Performance Analysis of a Reduced Rank Spatial Filter for Interference Cancellation

Abstract

In the interference mitigation context, it has been shown by simulations in Fety et al. (International symposium on wireless communication systems, pp 241–245, 2012), the outperformance of the coefficient constraints (CC) versus the power constraint on the channel impulse response, in terms of BER about 1–3 dB. However, no theoretical justification has been introduced. In this paper, we have proved theoretically this result. Moreover, we have investigated an interesting issue of the CC constraint concerning the choice of the coefficient position; we have given a full theoretical framework analysis about this feature. Two substantial propositions have been introduced to this end. Theoretical results were validated by simulations.

Appendix

Equation (27) can be rewritten as,

$$ \hbox{min}_{a} Ra^{2} \backslash a\left( i \right) = 1,\quad 2L < i \le N $$

Define the sub matrix $\varvec{R}_{i} \in C^{N \times N - 1}$ as the matrix R except the ith column vector, the vector $- \varvec{r}_{i} \in C^{N \times 1}$ the ith column vector of R and a _i is a vector without the the ith component. Therefore,

$$ \varvec{Ra} = \varvec{R}_{i} \varvec{a}_{i} - \varvec{r}_{i} $$

Then the last equation becomes,

$$ \hbox{min}_{{a_{i} }} \left( {R_{i} a_{i} - r_{i} } \right)^{H} \left( {R_{i} a_{i} - r_{i} } \right) $$

By nulling the first derivation with respect to a _i , then a _i is solution of the following linear system,

$$ a_{i} = \arg_{{a_{i} }} R_{i}^{H} R_{i} a_{di} - R_{i}^{H} r_{i} = 0 $$