IEEE 802.11b Complementary Code Keying and Complementary Signals Derived from Biorthogonal Sequences

Abstract

Two classes of complementary signal sets are compared in terms of their complementary properties and their error probabilities for channels with thermal noise and multipath interference. One class consists of the high-rate (11 Mbps and 5.5 Mbps) signals employed in the IEEE 802.11b standard, and the other class includes full-rate (11 Mbps) complex signals derived from biorthogonal sequences and half-rate (5.5 Mbps) biorthogonal signals. We examine several types of complementary properties of each class of signals and give performance comparisons for the signals when employed on channels in which thermal noise is the only disturbance and channels with thermal noise and multipath interference. For standard IEEE 802.11b complementary-codekey (CCK) modulation, we find the performance is strongly dependent on the differential multipath delay. For systems that employ binary error-control coding, the signals that are based on biorthogonal modulation are superior to the two IEEE 802.11b CCK signal sets.

Properties and performance of the IEEE 802.11b complementary-code-key signal sets

“…If y i,k denotes the element in the ith row and kth column of the matrix Y 0 , then c k = (y 1,k , y 2,k , y 3,k , y 4,k ) is the kth column of Y 0 . The arguments employed in [28] show that c k , c n = 0 for all k and n (k = n) except when n = k+2 and k ∈ {1, 2, 5, 6}. This proves that Γ m = 0 for m = 2.…”

“…If X m = exp( jmπ/2)X 0 for 1 ≤ m ≤ 3, then the rows of X m are the sequences from X m . The proof that the columns of X 0 are orthogonal is given in [28]. It follows that the columns of X m are orthogonal for each m, which in turn implies orthogonality of the columns of the full 256×8 signal matrix X and establishes that the signals in the full-rate set satisfy (6), the OCC.…”

“…It is shown in [28] that the half-rate CCK signal set does not satisfy the OCC. Here we show that it does satisfy (5), the NSC.…”

“…The corresponding result for the half-rate CCK signal set is a special case of the partition used for the full-rate CCK set that is obtained by setting ϕ 3 = 0 and allowing ϕ 4 to take only two values, 0 and π. The details are given in [28]. The pairwise-complementary orthogonal signal set given in Table I corresponds to a Hadamard matrix of order 8.…”