Yi,e == sign(ri,e) E {-I, I}, for c E {R,I}, I~i~N. (2) Throughout our paper, a.; denotes the i-th element of the vector a and [a]i,e == ai,e with c E {R, I} is the real or imaginary part of ai. The operators (.)H and tr(·) stand for Hermitian transpose and trace of a matrix, respectively. (1) We consider a point-to-point quantized MIMO channel with M transmit dimensions (e.g. antennas) and N receive dimensions at the receiver. Fig. 1 shows the general form of a quantized MIMO system, where H E e N x M is a random channel matrix. The entries of this channel matrix are jointly complex circular Gaussian with zero-mean and possible mutual correlations. The channel realizations are unknown to both the transmitter and receiver. The vector x E eM comprises the M transmitted symbols, assumed to be subjected to a some average power constraint and peak power constraint. The vector 11 represents the additive noise, whose entries are i.i.d. and distributed as eN(0, I). TEeN is the unquantized channel output where p represents the signal-to-noise ratio. In our system, the real parts r i,R and the imaginary parts r i,I of the receive signals ri, I~i~N, are each quantized by a l-bit resolution quantizer. Thus, the resulting quantized signals read as [12] , [13] , [14] . In particular, automatic gain control (AGC), linearity requirements of RF components and multipliers for signal correlation are no more necessary. Our paper is organized as follows. Section II describes the system model and notational issues. In Section III we give the general expression of the mutual information between the inputs and the quantized outputs of the MIMO system, then we expand it into a Taylor series up to the second order of the SNR in Section IV. Finally, in Section V, we utilize these results to elaborate on the asymptotic capacity of I-bit multiple receive antennas (SIMO) channels with delay spread and receive correlation in a Rayleigh flat-fading environment. Abstract-We consider general multi-antenna fading channels with coarsely quantized outputs, where the channel is unknown to the transmitter and receiver. This analysis is of interest in the context of sensor network communication where low power and low cost are key requirements (e.g, standard IEEE 802.15.4 applications). This is also motivated by highly energy constrained communications devices where sampling the signal may be more energy consuming than processing or transmitting it. Therefore the analog-to-digital converters (ADCs) for such applications should be low-resolution, in order to reduce their cost and power consumption. In this paper, we consider the extreme case of only J-bit ADC for each receive signal component. We derive asymptotics of the mutual information up to the second order in the signal-to-noise ratio (SNR) under average and peak power constraints and study the impact of quantization. We show that up to second order in SNR, the mutual information of a system with two-level (sign) output signals incorporates only a power penalty factor of almost~(1.96 dB) com pared to the system with infinite resolution for all channels of practical interest. This generalizes a recent result for the coherent case [1].
Achievable rates in REF are provided only for the SIMO channel and only in the asymptotic case of low SNRs.
Analysis of 1-bit output noncoherent fading channels in the low SNR regime
2009 IEEE International Symposium on Information Theory
2009 IEEE International Symposium on Information Theory
Mathematics Computer Science