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

Abstract

This paper derives a Karhunen-Loève (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.

Stochastic Modeling and Simulation of Frequency-Correlated Wideband Fading Channels

“…. , L − 1) [13], [14]. Each subinterval I corresponds to the range within which a number of multipath components are combined to the th tap.…”

Nondata-Aided Channel Estimation for OFDM Systems With Space-Frequency Transmit Diversity

“…A different approach is adapted here to explicitly model the channel parameters by a Karhunen-Loeve (KL) series representation, since a KL expansion allows one to tackle the estimation of correlated parameters as a parameter estimation problem of the uncorrelated coefficients. Note that the KL expansion is well known for its optimal truncation property [19]. That is, the KL expansion requires the minimum number of terms among all possible series expansions in representing a random channel for a given mse.…”

“…Due to the orthogonality of the SFBC system based on the Alamouti orthogonal design, as well as the KL expansion of the multipath channel that yields simple exact iterative expressions for the unknown channel parameters in frequency domain which do not require any matrix inversion [18], [19]. Moreover, the optimal truncation property of the KL expansion can further reduce the computational load on the channelestimation algorithm.…”

Optimal Detection and Signalling in Fast Fading Channels

“…Some researchers collect their own data and construct their own channel models [71] while others study the existing experimental data with their own models or improve previous models [72,73]. The demand for research in this topic has also inspired the development in specific mathematical techniques [46,[74][75][76] and new statistical models [77]. The characteristics and effects of the channel on the various aspects of system performance (e.g., error rate under specific settings, channel capacity, etc.)…”

“…To ensure the system is performing up to the design specifications, a computer or hardware simulation is required. Therefore, many different simulation schemes have been proposed for different settings [76,82,83]. These analyses are often case-specific [42,43,45,46,51,74,[84][85][86][87][88][89][90][91][92].…”