A blind adaptive channel shortening algorithm using any lag auto correlation minimization (ALAM)

The purpose of channel shortening is to condense the channel in a shorter span to make the Multi Carrier Communication Systems bandwidth and power efficient. The autocorrelation minimization based channel shortening algorithms are investigated in this paper. If a white signal is input to a filter having a short span, the autocorrelation introduced in the output signal is small. The SAM algorithm expects that the reverse might also be true. Therefore, it performs channel shortening by minimizing the sum-squared autocorrelation of the output of the channel for a range of lags. It is shown that minimizing the autocorrelation of the channel output as in SAM is not equivalent to condensing the channel in a contagious window. As long as the ADSL channels are concerned, identical channel shortening can be achieved by using a single autocorrelation in the cost function. Using a range of autocorrelations is unintelligent and overkill. Furthermore, this single autocorrelation is not specific to any particular value of lag. This finding not only reduces the computational complexity of SAM as in SLAM but also serves as an insight into the dynamics of the autocorrelation based channel shortening algorithms. The algorithm is named Any Lag Autocorrelation Minimization (ALAM). The simulations support the ideas presented in the paper. The reasons behind the diverging behavior of autocorrelation based algorithms to shorten the ADSL channels are also elaborated. The paper also serves to identify lags which can be minimized in the true sense of channel shortening. It is found that these lag values are not driven by the nature of the impulse response of the underlying channel. They always try to shorten a channel around its mid point. Therefore, it is conjectured that if the channel has its mass of energy around its mid point, ALAM is flexible and will successfully shorten it to different desired window lengths without any diverging behavior. On the other hand, SAM, which blindly minimizes all of the channel taps in its cost function, is expected to fail in such situations. The failure will come in the form of no shortening at all OR divergence from the optimal point.