The peak power distributions considered in the previous chapter are derived under the assumption that the coefficients are chosen independently from a constellation. In this chapter, I will consider a more complicated situation when there exists a dependence between subcarriers. In Section 6.1 the PMEPR distribution in spherical codes is considered. The only restriction on these signals is that they have constant energy. I prove results about concentration of the PMEPR distribution. In Section 6.2, I study the existence of spherical codes with a given minimum (Euclidean or Hamming) distance and PMEPR. In Section 6.3, I relate the PMEPR distribution of coded signals to the distance distribution of codes. In Section 6.4, I specify the previous analysis to the case of BCH codes. I show that when the length grows, the distance distribution of BCH codes approaches the normalized binomial distribution. This allows analysis of the PMEPR distribution for a subclass of BCH codes. In Section 6.5, I show how the PMEPR of a code can be computed in an efficient way if the code possesses a fast maximum likelihood decoding.

6.1 Spherical Codes

An n-dimensional constellation has a spherical distribution if the points of the constellation are uniformly distributed over the n-dimensional complex sphere with radius denoted .

Theorem 6.1

Let c be spherically distributed. Then

where r > 1 is an integer.

Proof We will study first the situation when the coefficients are circularly Gaussian distributed with unit power. Let c be...