Design Precoded Space-Time-Frequency 4 x 1 and 4 x 2 OFDM Architectures in Frequency-Selective Fading Channels

This paper presents precoded space-time-frequency (STF) 4 x 1 and 4 x 2 orthogonal frequency-division multiplexing (OFDM) systems in frequency-selective fading channels. First, a regular 2 x 1 space-time (ST) block code OFDM system is presented as the baseline. Second, further developing this 2 x 1 ST OFDM, both novel 4 x 1 and 4 x 2 STF OFDM architectures and computing algorithms are developed, specifically at a code rate 3/4. Third, four orthogonal transforms, Walsh-Hadamard, Slant, Harley, and Haar, are employed as the precoder to form four different 4x1 and 4x2 precoded STF OFDM systems, respectively. All four precoded systems improve the bit error rate (BER) without expanding power or bandwidth in comparing with the regular 4 x 1 and 4 x 2 STF OFDM schemes. Simulations indicate that the precoded 4x2 STF OFDM system has the best BER; the 4x2 STF OFDM system, the precoded 4 x 1 STF OFDM system, the 4 x 1 STF OFDM system, and the 2 x 1 ST OFDM system follow in order due to the achieved diversity order in fading channels. All systems are well-matched with the current OFDM system. They may serve as basic modules in the fourth-generation (4G) and future planned 5G multiple input multiple output (MIMO) OFDM systems.