## New Design Method: Information Outage Minimization

For a fixed rotation and fixed MIMO channel matrices , , defined by the fading blocks, let denote the average mutual information of the equivalent channel with QAM input and complex output as in (1). The expression of is

 (6)

where is the conditional mathematical expectation over and . The channel likelihood is written in its classical form

 (7)

Expression (6) assumes that the precoder does space-time spreading within the same fading block . Its main role is to collect transmit diversity. Time diversity is collected by the convolutional code whereas receive diversity is naturally collected by the detector. The information rate transmitted by the space-time BICM is bits per time periods. An outage occurs if the instantaneous capacity, i.e. in our case, is less than . The outage probability associated to the rotation at a given signal-to-noise ratio is

 (8)

The new design, called IOM (Information Outage Minimization), selects a matrix within the ensemble of random unitary matrices such that

 (9)

As an example, choosing the best rotation within an ensemble limited to 2000 matrices yields the matrix written below, for QPSK alphabet with and coding rate

A smaller set of random unitary matrices is obtained by adding to the first genie constraint, i.e. orthogonal sub-rows in . This second design, called G-IOM, selects a matrix satisfying

 (10)

As an example, choosing the best rotation within an ensemble limited to 2000 matrices yields the matrix written below, for QPSK alphabet with and coding rate

In a similar fashion, a DNA-IOM precoder minimizes the information outage and satisfies DNA constraints [10]. The matrix given below corresponds to and . The DNA-IOM precoder is obtained by combining with . Also, the DNA cyclotomic precoder is constructed by combining to given previously in (3).

Figures 2 and 3 show the outage limit for different type of precoders in terms of Word Error Rate versus signal-to-noise ratio. The outage probability has been also evaluated for other system parameters. Surprisingly, algebraic precoders satisfying the first genie condition perform as good as G-IOM precoding. Cyclotomic rotation and Golden code are superimposed with G-IOM in Figure 2. All outage evaluations have been made by (6) and (8), without gaussian and analytical approximations when the channel input is a gaussian alphabet as in [18][20].
Joseph Jean Boutros 2005-05-07