Some signal design/analysis problems relevant to wireless communication are under investigation. Problems in the first class relate to a code-division multiple-access (CDMA) communication scheme in which the receiver makes optimum multi-user decisions. The effect the selection of a particular sequence family has on the performance of the system is under study. One measure of performance is the capacity, i.e., the number of active users that the system can support. Signature sequences influence this number through their periodic and aperiodic correlation properties. These correlation values tend to diminish performance by reducing the minimum Euclidean distance between distinct multi-user signal sets. Preliminary investigations turned up an interesting example involving Gold sequences of small length in which correlations reduced the Euclidean distance between a multi-user signal and its nearest neighbour to zero. The obvious upper bound on capacity obtained by replacing each aperiodic correlation by the maximum over the entire sequence family provides much too conservative an estimate. Thus improved upper bounds are currently being sought. This requires a better understanding of the distribution of aperiodic correlation values obtained by picking a randomly-delayed random subset of the entire family of signature sequences. This distribution is under study both for a family of signature sequences in general as well as for specific families known to be efficient with respect to periodic correlation measures. The understanding gained, will be used in the design of improved signal sets. For example, preliminary investigations suggest that when communicating data using phase-shift keying, improved performance will result if each user's phase transitions never exceed 90 degrees since this has the effect of distributing the aperiodic correlations across the real and imaginary axes as opposed to simply the real axis. The second class of problems under investigation deals with the IS-54/IS-136 North American digital cellular standard. Here the goal is to come up with an efficient forward error-correction (FEC) scheme well matched to the IS-54/136 channel. The motivtion came from previous work in which a nonlinear binary FEC code identified by the author (the Nordstrom Robinson code) turned out under soft-decision decoding, to improve uniformly upon the performance of the convolutional code used in the current IS-54 standard. This was to the surprise of many in both industry and academia as the binary code is of short block length (16) and has a small minimum distance (6), whereas the IS-54 employs a rate 1/2 convolutional code of contraint length (6). The reason for this improved performance is under investigation and attempts are under way to identify the code best matched to this channel. Some other problems of a miscellaneous nature, all relevant to improved wireless communcation are also being studied.
