A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).

Multi-antenna relay transport protocols are analysed, the transmitting matrix of relay node can split into a forward and a backward filters, and these two filters are cascade connection. Based on the zero-forcing relaying protocol, a spatial channel mapping matrix is added between these two filters, and a unified framework of spatial channel mapping matrix is proposed. Then, various linear system designs are summarized, the spatial channel mapping matrix is used to reduce destination noise, so that the relaying noise is suppressed in destination node, and the transmitting power of relay is efficiently utilized. Meanwhile, source node preprocessing operation and destination node equalizer are considered. Simulation results show that the spatial channel mapping matrix has an advantage in terms of system outage probability and capacity performance, and the result is consistent with theoretical analysis.

A novel analog decoding method using only 90-degree phase shifters is proposed to simplify the decoding method for short-range multiple-input multiple-output (MIMO) transmission. In a short-range MIMO transmission, an optimal element spacing that maximizes the channel capacity exists for a given transmit distance between the transmitter and receiver. We focus on the fact that the weight matrix by zero forcing (ZF) at the optimal element spacing can be obtained by using dividers and 90-degree phase shifters because it can be expressed by a unitary matrix. The channel capacity by the proposed method is next derived for the evaluation of the exact limitation of the channel capacity. Moreover, it is shown that an optimal weight when using directional antennas can be expressed by using only dividers, 90-degree phase shifters, and attenuators, regardless of the beam width of the directional antenna. Finally, bit error rate and channel capacity evaluations by both simulation and measurement confirm the effectiveness of the proposed method.

A class of zero-correlation zone (ZCZ) sequences constructed by the recursive procedure from a perfect sequence and a unitary matrix was proposed by Torii, Nakamura, and Suehiro [1] . In the reference [1] , three parameters, s.t., the sequence length, the family size and the length of the ZCZ, were evaluated for a general estimate of the performance of the ZCZ sequences. In this letter, we give more detailed distributions of that correlation values are zero on their ZCZ sequence sets.

In this letter, we propose an iterative decoding with LDPC based unitary matrix modulated OFDM with splitting the diagonal components over the coherence bandwidth. The proposed system can obtain a frequency diversity gain by splitting the diagonal components of unitary matrix modulated symbols, and also obtain large coding gain by using LDPC code.