Turbo equalization of doubly selective channels

In this paper, turbo equalization for transmission over doubly selective channels is proposed. The maximum a posteriori probability (MAP) algorithm is used for channel detection as well as for channel decoding. The detection/decoding constituents can exchange soft information in an iterative manner resulting in the so-called turbo equalization. The time-varying multi-path fading channel is modeled using the basis expansion model (BEM). In this BEM, the time-varying channel is viewed as a bank of time-invariant finite impulse response filters, and the time variation is captured by means of time-varying complex exponential basis functions. Therefore, the time-varying transition tables that characterize the time-varying channel can also follow a similar BEM. The complexity of the MAP channel detector is rather prohibitive for practical applications. This motivates the search for lower-complexity soft-output channel detectors. For this purpose, soft-output linear minimum-mean square error (LMMSE)-based channel detectors are proposed for single carrier as well as for multi-carrier systems. With the use of Gaussian approximation, expressions for the a posteriori and extrinsic log-likelihood ratios have been derived. The performance of the proposed turbo equalization schemes are evaluated using numerical simulations.