On the fading number of multiple-input single-output fading channels with memory

We derive new upper and lower bounds on the fading number of non-coherent multiple-input single-output (MISO) fading channels of general (not necessarily Gaussian) regular law with spatial and temporal memory. The fading number is the second term, after the double-logarithmic term, of the high signal-to-noise ratio (SNR) expansion of channel capacity. In case of an isotropically distributed fading vector it is proven that the upper and lower bound coincide, Le., the general MISO fading number with memory is known precisely. The upper and lower bounds show that a type of beam-forming is asymptotically optimal.