In this work, we consider a 1-bit quantized massive MIMO channel with superimposed pilot (SP) scheme, dubbed QSP. With linear minimum mean square error (LMMSE) channel estimator and maximum ratio combining (MRC) receiver at the BS, we derive an approximate lower bound on the achievable rate. When optimizing pilot and data powers, the optimal power allocation maximizing the data rate is obtained in a closedform solution. Although there is a performance gap between the quantized and unquantized systems, it is shown that this gap diminishes as the number of BS antennas is asymptotically large. Moreover, we show that pilot removal from the received signal by using the channel estimate doesn't result in a significant increase in information, especially in the cases of low signal-to-noise ratio (SNR) and a large number of users. We present some numerical results to corroborate our analytical findings and insights are provided for further exploration of the quantized systems with SP.
A subspace method for channel estimation has been recently proposed [1] for tackling the pilot contamination effect, which is regarded by some researchers as a bottleneck in massive MIMO systems. It was shown in [1] that if the power ratio between the desired signal and interference is kept above a certain value, the received signal spectrum splits into signal and interference eigenvalues, namely, the "pilot contamination" effect can be completely eliminated. However, [1] assumes an independently distributed (i.d.) channel, which is actually not much the case in practice. Considering this, a more sensible finite-dimensional physical channel model (i.e., a finite scattering environment, where signals impinge on the base station (BS) from a finite number of angles of arrival (AoA)) is employed in this paper. Via asymptotic spectral analysis, it is demonstrated that, compared with the i.d. channel, the physical channel imposes a penalty in the form of an increased power ratio between the useful signal and the interference. Furthermore, we demonstrate an interesting "antenna saturation" effect, i.e., when the number of the BS antennas approaches infinity, the performance under the physical channel with P AoAs is limited by and nearly the same as the performance under the i.d. channel with P receive antennas.Index Terms-massive MIMO, physical channel, subspace method, random matrix theory, asymptotic eigenvalue distribution 1536-1276 (c)
In this study, we consider the physical layer security in the downlink of a Massive MIMO system employing one-bit quantization at the base station (BS). We assume an active eavesdropper that attempts to spoiling the channel estimation acquisition at the BS for a legitimate user, whereas overhearing on downlink transmission. We consider the two most widespread methods for degrading the eavesdropper's channel, the nullspace artificial noise (NS-AN) and random artificial noise (R-AN). Then, we present a lower bound on the secrecy rate and asymptotic performance, considering zero-forcing beamforming (ZF-BF) and maximum-ratio transmission beamforming (MRT-BF). Our results reveal that even when the eavesdropper is close enough to the intercepted user, a positive secrecy rate-which tends to saturation with increasing the number of BS antennas N-is possible, as long as the transmit power of eavesdropper is less than that of the legitimate user during channel training. We show that ZF-BF with NS-AN provides the best performance. It is found that MRT-BF and ZF-BF are equivalent in the asymptotic limit of N and hence the artificial noise technique is the performance indicator. Moreover, we study the impact of power-scaling law on the secrecy rate. When the transmit power of BS is reduced proportional to 1/N , the performance is independent of artificial noise asymptotically and hence the beamforming technique is the performance indicator. In addition, when the BS's power is reduced proportional to 1/ √ N , all combinations of beamforming and artificial noise schemes are equally likely asymptotically, independent of quantization noise. We present various numerical results to corroborate our analysis.
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