Minimally redundant maximally robust linear precoders

Precoding data prior to its transmission over a fading channel can improve performance. When the channel is unknown, it may be desirable to use a linear precoder whose worst case performance is no worse than that of any other linear precoder. Such a precoder is said to be maximally robust. This paper derives necessary and sufficient conditions for a linear precoder to be maximally robust. It is proved that maximally robust linear precoders eliminate fading completely. Also derived is an explicit expression for a maximally robust linear precoder which introduces the least amount of redundancy possible.