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On the effect of antenna coupling on spectrum sensing using a cross-correlation spectrum analyser with two antennas

Spectrum sensing for cognitive radio is a technique to find unused pieces of spectrum which can then be used to transmit and receive data. 
This requires sensitive, low noise, measuring. For that purpose it has been proposed to use a cross-correlation spectrum analyser. Such a system can use one antenna and a splitter to two receiver paths. Alternatively, a second antenna can be used instead of a splitter. 
In this report the signal reception and system noise reduction of both designs are compared analytically, in case the antennas are dipole antennas, positioned in parallel, collinear or in echelon. The antenna coupling 
is described using an impedance matrix of which the entries are expressed according to the induced electromagnetic force method. For this purpose it is assumed that the environment is reflection-free and time-invariant. 
The contribution of signals and (thermal) noise from the passive front-end, consisting of an H-type resistive attenuator, to the best achievable signal to noise ratio at the output of the receivers is derived. Some approaches for optimization of the two-antenna design are discussed, supported by plots.