transmitter and receiver being mobile. We then derive more detailed results for the case of a stationary base station. We derive an infinite Bessel series for /spl phi//sub h/(/spl tau/;/spl Delta/t) and a closed-form expression for S/sub h/(/spl tau/; /spl lambda/). These results generalize the well-known classical approximation for the time-correlation function /spl phi/~/sub h/(/spl Delta/t)=/sup def//spl int//spl phi//sub h/(/spl tau/;/spl Delta/t)d/spl tau//spl ap/ J/sub 0/(2/spl pi//spl lambda//sub m//spl Delta/t), which corresponds to the zeroth term of our Bessel series.

Karhunen-Loeve expansion of the WSSUS channel output and its application to efficient simulation

This paper derives a Karhunen-Loeve (K-L) expansion of the time-varying output of a multipath Rayleigh fading wide-sense-stationary uncorrelated-scattering (WSSUS) channel. It is shown that under the same mean-squared error condition, the number of terms required by the truncated K-L expansion is less than that of the series expansion obtained by using the discrete-path approximation of the channel so that simulation using the K-L expansion is more efficient. This computational advantage becomes more significant as higher simulation accuracy is required. The derived K-L expansion is applied to develop an efficient simulation technique for digital transmission over a multipath Rayleigh fading WSSUS channel using an optimum receiver. We show that the proposed technique requires shorter computation time than two other known simulation techniques.

Discrete-time model for digital communications over a frequency-selective Rician fading WSSUS channel

The paper develops a discrete-time model for digital communications via a frequency-selective Rician fading, wide-sense-stationary uncorrelated-scattering (WSSUS) channel with arbitrary pulse shaping and receiver filtering. As a special case, the discrete-time model is also applicable to a frequency-selective Rayleigh fading WSSUS channel. The model is expressed in the form Ξk = Nk + Σbk-mgm(t), where Ξk is the complex-valued receiver output, bk-m is the transmitted symbol, Nk is the complex-valued output noise due to AWGN, and gm(t) is the time-varying gain of bk-m. Statistical characteristics of Nk and gm(t) are derived. It is found that {Nk} is a zero-mean complex Gaussian sequence, and gm(t)s ∀ m follow a wide-sense-stationary, jointly complex Gaussian random process. Simple closed-form formulas computing statistical parameters of Nk and gm(t)s are derived. Several aspects regarding the use of the proposed model to analytic works and efficient computer simulations are discussed. Finally, three illustrative examples are given.

Efficient simulation of digital transmission over WSSUS channels

This paper proposes an efficient Monte Carlo method which reduces computation for digital communication simulations over a multipath Rayleigh fading, wide-sense-stationary uncorrelated-scattering (WSSUS) channel. An equivalent discrete-time channel representation, which can be realized by a FIR filter with time-variant tap gains, is employed. In the proposed method, the tap gains are generated from a linear transformation of a set of orthogonal zero-mean complex Gaussian random processes. By the central limit theorem, each random process is approximated by summing a finite number of randomly generated phasors (Monte Carlo approximation). When compared with the tap gain generation method, which approximates the physical channel by the Monte Carlo approximation first and then generates the tap gain values, the proposed method demonstrates a considerable reduction in the required simulation time as well as improved accuracy under similar conditions.

Analysis of Direct-Sequence Spread-Spectrum Multiple-Access Communication Over Rician Fading Channels

This paper is concerned with the performance of biphase direct-sequence spread-spectrum multiple-access communication for a general class of fading channels. The channels considered are those for which the channel output consists of a strong stable specular signal plus a faded version of this signal. Such channels, which are referred to as Rician fading (or Rice fading) or specular-plus-Rayleigh fading, are the result of a transmission medium which gives rise to a major stable communication path and a number of additional weaker communication paths. The fading channel is modeled as a general wide-sense-stationary uncorrelatedscattering (WSSUS) channel-a model which is general enough to exhibit both time and frequency selectivity and to impose no restrictions on the fading rate. For the general WSSUS model, results are obtained on the average signal-to-noise ratio at the receiver output in terms of the spread-spectrum signature sequences and the covariance function for the fading process. These results are then specialized to each of two important classes of WSSUS channels: time-selective fading channels and frequency-selective fading channels. Numerical evaluations are presented for specific examples of each of these two types of channels. Analytical expressions are derived for a spread-spectrum multiple-access system with random signature sequences, and the use of these expressions in preliminary system design is discussed.

Characterization of Randomly Time-Variant Linear Channels

This paper is concerned with various aspects of the characterization of randomly time-variant linear channels. At the outset it is demonstrated that time-varying linear channels (or filters) may be characterized in an interesting symmetrical manner in time and frequency variables by arranging system functions in (timefrequency) dual pairs. Following this a statistical characterization of randomly time-variant linear channels is carried out in terms of correlation functions for the various system functions. These results are specialized by considering three classes of practically interesting channels. These are the wide-sense stationary (WSS) channel, the uncorrelated scattering (US) channel, and the wide-sense stationary uncorrelated scattering (WSSUS) channel. The WSS and US channels are shown to be (time-frequency) duals. Previous discussions of channel correlation functions and their relationships have dealt exclusively with the WSSUS channel. The point of view presented here of dealing with the dually related system functions and starting with the unrestricted linear channels is considerably more general and places in proper perspective previous results on the WSSUS channel. Some attention is given to the problem of characterizing radio channels. A model called the Quasi-WSSUS channel is presented to model the behavior of such channels. All real-life channels and signals have an essentially finite number of degrees of freedom due to restrictions on time duration and bandwidth. This fact may be used to derive useful canonical channel models with the aid of sampling theorems and power series expansions. Several new canonical channel models are derived in this paper, some of which are dual to those of Kailath.