Physical Communication 25 (2017) 26–33 Contents lists available at ScienceDirect Physical Communication journal homepage: www.elsevier.com/locate/phycom Full length article Performance analysis of non-coherent MIMO MRC scheme with training using finite-SNR diversity and multiplexing tradeoff Nandita Lavanis * , 1 , Devendra Jalihal Department of Electrical Engineering, IIT Madras, Chennai, India article info Article history: Received 30 December 2016 Received in revised form 13 August 2017 Accepted 15 August 2017 Available online 23 August 2017 Keywords: MIMO MRC Diversity-multiplexing tradeoff Finite-SNR Channel estimation Imperfect CSIR abstract The inherent tradeoff between the twin benefits offered by multiple antenna systems, namely, the diversity gain and the multiplexing gain is captured as the diversity multiplexing tradeoff (DMT). The DMT at asymptotically high signal-to-noise ratio (SNR) is optimistic, whereas at finite SNR, it is practical. In this paper, point-to-point multiple input multiple output (MIMO) systems are considered under the assumption of coherent and non-coherent communication implying, respectively, whether perfect channel state information is available at the receiver (CSIR) or not. The literature mainly addresses non- coherent communication with training at asymptotically high SNR, whereas the finite-SNR analysis is more relevant in practice. We address the performance analysis of a MIMO maximal ratio combining scheme by deriving closed-form expressions of the DMT at finite SNR under non-coherent communication with training. At a fixed multiplexing gain and finite SNR, a reduction in the diversity gain is observed when coherent communication is replaced by non-coherent communication with training. We also show that for a high multiplexing gain, the reduction in diversity gain is much more pronounced as compared to that at a low multiplexing gain. A training-based channel estimation scheme discussed in the literature is used in two modes of power allocation, namely, the capacity optimal power allocation and equal power allocation (EPA). In both modes, at a fixed average SNR and with equal duration of training, we observe that the power allocation mode does not make a significant impact on the finite-SNR DMT of the MIMO scheme. We also observe that in the EPA mode, the diversity gain reduces with increase in training duration. © 2017 Elsevier B.V. All rights reserved. 1. Introduction With potential for high data rates and high reliability, multiple antennas are increasingly gaining adoption in modern wireless systems. Recent wireless communication standards, namely, the LTE (Long term evolution) and LTE-A (LTE-Advanced) along with IEEE 802.11n, IEEE 802.11ac, IEEE 802.16e have proposed and implemented the use of multiple input multiple output (MIMO) scheme to provide higher data rates and reliability [1,2]. Massive MIMO systems consisting of a large number of antenna elements are under consideration as a part of the 5G initiative [3]. These MIMO systems might work either in a fixed wireless or a mobile wireless environment. In a fixed wireless environment, it is as- sumed that the channel coefficients are known accurately, leading to coherent communication. However, in a mobile wireless envi- ronment the channel coefficients change extremely fast and there may not be enough time to estimate these coefficients accurately, * Corresponding author. E-mail addresses: nandital@ssn.edu.in (N. Lavanis), dj@ee.iitm.ac.in (D. Jalihal). 1 The author is currently a faculty at SSN College of Engineering, Chennai, India. leading to non-coherent communication [4]. In a mobile wireless environment, the data throughput will reduce if more time is spent on channel estimation. This leads to a tradeoff between the time spent on channel estimation and that spent on data communi- cation. Considering these factors, it is imperative to analyze the performance of non-coherent MIMO communication with training. Some of the information-theoretic measures for the multiple antenna fading wireless channels are ergodic capacity, the distri- bution of capacity (capacity-versus-outage), and the diversity mul- tiplexing tradeoff (DMT) as proposed by Zheng et al. in [5]. Multiple antenna wireless channels offer twin gains, namely, the diversity gain and the multiplexing gain. The DMT framework proposed in [5] for asymptotically high signal-to-noise ratio (SNR), and gen- eralized in [6] for finite SNR, provides a clear view on how the two gains are traded off for each other. A size-asymptotic DMT which is complementary to the SNR-asymptotic DMT is proposed in [7]. In [8], exact closed-form expressions of the finite SNR-DMT for two antennas, either at the transmitter or receiver, are provided. In [5] and [6], the DMT has been analyzed with perfect channel state information at the receiver (CSIR) and without channel state information at the transmitter (CSIT). In [9,10], and [11] the DMT http://dx.doi.org/10.1016/j.phycom.2017.08.012 1874-4907/© 2017 Elsevier B.V. All rights reserved.