Exact BER analysis for QAM transmission on arbitrary fading channels with maximal-ratio combining and imperfect channel estimation

In this contribution, we investigate the effect of imperfect channel estimation on the bit error rate (BER) performance of uncoded quadrature amplitude modulation (QAM) with maximal-ratio combining (MRC) multichannel reception. The propagation channels from the transmitter to each of the Nr receive antennas are assumed to be affected by (possibly correlated) flat block fading with an arbitrary fading distribution. The MRC receiver makes use of estimated channel coefficients, obtained from known pilot symbols sent among the data. The resulting average BER for QAM can easily be written as an expectation over 4Nr random variables, but the computing time needed for its numerical evaluation increases exponentially with Nr. We point out that the BER can be expressed in terms of the distribution of the norm of the channel vector, rather than the joint distribution of all channel coefficients. This allows to reduce the BER expression to an expectation over only 4 random variables, irrespective of the number of receive antennas. Moreover, we show that for real-valued constellations and/or real-valued channels, the BER expression reduces to an expectation over less than 4 variables. For practical BER levels, the numerical evaluation of the BER is much less time-consuming than a straightforward computer simulation. The presented BER expression is useful not only when the fading distribution is given in closed form, but also when only experimental data (e.g. a histogram) on the fading are available.