Constructions of Complementary Sequences for Power-Controlled OFDM Transmission

We present constructions of polyphase sequences suitable for the use as codewords in orthogonal frequency-division multiplexing (OFDM) with strictly bounded peak-to-mean envelope power ratio (PMEPR). Our first construction establishes that each polyphase sequence of length 2 lies in a complementary set, whose size depends on a special property of its associated generalized Boolean function. Thus we identify a large family of sequences with PMEPR at most 2, where k is a non-negative integer. Our second construction yields sequences that lie in so-called almost complementary pairs and have PMEPR at most 3. A number of coding schemes for OFDM with low PMEPR is then presented. These schemes extend and complement previously proposed coding options.