quences, modulation formats, and the receiver's detector structure. This section will explore one tractable criterion for DS-SSMA sig- nal design, namely minimization of the absolute value of periodic correla- tion between signals. Consider a set of J sequences, each with period N, denoted by {a@},j , J. The periodic cross-correlation Pik(T) at shift T between sequences from this collection is defined as (5.232) The maximum out-of-phase periodic autocorrelation magnitude PA for this signal set is defined as (5.233) and the maximum cross-corelation magnitude Pc between signals in this set Direct-Sequence Multiple-Access Designs is given by (5.234) The signal sets to be discussed here all are designed to minimize Pmax = max(PA,Pc). (5.235) This criterion for sequence selection may not correspond to any DS-SSMA network performance measure, but it can be argued that a signal set which optimized network performance probably has a small value of Pmax; hence, one should find good signal sets among those with small Pmax Furthermore, from an analytic viewpoint, no other design criteria have proven tractable in choosing long-period sequences. In situations in which a capability against repeater jamming is not a requirement, the code period N may be relatively short, its value in most instances being underbounded by the multipath time-spread of the channel. Hence, in some multiple access designs which require no AJ provisions, cor- relations may be calculated over full periods. Conversely, when intelligent jamming is a possible threat, then the SS direct sequence must possess a large period and large linear span; shortening the DS period in this situation for the sake of somewhat improved multiple access capability would allow the possibility of catastrophic consequences. 5.7.2 Welch's Inner Product Bound The correlation computation of (5.232) can be viewed as an inner product between the N-tuples (ait ) and (a(k), , al) This connection will be exploited in applying the following theorem to determine a bound on Pmax THEOREM