New General Approach to the Design of Arbitrary Radix-4 QAM Sequences for Low PMEPR and High Code-Rate

Orthogonal frequency division multiplexing (OFDM) is a prevalent telecommunication technology to mitigate the common multi-path problem and it is widely adopted with high-order modulations such as quadrature amplitude modulation (QAM) in many communication systems. However, uncoded OFDM systems have a serious drawback of high peak-to-mean-envelope-power ratio (PMEPR). On the other hand, coded OFDM systems, although mitigating the PMEPR problem, often lead to low code rates. Obviously, there exists a tradeoff between PMEPR and code rate in the design of OFDM systems. Nevertheless, hardly exists any approach to address this tradeoff so far in the literature. In this paper, a new general design framework for OFDM M-QAM sequences is proposed, in which the constellation size M can be any arbitrary radix-4 number (i.e. M = 4^h) and the sequence length n can be any radix-2 number (i.e. n = 2m). Theoretical studies on PMEPR and code rate are presented so that both metrics can be determined for arbitrary radix-4 M and radix-2 n. This new general approach can be used to construct numerous families of sequences achieving low PMEPR, high code rate, or balancing these two metrics. Our proposed novel general design framework can be deemed very promising for the future OFDM transmission systems.