We quantify the performance of wireless transmissions over random fading channels at high signal-to-noise ratio (SNR). The performance criteria we consider are average probability of error and outage probability. We show that as functions of the average SNR, they can both be characterized by two parameters: the diversity and coding gains. They both exhibit identical diversity orders, but their coding gains in decibels differ by a constant. The diversity and coding gains are found to depend on the behavior of the random SNR's probability density function only at the origin, or equivalently, on the decaying order of the corresponding moment generating function (i.e., how fast the moment generating function goes to zero as its argument goes to infinity). Diversity and coding gains for diversity combining systems are expressed in terms of the diversity branches' individual diversity and coding gains, where the branches can come from any diversity technique such as space, time, frequency, or, multipath. The proposed analysis offers a simple and unifying approach to evaluating the performance of uncoded and (possibly space-time) coded transmissions over fading channels, and the method applies to almost all digital modulation schemes, including M-ary phase-shift keying, quadrature amplitude modulation, and frequency-shift keying with coherent or noncoherent detection.
Bibliographical noteFunding Information:
Paper approved by G. M. Vitetta, the Editor for Equalization and Fading Channels of the IEEE Communications Society. Manuscript received May 30, 2002; revised November 4, 2002. This work was supported in part by the NSF Wireless Initiative under Grant 99-79443, in part by the NSF under Grant 01-0516, and in part by by the ARL/CTA under Grant DAAD 19-01-2-011. This paper was presented in part at IEEE Globecom, Taiwan, November 2002.
- Coding gain
- Diversity combining
- Fading channels
- Outage probability