enna face for each user terminal. Clearly, this is an overwhelmingly complex mathematical computation, so instead we do some approximation approaching this ideal solution. The best smart antennas present radiation patterns of a few tens of degrees. There are large and complex adaptive phased arrays that have a 40-degree arc of high signal path gain, but time division synchronized CDMA (TD-SCDMA) antennas are claiming path gain improvements of 8 dB, consistent with 60-degree arcs. If we divide the cell into 12 virtual sectors of 30 degrees each, then we have a collection of user communi- ties with reasonably common radio characteristics. The set of equations has 4 times as many variables as the three-sector system, with 16 times as many terms in the matrix M, but it is still manageable to solve these equations for a large system on a personal computer. 28.2.4 Dynamic channel allocation TD-SCDMA offers dynamic channel allocation to optimize CDMA performance. The system selects a carrier and time slot so that the TDMA/CDMA channel has minimum interference with other channels. Other CDMA systems also may select the carrier with the best radio conditions as each call is established. This certainly improves sys- tem performance when the wireless telephone system is less than full, but does it in- crease the maximum capacity of a system? The answer is yes in the multicellular arena, but not for a single-cell sector. If all the carriers, time slots, and pseudonoise (PN) codes of a cell are as busy, as they can be, then no dynamic channel assignment is going to squeeze out one more channel. In other words, the value of a is not affected by a better choice of carriers, time slots, or PN codes. It is the reduction of intercell interference that makes carrier choice important for each call. The ability of a system to keep new calls away from interference generated by existing calls should reduce (and therefore improve) the Mbc components of inter- ference from one cell sector to another. As the system gets busy, this effect 