The purpose of this paper is to calculate the bit error rate (BER) of a multiband non coherent on-off keying (OOK) demodulation. The results fit perfectly the simulations of the system. It allows us to study the influence of the filter and the decimation factor on the modulation performance. It is also possible to optimize the system, by means of other criteria (e.g. system complexity, jammer sensitivity) thus avoiding time consuming simulations.