On the average power of multiple subcarrier intensity modulated optical signals: Nehari´s problem and coding bounds

Multiple subcarrier modulation (MSM) is an attractive technique for optical wireless communication for high speed applications. The main disadvantage of this scheme is its low average power efficiency which is in an analogous problem to the high peak to mean envelope power ratio (PMEPR) of multicarrier signals. In this paper, we consider the achievable average power reduction of MSM signals by using optimized reserved carriers and coding methods. Based on Nehari´s result we present a lower bound for maximum average power of the signal after adding the reserved carriers. It is shown that the mean value of the average required power behaves very close to √(2n log log n) for a BPSK constellation where n is the number of subcarriers. We then consider finding the optimum values for the carriers and the effect of having finite bandwidth for reserved carriers. In the next section, mainly based on recent coding results for PMEPR of multicarrier signals, we show the existence of very high rate codes with average power of O(√(n log n)) for large values of n, and furthermore the existence of codes with non-vanishing to zero rate and the average power of O(√n) asymptotically.