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We derive exact closed-form expressions for Long Range (LoRa) bit error probability and diversity order for channels subject to Nakagami-m, Rayleigh and Rician fading. Analytical expressions are compared with numerical results, showing the accuracy of our proposed exact expressions. In the limiting case of the Nakagami and Rice parameters, our bit error probability expressions specialize into the non-fading case.

Transmit antenna selection with receive maximal-ratio combining (TAS/MRC) and transmit antenna selection with receive selection combining (TAS/SC) are two attractive multiple-input–multiple-output (MIMO) protocols. In this paper, we present a framework for the comparative analysis of TAS/MRC and TAS/SC in a two-hop amplify-and-forward relay network. In doing so, we derive exact and asymptotic expressions for the symbol error rate (SER) in Nakagami-m fading. Using the asymptotic expressions, the SNR gap between the two protocols is quantified. Given that the two protocols maintain the same diversity order, we show that the SNR gap is entirely dependent on the array gain. Motivated by this, we derive the SNR gap as a simple ratio of the respective array gains of the two protocols. This ratio explicitly takes into account the impact of the number of antennas and the fading severity parameter m. In addition, we address the fundamental question of “How to allocate the total transmit power between the source and the relay in such a way that the SER is minimized?” Our answer is given in the form of new compact expressions for the power allocation factor, which is a practical design tool that optimally distributes the total transmit power in the network. [ABSTRACT FROM PUBLISHER]

Block fading is a popular channel model that approximates the behavior of different wireless communication systems. Automatic-repeat request (ARQ) protocols are used to provide reliable communication in wireless networks. In this paper the throughput of the basic selective-repeat (SR) ARQ in block fading environments is derived. Single-antenna ARQ systems employing both coherent BPSK and QPSK and noncoherent orthogonal BFSK are analyzed over block fading channels characterized by Rician and Nakagami fading distributions. Moreover, the performance of multi-input multi-output (MIMO) ARQ systems employing space-time block codes (STBCs) is derived. The effect of antenna correlation in MIMO ARQ systems is investigated analytically. Results show that longer block lengths improve the performance of basic ARQ protocols. Furthermore, the throughput gain obtained by increasing the block length is a decreasing function of the block length. As the fading severity of the channel increases, the performance improvement resulting from increasing the block length increases. [ABSTRACT FROM AUTHOR]

We derive exact closed-form expressions for Long Range (LoRa) bit error probability and diversity order for channels subject to Nakagami-m, Rayleigh and Rician fading. Analytical expressions are compared with numerical results, showing the accuracy of our proposed exact expressions. In the limiting case of the Nakagami and Rice parameters, our bit error probability expressions specialize into the non-fading case. [ABSTRACT FROM AUTHOR]

We develop a unified framework for the symbol error rate (SER) of distributed transmit antenna selection with receiver maximal-ratio combining (TAS/MRC) in multiple-input multiple-output (MIMO) relay networks. We focus on nonregenerative relaying with NS, NR, and ND antennas at the source, relay, and destination, respectively. We consider the general fading scenario of Nakagami-m fading with distinct m fading parameters in the source-to-relay and the relay-to-destination links. We present new analytical expressions for the statistics of the end-to-end signal-to-noise ratio (SNR). Specifically, we derive exact expressions and first order expansions for the cumulative distribution function and moment generating function of the end-to-end SNR. Based on these, we derive new closed-form expressions for the asymptotic SER under M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM). Our asymptotic solutions accurately identify the diversity order and the array gain as two key design components of the network. [ABSTRACT FROM AUTHOR]