Multiplexing With Multi-Level ASK and Noncoherent MIMO in Rayleigh Fading

For an
N_t
-input
N_r
-output system, noncoherent reception of spatially multiplexed one-sided
L
-level amplitude-shift keying symbols transmitted over a flat Rayleigh fading channel, with energy detection, is considered. The symbol vector is passed through an
N_t
×
N_t
deterministic precoder matrix. Two precoders are presented:
diagonal
, having positive diagonal elements in geometric progression (GP);
rank-one
, having positive row elements in GP. Each symbol vector is transformed into a precoded scalar. For a one-to-one correspondence between integers 0, 1,...,
L
^N_t
- 1 and precoded scalars, a sufficient condition relating the precoder GP ratio ρ to the amplitude levels is derived for each precoder. To ease the difficulty of computing the exact symbol vector error probability (SVEP) for large
N_r
, a Gaussian approximation of the received signal energy is made and a closed form expression for a large
N_r
SVEP approximation is derived. With first level zero, the cases of: levels in arithmetic progression, non-zero levels in GP with amplitude ratio ϵ, are considered. Parameters ρ and ϵ are chosen to minimize the SVEP saturation value (approached at high signal-to-noise ratio). Furthermore, symbol-vector-dependent scale factors are introduced for error performance enhancement. Visible light communication and sensor network are two practical application scenarios for this work.