Fractional biorthogonal partners in fractionally spaced equalizers

The concept of fractional biorthogonal partners has been introduced recently by the authors. They arise in many different contexts, one of them being channel equalization with fractionally spaced equalizers. If the amount of oversampling at the receiver is not an integer, but a rational number, the problem of fractionally spaced equalization can be treated using the fractional biorthogonal partner setting. This approach is adopted here. We consider fractionally spaced equalizers with a rational amount of oversampling, show that the FIR solution (if it exists) is not unique and can be chosen to minimize the noise power at the receiver. These findings are demonstrated by examples where we compare the performance of fractionally spaced zero forcing equalizers to that of the corresponding minimum mean-squared error solution.