Blind SIMO Channel Estimation Subspace Method with Linear Constraints and Channel Overmodeling: A Sensitivity Study

SIMO Blind Channel Estimation and the problem it is encompassed by, Multichannel Blind Deconvolution, have been the topic of numerous works over the past several decades. Many methods have been developed to estimate the unknown channels and/or the signal based on assumptions made about them. One class of methods are the Subspace methods, which transform the problem into identifying the subspace of a matrix formed from the received signal observations across all channels. However, these approaches depend on a number of identifiability conditions that are often not met in practice, such as knowledge of the channel order; they do not perform well when conditions are not close to being met. These methods typically apply a quadratic, fixed-energy constraint to the estimated channels. However, results from previous works have noted that applying a linear constraint appears to make the Subspace methods more robust in certain cases, particularly when the channel is overmodeled. In this work, we compare the performance and robustness of Subspace methods subjected to the traditional quadratic constraint, as well as various sets of linear constraints, using both measured wireless communications channels, and simulated channels composed of varying numbers of Rayleigh fading multi-path components. We find that this type of constraint can indeed improve the robustness to overmodeling, and propose a constraint that does not depend on knowledge of the delay of the strongest path in the channel.