# Order Statistics Based Analysis of Pure ALOHA in Channels with Multipacket Reception

TL;DR: A novel order statistics based technique is devised to derive the exact expression for the throughput of pure ALOHA in a channel that supports Multi-Packet Reception (MPR).

Abstract: In this letter, we devise a novel order statistics based technique to derive the exact expression for the throughput of pure ALOHA in a channel that supports Multi-Packet Reception (MPR). Our technique is general and can also be used in the analysis of other unslotted MAC protocols. Our analytical results are verified using simulations.

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TL;DR: This paper investigates TI sequences for γ ≥ 1.

Abstract: Consider a time-slotted communication channel that is shared by $K$ active users transmitting to a single receiver. It is assumed that the receiver has the ability of the multiple-packet reception to correctly receive up to $\gamma$ ( $1 \leq \gamma ) simultaneously transmitted packets. Each user accesses the channel following a deterministic binary sequence, called the protocol sequence, and transmits a packet within a channel slot if the sequence value is equal to one. If the users are not time synchronized, the relative shifts among them can cause significant fluctuation in throughput. If the throughput of each user is independent of relative shifts, then the adopted protocol sequence set is said to be throughput-invariant (TI). If we define worst-case system throughput as the minimal system throughput that can be guaranteed for any set of relative shifts, then TI sequences maximize it and hence are of fundamental interest. This paper investigates TI sequences for $\gamma \geq 1$ . Several new results are obtained including throughput value as a function of the duty factors, a lower bound on the sequence period, a construction that achieves the lower bound on the sequence period, and theorems on the intrinsic structure that establish connections with some other families of binary sequences.

24 citations

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TL;DR: Through a parsimonious modeling approach, relatively simple analytical expressions are derived and insight and quantitative understanding are gained on the fundamental tradeoffs between pure and slotted ALOHA and on the scaling of maximum achievable throughput with $K$ .

Abstract: Multiple packet reception (MPR) is becoming a viable reality for wireless random access protocols thanks to advances in the physical layer and new coding techniques. In the simplest $K$ -MPR model, a receiver can resolve up to $K\geq 1$ parallel transmissions. We extend the classical analysis of pure and slotted ALOHA to $K$ -MPR devices with arbitrary degree $K$ for fixed and variable packet size. Through a parsimonious modeling approach, we derive relatively simple analytical expressions. In this way, we gain insight and quantitative understanding on the fundamental tradeoffs between pure and slotted ALOHA and on the scaling of maximum achievable throughput with $K$ .

11 citations

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TL;DR: The proposed MC-PCA-DA MAC protocol can achieve significant throughput gain over the basic Pure Aloha MAC protocol and the exact theoretical formulation of the throughput is derived in this paper.

Abstract: One of the key enabling technologies for Internet-of-Things (IoT) is the satellite network. Communications in the uplink segment of a satellite network is achieved using a medium access control (MAC) protocol. This paper proposes an asynchronous Multi-Channel Pure Collective Aloha MAC protocol with a Decollision Algorithm (MC-PCA-DA). The exact theoretical formulation of the throughput is derived in this paper. The theoretical results are verified by simulation results. Numerical results show that the maximum throughput of the MC-PCA-DA MAC protocol can be up to 10 times (10x) for a single frequency channel as compared to that of the asynchronous Pure Aloha MAC protocol in a single frequency channel, up to 20 times (20x) for two frequency channels and up to 40 times (40x) for four frequency channels, respectively. Thus, the proposed MC-PCA-DA MAC protocol can achieve significant throughput gain over the basic Pure Aloha MAC protocol.

10 citations

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TL;DR: Comparisons between CI sequences and random access in an application of group-based detection in a wireless sensor network are presented and the minimum period L of CI sequences for MPR is investigated as L is a fundamental factor that affects the worst-case delay.

Abstract: In this paper, we study completely irrepressible (CI) sequences. For a slot-asynchronous communication system supporting $K$ users with such sequences, a key feature is that each user is guaranteed to be able to send out at least one contention-free packet in one common sequence period. This is a desirable property since it provides a bounded delay guarantee for medium access control (MAC) layer contention, in contrast to random access schemes. Generalizing previous studies on CI sequences, we investigate systems endowed with multiple-packet reception (MPR) capability $\gamma$ , $\mbox{2} \leq \gamma . That is, a packet transmission is successful if and only if the total number of transmissions in the channel at any point in time during its transmission is less than or equal to $\gamma$ . We investigate the minimum period $L$ of CI sequences for MPR as $L$ is a fundamental factor that affects the worst-case delay. The main result is that $L$ is asymptotically upper bounded by $\mbox{2}K^2/(\gamma-\mbox{2})$ when $\gamma \geq \mbox{3}$ . For $\gamma = \mbox{2}$ , the corresponding bound is $\mbox{2}K^2$ . In contrast, the bound for the single-packet reception system $(\gamma=\mbox{1})$ is $\mbox{4}K^2$ . Simulation results verify our analysis and present comparative studies between CI sequences and random access in an application of group-based detection in a wireless sensor network.

7 citations

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TL;DR: It can be shown that implementing Multi-Packet Reception (MPR) capability to the DC improves the performance of the FSA protocol and the asymptotic limits of throughput, delay and energy efficiency based on MPR-FSA protocol are derived.

Abstract: We consider a Machine-to-Machine (M2M) network where a large number of user nodes (STAs) communicate with a Data Collector (DC). We consider the case where all the user nodes periodically transmit their data packets to the DC and the network is in saturation. Recently protocols based on Frame Slotted Aloha (FSA) have been shown to be suitable as MAC protocols for M2M data collection networks under saturated conditions. It can be shown that implementing Multi-Packet Reception (MPR) capability to the DC improves the performance of the FSA protocol. In this work we propose a Multi-Packet Reception (MPR) based FSA (MPR-FSA) protocol and study its performance. We derive the asymptotic limits of throughput, delay and energy efficiency based on MPR-FSA protocol. We also derive the limiting value of MPR (K lim ) parameter for a given FSA based data collection network at which asymptotic performance is achieved. A mathematical model is proposed and the analytical values are validated using extensive simulations.

6 citations

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TL;DR: In this paper, the authors use order statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes to measure moment relations, bounds, and approximations.

Abstract: Basic Distribution Theory Discrete Order Statistics Order Statistics from Some Specific Distributions Moment Relations, Bounds, and Approximations Characterizations Using Order Statistics Order Statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes.

1,604 citations

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TL;DR: The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered and it is shown that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity.

Abstract: The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered. This channel is a generalization of the usual collision channel, in that it allows the correct reception of one or more packets involved in a collision. The number of successfully received packets in each slot is modeled as a random variable which depends exclusively on the number of simultaneously attempted transmissions. This general model includes as special cases channels with capture, noise, and code-division multiplexing. It is shown by drift analysis that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity. The properties of the backlog in the nonergodicity region are examined. >

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130 citations

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TL;DR: This paper addresses the problem of computing the probability that r out of n interfering wireless signals are "captured," i.e., received with sufficiently large Signal to Interference plus Noise Ratio to correctly decode the signals by a receiver with multi-packet reception (MPR) and Successive Interference Cancellation (SIC) capabilities.

Abstract: In this paper, we address the problem of computing the probability that r out of n interfering wireless signals are "captured," i.e., received with sufficiently large Signal to Interference plus Noise Ratio (SINR) to correctly decode the signals by a receiver with multi-packet reception (MPR) and Successive Interference Cancellation (SIC) capabilities. We start by considering the simpler case of a pure MPR system without SIC, for which we provide an expression for the distribution of the number of captured packets, whose computational complexity scales with n and r. This analysis makes it possible to investigate the system throughput as a function of the MPR capabilities of the receiver. We then generalize the analysis to SIC systems. In addition to the exact expressions for the capture probability and the normalized system throughput, we also derive approximate expressions that are much easier to compute and provide accurate results in some practical scenarios. Finally, we present selected results for some case studies with the purpose of illustrating the potential of the proposed mathematical framework and validating the approximate methods.

99 citations

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TL;DR: An overview of MPR-related research work is provided covering the theoretically proved impacts and advantages of using MPR from a channel perspective to network capacity and throughput, and a scheduling method that targets full utilization of M PR capability is detailed.

Abstract: Multipacket reception (MPR) is the capability of simultaneous decoding of more than one packet from multiple concurrent transmissions. Continuous investigations on increasing the reception capability are giving new scientific contributions. In this paper, we provide an overview of MPR-related research work covering (1) the theoretically proved impacts and advantages of using MPR from a channel perspective to network capacity and throughput; (2) the various technologies that enable MPR from transmitter, transreceiver, and receiver perspectives; (3) previous work on protocol improvement to better exploit MPR. Indeed, MPR approaches have been applied in modern wireless mobile systems but the focus of this paper is to discuss MPR in random access wireless networks. Using MPR in such multihop environments calls for new adaptation on protocols, especially a cross-layer approach. To this end, we detail a scheduling method that targets full utilization of MPR capability.

38 citations