# Efficient Modulation Scheme for Intermediate Relay-Aided IoT Networks
## 1 Introduction
### Related Works  
There are several known studies on modulation diversity for HARQ [17], relay networks [18; 19] and relay-HARQ systems [20]. Despite the promising performance gains, these methods are developed for relay network settings that tend to consume substantial bandwidth for which (re)transmissions on the source to destination link and the relay to destination links occupy orthogonal channels (frequency bands or time slots). In a similar manner, the authors of [21] proposed a HARQ-based minimum mean-square-error equalizer to improve the efficiency of an offset quadrature amplitude modulation-based filter bank sub-carrier. In terms of block error rate, their proposed approach appears to provide significant gains. [PERSON] et al. in [22] provided an energy-efficient resource allocation scheme for Type-1 HARQ network. With the help of fractional programming and convex optimization framework, they derived the closed-form solution for the resource allocation problem. They also concluded that significant performance gains could be achieved for line-of-sight (LOS) communication between transmitter and receiver. Some other works [23; 24; 25] also take into account the physical layer security aspects of HARQ networks. A novel codeword solution invoking the HARQ mechanism was provided by the authors of [26]. Specifically, they retransmitted the unreliable bits of the message using carefully constructed codewords. Some of the studies have also attempted to improve the throughput of the network. For instance, [PERSON] et al. in [27] utilized the intermediate values of the polar codes to improve upon the effective throughput. An intermediate polar code value was transmitted as redundant bits. The authors of [28] proposed a novel approach to encode the new data bits with the previous transmission. A range of different puncture techniques was also investigated in the literature of HARQ systems. In this regard, the authors of [29] proposed a stopping-tree puncturing method, whereas the authors of [30] provided a quasi-uniform puncturing technique. More recently, the authors of [31; 32] exploited the flexible design of the HARQ scheme by proposing the replication of error-prone bits of the data. However, they focused on the traditional long or moderate packet transmission, which may not be more feasible for IoT applications. In this backdrop, the authors of [33; 34] provided a novel short packet HARQ design, which, despite degrading the performance, is a more practical approach to handle delay-sensitive applications. [PERSON] et al. in [35] proposed an index modulation-based multi-hop relaying system. They also derived the outage probability and block error rate expressions. Their proposed sub-carrier activation method improves the performance of orthogonal frequency division multiplex systems. Similar works have been reported by the authors of [36; 37; 38; 39] wherein the authors provide the interleaving method, deep learning modulation techniques and the random linear network coding methods. The authors of [40] study modulation diversity design for the relay-HARQ configuration in which the source to destination and relay to destination links are co-channel and additive. Such a configuration specifically forms a 2-by-1 multiple-input single-output (MISO) diversity transmission. For this system configuration, we formulate the bit error rate (BER) minimization modulation diversity design in a quadratic assignment problem. As this is NP-hard, our modulation diversity design cannot be solved exactly, even for a moderately sized constellation, such as 16-QAM. Fortunately, there exist a number of heuristic algorithms [41] for its reduced form, known as the quadratic assignment problem, that result in high-quality solutions over the quadratic assignment problem library dataset. The authors of [42] argued that the simultaneous wireless information and power transfer system designed using Gaussian distributed input signals may result in degradation of performance.