Mathematical Description
In a narrowband flat-fading channel with transmit antennas and receive antennas (MIMO), the propagation channel is modeled as
where and are the receive and transmit vectors, respectively. The noise vector is denoted . The th element of the channel matrix describes the channel from the th transmit antenna to the th receive antenna.
When modeling spatial correlation it is useful to employ the Kronecker model, where the correlation between transmit antennas and receive antennas are assumed independent and separable. This model is reasonable when the main scattering appears close to the antenna arrays and has been validated by both outdoor and indoor measurements.
With Rayleigh fading, the Kronecker model means that the channel matrix can be factorized as
where the elements of are independent and identically distributed as circular symmetric complex Gaussian with zero-mean and unit variance. The important part of the model is that is pre-multiplied by the receive-side spatial correlation matrix and post-multiplied by transmit-side spatial correlation matrix .
Equivalently, the channel matrix can be expressed as
where denotes the Kronecker product.
Read more about this topic: Spatial Correlation
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