BER estimation with random phase summation applied to ray tracing

When a bit error rate (BER) of the order of 10^-5 is estimated from measurements or a hardware/software simulator, more than 10⁵ random data are required. Moreover, dozens of the 10⁵ random data are needed to compensate the ambiguity in the estimated phases. These operations require a huge time to obtain the BER characteristics. The closed-form analytical equations, based on the characteristic function method, reduces the time for accumulating this huge data. The numerical examples showed that the proposed method could reduce the estimation time by less than 1/1000 times compared to that of the equivalent baseband method