Widely-Linear Selected Mapping for Peak-toAverage Power Ratio Reduction

Peak-to-average power ratio reduction in OFDM using antenna arrays (MIMO OFDM) is considered. In particular, a generalisation of selected mapping (SLM), we call it directed SLM (dSLM), is introduced. It is shown that, in contrast to schemes proposed in literature, dSLM utilises the potential offered by MIMO transmission. As a result, the complementary distribution function of the PAR exhibits a steeper decay, increased by a factor equal to the number of transmit antennas. This effect is similar to the diversity gain in error performance when using MIMO transmission. This work was supported in parts by Deutsche Forschungsgemeinschaft (DFG) within the framework TakeOFDM under grant FI 982/1-1. 2Introduction — Multicarrier modulation, in particular its implementation as orthogonal frequency-division multiplexing (OFDM), is very popular for transmission over frequency-selective channels [3]. Since for future applications the use of antenna arrays is envisaged, parallel OFDM transmission, often denoted as MIMO OFDM (multiple-input/multiple-output), is the most important candidate for next-generation wireless communication, e.g., [7]. We assume NT transmit antennas, over which independent data streams should be communicated. In each of the NT parallel OFDM transmitters a block of D distinct complex-valued carriers Aµ,ν, ν