Reed–Solomon and Simplex Codes for Peak-to-Average Power Ratio Reduction in OFDM

New schemes for peak-to-average power ratio reduction in orthogonal frequency-division multiplexing (OFDM) systems are proposed. Reed-Solomon (RS) and simplex codes are employed to create a number of candidates, from which the best are selected. Thereby, in contrast to existing approaches, the codes are arranged over a number of OFDM frames rather than over the carriers, hence a combination of the principles of multiple signal representation with selection (as done in selected mapping) and the use of channel coding is present. In particular, in multiple-antenna transmission, the proposed schemes do not cause any additional delay, but due to the utilization of the dimension space, additional gains can be achieved. Moreover, the schemes are very flexible; due to the selection step, any criterion of optimality can be taken into account. Besides multiple-antenna transmission, packet transmission is briefly considered, which, moreover, covers the appealing similarities with incremental redundancy check schemes in automatic repeat request (ARQ) applications and with decoding of codes transmitted over the erasure channel. The performance of the schemes is (using some approximations) derived analytically and is covered by numerical results that are in very good agreement with the theory. Significant gains can be achieved with these very flexible and versatile methods.