7) When the sequence period N is large compared to the processing gain, as it is in many systems, the full period correlation Paa(T) loses some of its value as a design parameter. Correlation calculations in this case typically are car- ried out over blocks of K symbols, where K may be larger than the linear span L and much smaller than the period N. A more appropriate statistic for study in this case is the partial-period correlation defined as (5.88) Statistical Properties of M-Sequences which computes the cross-correlation between two blocks of K symbols from {an}, one block located T symbols from the other. Unlike full-period correlation calculations, partial-period correlation val- ues depend on the initial location n in the sequence where the correlation computation begins. Hence, an explicit description of the function PaaK, n, T) must include values over the range 0 (n, N of n. Often the size of N pre- cludes direct calculation of all these values, and computable time averages therefore are substituted to give a statistical description of the partial- period correlation function. Denoting the time-average operation by <.), the first and second time-average moments of Paa(K,n,T) are given by (5.89) (5.90) where the parameter over which the average is being computed is N. Property R-6. Let {an} be a complex m-sequence of period N, composed of p-th roots of unity. The time-averaged first and sceond moments of the partial-period cor- relation function of {an} are given by ) mod (5.91) T = 0 mod N (5.92) T=0mod N respectively, for K K N Proof. The first moment calculation is straightforward: (5.93) and (5.91) follows directly from Property R-5. The derivation of the second moment uses the additional fact that Property R-3 for an m-sequence over GF(p) translates via (5.80) into the property all n, (5.94) Pseudonoise Generators when T # 0 mod N. Hence, K-1 K-1 (5.95) Noting that there are K terms for which j=k,and K(K - 1) terms for which j # k, the final result follows immediately by applying Property R-5 to (5