Maximum likelihood semi-blind equalization of doubly selective channels

Maximum likelihood semi-blind joint channel estimation and equalization for doubly selective channels in single carrier systems is proposed. The method is based on the expectation maximization (EM) principle combined with a basis expansion model (BE) of the doubly selective channel. To alleviate the problem of convergence of the EM to a local maximum, we propose an initialization scheme to the EM iterations based on a small number of pilot symbols. We further derive an optimal pilot positioning scheme to minimize the probability of convergence to a local maximum. The resulting algorithm is shown to be superior over previously proposed equalization schemes and to perform in many cases close to the maximum likelihood equalizer with perfect channel knowledge. Our proposed method is also applicable to the case of short, independent fading blocks.