Channel Quantization Based on the Statistical Characterization of Spatially Correlated Fading

Multiuser multiple-input-multiple-output (MU-MIMO) techniques, such as scheduling and precoding, have shown to improve the spectral efficiency of wireless communication systems. However, these techniques require an accurate knowledge of the channel of the different users at the transmitter. In frequency-division duplex (FDD) systems, this information has to be provided by the different users, motivating the research of efficient limited feedback schemes. This paper presents a novel statistical characterization of the spatial multiple-input-single-output (MISO) channel. In this characterization, one antenna is selected as the reference, and the channel fading experienced from this antenna is also considered to be the reference. The conditional probability density functions (CPDFs) of the envelope and phase of the channel fading coefficients from the rest of the antennas (denoted as nonreference channel fading and nonreference antennas) are obtained given the reference one. Based on this statistical characterization, this paper proposes a channel quantization scheme that individually quantizes the channel fading coefficient of each transmit antenna that is seen by each user. The envelope and phase of the reference channel fading are quantized considering a Rayleigh distribution and a uniform distribution, respectively. The nonreference channel fading coefficients are quantized according to their respective CPDFs, which in turn depend on the spatial correlation between each channel fading and the reference channel fading. Numerical simulations have been carried out to compare the performance of the proposed conditional quantization (CQ) scheme with a polar quantization (PQ) and with a quantization based on the Karhunen-Loève (KL) transform. PQ does not consider spatial correlation, CQ needs one spatial correlation coefficient per nonreference antenna, and the KL scheme makes use of the full spatial correlation matrix. The results show that CQ achieves a lower quantization mean square error (MSE) than the other two schemes in highly and moderately correlated environments. When the spatial channel model (SCM) is considered, the proposed scheme allows the spatial correlation to be successfully exploited in arrays with
N
= 4 and
N
= 8 transmit antennas for antenna separations that are lower than
d
= 1.3λ and d=0.75λ, respectively.