Effective Channel Order Estimation Based on Nullspace Structure and Exponential Fit

The selection criteria for the order of a single-input multiple-output (SIMO) channel generally use the singular values of the estimated least squares matrix. Using these values ignores important information that can be obtained from the nullspace of the least squares matrix. The nullspace has a structured basis that can be utilized to quantify the quality of channel coefficient estimates. These quantities cluster in the nullspace and spread in the signal space, when compared to the singular values. A simple exponential curve fit is used to further improve the estimate of the effective channel order. The new criterion outperforms other known criteria in a wide variety of scenarios at both high and low SNR.