On The Tradeoff Between Two Types of Processing Gain October 30 , 2002

One of the features characterizing almost every multiple access (MA) communication system is the processing gain. For example, the processing gain of a direct sequence code division multiple access (CDMA) system represents the ratio between the actual bandwidth used by the system and the bandwidth required by an unspread system transmitting at equal rate. Through the use of spreading sequences, the processing gain of Random CDMA systems (RCDMA), or any other CDMA systems, is devoted to both bandwidth expansion and orthogonalization of the signals transmitted by different users. Another type of multiple access system is Impulse Radio (IR). IR systems promise to deliver high data rates over ultra wideband (UWB) channels with low complexity transmitters and receivers. In many aspects, IR systems are similar to time division multiple access (TDMA) systems, and the processing gain of IR systems represents the ratio between the actual transmission time and the total time between two consecutive transmissions (on-plus-off to on ratio). While CDMA systems, which constantly excite the channel, rely on spreading sequences to orthogonalize the signals transmitted by different users, IR systems transmit a series of short pulses and the orthogonalization between the signals transmitted by different users is achieved by the fact that most of the pulses do not collide with each other at the receiver. In this paper, a general class of MA communication systems that use both types of processing gain is presented, and both IR and RCDMA systems are demonstrated to be two special cases of this more general class of systems. The bit error rate (BER) of several receivers as a function of the ratio between the two types of processing gain is analyzed and compared under the constraint that the total processing gain of the system is large and fixed. This comparison is carried out for systems transmitting over either flat or frequency selective channels. It is shown that under certain conditions, a performance tradeoff in favor of the second type of processing gain exists. As a result, the sub-optimality of RCDMA systems in frequency selective channels is established. October 30, 2002 DRAFT