Achievable Diversity Order Research Articles

Network-Coded Cooperative Systems With Generalized User-Relay Selection

We consider a network-coded cooperative (NCC) system that consists of N ≥ 2 sources, M ≥ 1 decode- and-forward (DF) relays, and a single destination. The relays perform network coding (NC) on the received sources' symbols using maximum distance separable (MDS) codes. For this system, we propose the most generalized user-relay selection (GURS) scheme in the literature that selects any arbitrary subsets of K users and any arbitrary subsets of L relays subject to practical constraints such as load balancing conditions and scheduling policy. Our analytical results and design guidelines generalize and subsume all existing results as special cases. To this end, we derive a new closed-form outage probability (OP) expression, assuming non-identically and independently distributed (n.i.i.d.) Rayleigh fading channels. The asymptotic outage expression at high signal-to-noise ratio (SNR) regime is further derived, based on which, the achievable diversity order and coding gain are quantified. The theoretical derivations are also validated through Monte-Carlo simulation.

Outage Performance for Mixed FSO-RF Transmission in Satellite-Aerial- Terrestrial Networks

This paper analyzes the outage performance of a satellite-aerial-terrestrial network (SATN), where the satellite-aerial and aerial-terrestrial links utilize free space optical (FSO) with Gamma-Gamma fading and radio frequency (RF) transmission with Rayleigh fading, respectively. In particular, by considering the impacts of pointing error in FSO links, and exploiting transmit beamforming (BF) with imperfect channel state information (CSI) in RF links, we derive an analytical expression for the outage probability (OP) of the considered SATN with a variable-gain amplify-and-forward (AF) protocol. Then, the asymptotical OP expression in high signal-to-noise ratio regime is presented to evaluate the achievable diversity order of the system. Finally, numerical results are given to confirm the validity of the theoretical formulas and reveal the effects of various parameters on the system performance.

Non-Orthogonal Multiple Access in the Presence of Additive Generalized Gaussian Noise

In this letter, we investigate the performance of non-orthogonal multiple access (NOMA), under the assumption of generalized Gaussian noise (GGN), over Rayleigh fading channels. Specifically, we consider a NOMA system with $L$ users, each of which is equipped with a single antenna, and derive an exact expression for the pairwise error probability (PEP). The derived PEP expression is subsequently utilized to derive a union bound on the bit error rate (BER) and to quantify the diversity orders realized by NOMA users in the presence of additive white (AW) GGN. Capitalizing on the derived PEP expression and the union bound, the error rate performance of NOMA users is further evaluated for different special cases of AWGGN. The derived analytical results, corroborated by simulation results, show that the shaping parameter of the GGN $(\alpha)$ has negligible effect on the diversity gains of NOMA users, particularly for large $\alpha $ values. Accordingly, as in the case of additive white Gaussian noise (AWGN), the maximum achievable diversity order is determined by the user’s order.

On the Distribution of the Sum of Málaga-$\mathcal {M}$ Random Variables and Applications

In this paper, a very accurate approximation method for the statistics of the sum of Malaga- $\mathcal {M}$ random variates with pointing error (MRVs) is proposed. In particular, the probability density function of MRV is approximated by a Fox's $H$ -function through the moment-based approach. Then, the respective moment-generating function of the sum of $N$ MRVs is provided, based on which the average symbol error rate is evaluated for an $N$ -branch maximal-ratio combining (MRC) receiver. The retrieved results show that the proposed approximate results match accurately with the exact simulated ones. Additionally, the results show that the achievable diversity order increases as a function of the number of MRC diversity branches.

Unified Performance Analysis of Multi-Hop FSO Systems Over Double Generalized Gamma Turbulence Channels With Pointing Errors

Free space optical (FSO) communication systems provide high bandwidth in unregulated spectrum and act as a powerful line-of-sight wireless connectivity solution. The performance of FSO systems can be seriously impaired by fading as a result of atmospheric turbulence and/or pointing errors due to misalignment. In the context of FSO systems, relaying was proposed as an effective fading mitigation technique due to the fact that the variance is distance-dependent in turbulence channels. In this article, we present a unified performance analysis of multi-hop FSO systems over Double Generalized Gamma (DGG) turbulence channels with pointing error impairments. We assume amplify-and-forward relaying and consider both heterodyne detection and intensity modulation with direct detection. We derive tight closed-form expressions for the outage probability and bit error probability of both fixed-gain and channel state information (CSI)-assisted relaying in terms of the bivariate Fox-H functions and Fox-H functions, respectively. We further analyze asymptotic behavior of the outage probability in terms of simple elementary functions and obtain the achievable diversity orders. Diversity gain is found to be a function of atmospheric turbulence parameters, pointing error, detection type and the number of hops. Monte Carlo simulation results are further provided to verify the accuracy of the derived expressions.

Coded OFDM-IM with iterative detection☆

Coded Orthogonal frequency division multiplexing with index modulation (OFDM-IM) has been proposed, where channel coding and soft decision are employed to exploit the multipath diversity for the information conveyed by the constellation symbols. However, the performance of coded OFDM-IM is dependent on the detection performance of subcarrier activation pattern (SAP) and the diversity order of the SAPs requires further investigation. In this paper, a lower-bound of LLR detector is derived to show that the maximum achievable diversity order is the minimum Hamming distance between the SAPs for the LLR detector. Based on the analyses, iterative detection is proposed to improve the performance of coded OFDM-IM, where information-assisted LLR detector is proposed to improve the detection performance of SAP by using the soft information of the constellation symbols. Simulation results are provided to corroborate the diversity analyses and show the advantage of the coded OFDM-IM with iterative detection.

Joint source‐pair and relay selection for relay‐assisted network

This study investigates the opportunistic joint source-pair and relay selection policy for cooperative networks. The investigation considers multi-user pair and multiple bi-directional amplify-and-forward based relays in the system model. The strategy selects an appropriate user-pair and relay among N candidate user-pairs and R available relays based on the maximum achievable sum-rate of each user pair and related relay terminal. Analytical, asymptotic, and Monte Carlo based computer simulation results reveal that the joint-selection strategy achieves multi-user and cooperative diversity order in high signal-to-noise ratios. The results also show that the opportunistic joint source-pair and relay selection strategy outperforms the max–min based selection policy. Moreover, the system contains a single relay, the joint-selection strategy achieves only a multi-user diversity and performs worse than the system that contains multiple relays. The results also show that the total achievable diversity order equals to the total number of possible paths between user-pairs and relays, which is , while in the multi-user and a single relay model, the diversity order only equals to N. Results also reveal that the proposed selection strategy provides an equal transmission opportunity for each of the user-pairs.

Monostatic MIMO Backscatter Communications

Backscatter communications have two major antenna configurations: the bistatic configuration, in which the reader employs two different sets of antennas to transmit and receive, and the monostatic configuration, in which the reader employs one set of antennas for both transmitting and receiving. In this paper, we provide a comprehensive study on the MIMO techniques for the M × L monostatic channel. Particularly we study on the joint design of the query and the coding matrices. We show that the maximum achievable diversity order of the monostatic channel is the diversity order achieved by the block-lever unitary query and orthogonal space-time block code (BUTQ-OSTBC) design pair, which is ML 2 , exactly the half of the diversity order of the conventional MIMO channel. Then we show that uniform query, the simplest query approach, cannot achieve the maximum achievable diversity order in the monostatic channel. We generalize BUTQ-OSTBC to the general augmenting approach, and show that unitary matrix is optimal in terms of SER performance among all possible query matrices, when OSTBC is employed. The above results further indicate that in the backscatter channel, additional diversity can be obtained by varying the query signals over time slots within the channel coherent time, which is quite different from the results from the conventional MIMO channels. We verify our results by Monte Carlo simulations.

On the Performance of NOMA-Assisted Overlay Multiuser Cognitive Satellite-Terrestrial Networks

In this letter, we investigate the performance of an overlay cognitive satellite-terrestrial network comprising a primary satellite source with its multiple terrestrial receivers and a secondary transmitter-receiver pair on the ground. Herein, the primary satellite source employs a non-orthogonal multiple access (NOMA) scheme to simultaneously serve its all users, while the secondary transmitter assists the primary communication through cooperative relaying technique in exchange for spectrum access. For this overall set-up, we obtain the closed-form expressions for the outage probability of primary satellite network and secondary terrestrial network by adopting pertinent heterogeneous fading models. Further, we derive the asymptotic outage behaviour at high signal-to-noise-ratio (SNR) for the primary and secondary networks, and thereby calculate the achievable diversity orders. Our analytical findings are corroborated through various numerical and simulation results.

Outage and ergodic sum‐rate performance of cooperative MIMO‐NOMA with imperfect CSI and SIC

SummaryIn this paper, we examine a half‐duplex cooperative multiple‐input multiple‐output non‐orthogonal multiple access system with imperfect channel state information (CSI) and successive interference cancelation. The base station (BS) and mobile users with multi‐antenna communicate by the assistance of a CSI based or fixed gain amplify‐and‐forward (AF) relay with a single antenna. The diversity schemes, transmit antenna selection, and maximal ratio combining are applied at the BS and mobile users, respectively. We study the system performance in terms of outage probability (OP) and ergodic sum‐rate. Accordingly, the exact OP expressions are first derived jointly for the CSI based and fixed gain AF relay cases in Nakagami‐m fading channels. Next, the corresponding lower and upper bound expressions of the OP are obtained. The high signal‐to‐noise ratio analyses are also carried out to demonstrate the error floor value resulted in the practical case and achievable diversity order and array gain in the ideal case. Moreover, the lower and upper bounds of the ergodic sum‐rate expressions are derived together for the CSI based and fixed gain AF relay cases. Finally, the Monte‐Carlo simulations are used to verify the correctness of the analytical results.

Diversity order of precoding‐aided spatial modulation using receive antenna selection

In this Letter, the authors analyse the diversity order of the precoding-aided spatial modulation (PSM) system with receive antenna subset (RAS) selection. It is shown that when there are N T transmit antennas, N R receive antennas, and N S selected receive antennas, the achievable diversity order is given by N T − N S + 1 N R − N S + 1 , where the product gain of N T − N S + 1 is achieved by the zero-forcing precoding scheme and another of N R − N S + 1 can be attained by the optimal RAS selection algorithm.

Code Design for Non-Coherent Index Modulation

This letter explores the concept of non-coherent index modulation (IM) in a general setting from the standpoint of coding theory. In doing so, we establish a bijective mapping from the set of activation patterns of an IM system to the set of codewords of a binary block code. We show that a non-coherent IM system whose active indices are independently affected by additive white Gaussian noise and Rayleigh fading can achieve a diversity order of $t+1$ if its activation patterns follow a $t$ -error correcting code designed for a Z-channel. Activation codes employed for IM systems are either constant or variable-weight codes. Using a variable-weight code requires a slightly higher detection complexity, but it can result in a diversity order significantly higher than the maximum achievable diversity order of a constant-weight code.

On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay With Application in Small-Cell Network

Satellite communication systems need to be integrated with emerging small-cell network to provide seamless connectivity and high-speed broadband access for mobile users in future wireless networks. In this paper, we study a hybrid satellite-terrestrial relay system (HSTRS) employing small cell transmission under interference constraint with macro-cell users. To characterize such HSTRS-assisted small-cell network, Shadowed-Rician fading for satellite links and Nakagami-$m$ fading for terrestrial links are adopted. We further deploy non-orthogonal multiple access (NOMA) to improve spectrum efficiency. To provide performance analysis, we derive exact formulas for outage probability and throughput of the considered HSTRS, and further examine its achievable diversity order. More importantly, we conduct the performance analysis by indicating performance gaps among two users, and such a gap depends on power allocation factors. We evaluate key performance metrics through the derived analytical expressions to provide useful framework of HSTRN and to characterize the impact of interference in different cells, and integer values of the per-hop fading severity parameters. The useful guidelines are introduced in the design of futuristic HSTRS for small-cell communications.

SWIPT-Enabled Cooperative NOMA With mth Best Relay Selection

Non-orthogonal multiple access (NOMA) was recently regarded as a potential technique for next generation wireless networks. Recent works on relay selection for cooperative NOMA systems have mainly addressed the best relay selection to forward its received signals to terminal nodes. Nonetheless, in practical scenarios, the best relay may be unavailable due to non-ideal conditions such as scheduling and overload constraints or possibly due to channel feedback delay. Therefore, there is compelling need to consider a more practical solution, in which the best available relay is selected. In this article, we examine the error rate performance for simultaneous wireless information and power transfer (SWIPT)-enabled NOMA, while considering the selection of the m th best available relay. In particular, we present an exact pairwise error probability (PEP) expression to obtain a bit error rate (BER) upper bound. The asymptotic PEP is investigated to evaluate the achievable diversity order for NOMA users. Finally, simulation results are provided to verify the accuracy of the derived PEP expressions and to give more insights into the system performance.

Transmit Antenna Selection for Precoding-Aided Spatial Modulation

This paper examines the impacts of transmit antenna subset (TAS) selection on the biterror-rate (BER) performance of linear precoding-aided spatial modulation (PSM) multiple-input multipleoutput (MIMO) systems. It is analytically shown that decreasing the number of active transmit antennas by TAS selection, which can be used to reduce the number of RF units at the transmitter side, always degrades the BER performance. The expression of a received signal-to-noise ratio (SNR) loss is also derived and its analytical results are shown to be well-matched with simulation results. Furthermore, it is analyzed that when there are NT transmit antennas, NS selected transmit antennas, and NR receive antennas, an achievable diversity order of the zero-forcing (ZF)-based PSM MIMO systems either with optimal TAS selection or without TAS selection can be given as N T -N R +1. To select an optimal TAS based on exhaustive search, an optimization criterion to maximize the received SNR of the selected TAS is employed. In addition, a low-complexity TAS selection scheme is presented using a decremental strategy. It is also observed that the decremental TAS selection algorithm can achieve almost the same BER and achievable rate performance as the optimal one while attaining much lower complexity. Finally, simulation results show that under the identical number of active transmit antennas, the ZF-PSM MIMO system with TAS selection outperforms the conventional ZF-PSM without TAS selection.

Achievable Diversity Order of HARQ-Aided Downlink NOMA Systems

The combination between non-orthogonal multiple access (NOMA) and hybrid automatic repeat request (HARQ) is capable of realizing ultra-reliability, high throughput and many concurrent connections particularly for emerging communication systems. This paper focuses on characterizing the asymptotic scaling law of the outage probability of HARQ-aided NOMA systems with respect to the transmit power, i.e., diversity order. The analysis of diversity order is carried out for three basic types of HARQ-aided downlink NOMA systems, including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR). The diversity orders of three HARQ-aided downlink NOMA systems are derived in closed-form, where an integration domain partition trick is developed to obtain the bounds of the outage probability specially for HARQ-CC and HARQ-IR-aided NOMA systems. The analytical results show that the diversity order is a decreasing step function of transmission rate, and full time diversity can only be achieved under a sufficiently low transmission rate. It is also revealed that HARQ-IR-aided NOMA systems have the largest diversity order, followed by HARQ-CC-aided and then Type I HARQ-aided NOMA systems. Additionally, the users’ diversity orders follow a descending order according to their respective average channel gains. Furthermore, we expand discussions on the cases of power-efficient transmissions and imperfect channel state information (CSI). Monte Carlo simulations finally confirm our analysis.

Leakage rate–based untrustworthy relay selection

AbstractThis paper investigates the leakage rate based untrustworthy relay selection strategies, which are based on the untrustworthy relay terminals operate in half‐duplex, full‐duplex, and hybrid modes. The investigation considers a dual‐hop one/two‐way half/full‐duplex wireless relaying network in the system model. The investigation also considers that a finite number of friendly jammers affect the untrustworthy relay terminals. According to analytical, asymptotic, and Monte Carlo simulation results, the LR‐based untrustworthy relay selection strategies achieve cooperative diversity order in high‐signal‐to‐noise ratio. However, friendly jammers and loop interference severely affect the system performance and degrade the achievable diversity order from M to 0 and also cause system coding gain losses. In addition, friendly jammers and loop interference also degrade the system achievable rate performance and cause saturation in high SNRs.

Performance Analysis of Cooperative NOMA Systems With Adaptive Mode Selection and Subchannel Allocation

In this paper, we study the mode selection and subchannel allocation for the downlink of a multi-user multi-subchannel cooperative non-orthogonal multiple access (C-NOMA) system. Specifically, each non-orthogonal multiple access (NOMA) pair can work in two different modes, i.e., non-cooperative NOMA (NC-NOMA) and C-NOMA, where the mode selection is based on the users’ channel conditions. We propose an adaptive mode selection, subchannel allocation and user pairing (AMS-SAUP) scheme and derive the achievable diversity order by analyzing the upper bound for the outage probability. Simulation results reveal that the AMS-SAUP scheme achieves the same diversity order as the exhaustive search scheme.

Performance analysis of multihop decode-and-forward relay networks with diversity in Nakagami fading channels

In this paper, we consider a multihop Decode-and-Forward (DF) relay network, in which each node receives the signals from its two preceding nodes. We assume Nakagami fading channels with integer fading parameters. In this network, the achievable diversity order is limited by the link between the source and the first relay. We derive the exact outage probability of fixed and selection relaying with spatial channel reuse, and demonstrate that applying selection relaying at the first relay is adequate to achieve full diversity. In order to derive the outage probability of this system in a Nakagami fading environment with integer fading parameters, a simple closed-form expression for the cumulative distribution function (CDF) of the sum of two independent, but not necessarily identically distributed, Erlang random variables is obtained. By approximating the outage probability for the high signal-to-noise ratio (SNR) region, we also derive the diversity order and coding gain of this selection relaying method and the fixed relaying method. The obtained asymptotic performance expressions are generalized for Nakagami fading channels with arbitrary real-valued fading parameters. Numerical and Monte Carlo results are provided which confirm the analytical expressions.

Performance evaluation of underlay cognitive hybrid satellite–terrestrial relay networks with relay selection scheme

The applicability of cognitive radio (CR) techniques into satellite communications has received considerable attention in recent years. This study considers the integration of relay transmission into CR-based satellite terrestrial network, which offers the advantages of not only increasing the overall spectral efficiency by spectrum sharing but also extending the wireless coverage through the deployment of relays. Specifically, the authors derive the exact closed-form expression of the outage probability (OP) for the cognitive network, which provide an efficient means to evaluate the impact of key parameters on the system performance. Furthermore, the asymptotic OP expression at high signal-to-noise ratio is presented, which reveals the achievable diversity order and coding gain of the considered network. Finally, numerical results are carried out to validate the theoretical results, and shows that although a higher transmit power or weaker shadowing severity of the satellite interference link has a severe detrimental impact on the outage performance of the cognitive network by reducing the coding gain, the achievable diversity order only depends on the fading severities and the number of relays of the cognitive network.