The amount of different environments where wireless communications is required has grown significantly, channel estimation has been known to be the path to take, but the necessity of Multiple-Input Multiple-Output (MIMO) systems has created a complex process of demodulation for the coherent paradigm. Non-coherent receivers achieve data detection without the overhead and computational complexity required by pilot based reception mechanisms. Additionally, difference modulation has some interesting properties of invariance that may be used against Doppler shifts and Carrier Frequency Offset. That is why, having an analytical approximation of the probability of error in terms of Bit Error Rate (BER) will be very useful. In this work, Chernoff Boundaries are proposed for an autocovariance receiver, which are easily scalable to any order of difference modulation. Also, the upper bound proposed could be calculated even when there is diversity at the receiver, that could be in time, frequency or space.
