Direct blind equalizers of multiple FIR channels: A deterministic approach (Q2732782)

The aim of the paper is to derive direct blind FIR equalizers of co-prime FIR channels using a sufficient number of multiple outputs. The only constraint on the inaccessible input comes from a minimum persistence of excitation conditions: the input can be deterministic or random with unknown colour or distribution. At moderate SNR (\(>\) 20 dB), the resulting algorithms remain operational even when using only 50 to 100 samples. This is because the equalizing solutions provided are algebraic and exact in the absence of noise. Complexity, persistence-of-excitation order, and mean-square error performance tradeoffs are delineated for equalizers of single-shift (semi-blind), pair, or multiple shifts estimated separately or simultaneously. Optimum and suboptimum combinations of the equalizers' outputs are also studied.NEWLINENEWLINENEWLINEThe main novelties introduced within the paper may be summarized as follows: (a) Derivation of minimum and maximum delay equalizers separately, when all data are available or when guards bits separate data records (a semi-blind approach); (b) A joint blind estimation of all the \(k\)th-order FIR equalizers, allowing the input to be either deterministic or (non-)white random; (c) Providing identifiability proofs that reveal the role of persistence-of-excitation on the input; (d) Methods to optimally combine the outputs of all equalizers corresponding to different delays.NEWLINENEWLINENEWLINEThe proposed algorithms are illustrated with simulations on two different channels and compared with dual deterministic channel identification algorithms.