Fractional Rate Non-Uniformly Spaced Equalization

The recently introduced non-uniformly spaced equalizers (NUSE) are realized by processing a select number of received symbols obtained from a sampler operating at L times the baud rate where L is an integer. We consider here the more challenging case where the sampler operates at L/M times the baud rate with L and M being coprime integers. We first propose a new and generic discrete time model that includes all previously proposed equalizers as special cases. Using this model, we can then derive necessary conditions for the existence of zero forcing FIR fractional rate NUSE (FR-NUSE) as well as closed form expressions for the minimum mean squared error FIR FR-NUSE. Our simulations show that the FR-NUSE has excellent performance at a much lower computational cost.