An Alternative Filter Bank View for Real Orthogonal STBC in Frequency Selective Channel

This paper presents an alternative approach for viewing a real orthogonal space time block code (ROSTBC) in frequency selective channel as a filter bank (FB). A communications system with multiple transmitting antennas and a single receiving antenna is considered. From the FB point of view, this system when employing a rate-1 ROSTBC, can be treated as a maximally decimated FB. Likewise, it becomes a non-maximally decimated FB, when a non-rate 1 ROSTBC is employed. The amount of redundancy can be observed from the number of channels between the analysis and the synthesis polyphase matrices versus the number of input channels. When there is redundancy, the block MIMO channel (describing the overall physical channels between the transmitter and receiver) becomes a tall matrix. Hence an FIR inverse (synthesis matrix) is more likely to exist at the receiver side. On the other hand, for all full rate ROSTBCs, the channel matrix becomes a square matrix. Its Smith form always consists of a nontrivial FIR term, prohibiting the existence of its FIR inverse. Simulations and examples are given to illustrate various concepts developed in this paper.