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We investigate the uplink (UL) performance of multicell massive MIMO (maMIMO) communication systems in frequency-selective fading channels, when the channel estimates are corrupted by pilot contamination, and the receiver employs maximum-ratio combining (MRC). Specifically, two fundamental schemes (receivers/waveforms) are considered: the time-reversal MRC (TRMRC) under single-carrier, and the conventional frequency-domain MRC (FDMRC) for orthogonal frequency-division multiplexing. We first derive approximate analytical expressions for the UL signal-to-interference-plus-noise ratio (SINR) performance of maMIMO systems, deploying both TRMRC and FDMRC. Then, lower bounds for the achievable rates of both systems are presented, and the derived expressions are validated by means of Monte-Carlo simulations. The performance of the investigated systems are compared regarding the variation of several parameters, such as the number of base station (BS) antennas M, number of users for each cell K, UL transmit power &#x03C1;<sub>u</sub>, and the number of taps of the time-dispersive channel L. Our results demonstrate that the attained SINR performance of both schemes are very similar, but, in terms of achievable rates, TRMRC in general outperforms FDMRC by not requiring cyclic prefix transmission. On the other hand, our computational complexity analysis demonstrates that the TRMRC scheme demands somewhat higher processing resources (O(LMK)) than FDMRC (O(MK)). Thus, we propose a reduced complexity implementation for the TRMRC receiver, by employing the fast convolution with overlap-and-add technique, which is able to achieve the same result of TRMRC with a complexity of O(log<sub>2</sub>(2L)MK). For a practical maMIMO setup, the complexity reduction is about 50%. Finally, based on the derived expressions, we propose an iterative way to obtain the number of users that is able to maximize the sum rate of the cell, and investigate its behavior with the variation of different parameters, such as number of antennas, data, and pilot transmit power, as well as different frequency and pilot reuse schemes.

Uplink Performance of Single-Carrier Receiver in Massive MIMO With Pilot Contamination