Channel shortening for OFDM systems: An improved algorithm in noisy environments

In this paper, we propose an efficient channel shortening algorithm, applied to OFDM systems, exploiting a particular decomposition of the Toeplitz convolution channel matrix and of the channel shortening filter (CSF). Unlike classical methods which optimize the CSF following one single criterion applied to the whole response of the filter, our decomposition allows for addition of complementary criteria. Similarly to classical CS techniques, the proposed method tries to concentrate most of the energy of the shortened channel impulse response (SCIR) within the tolerated delay-spread window. However, our second applied criterion aims at limiting the noise enhancement on each sub-carrier by minimizing the spectral distortions related to the filtering function. The performance of the algorithm in terms of computational complexity and bit error rate (BER) is studied by simulations and compared to the reference algorithm of the literature referred to as maximum shortening signal to noise ratio (MSSNR) algorithm.