The interference in wireless networks is temporally correlated, since the node or user locations are correlated over time and the interfering transmitters are a subset of these nodes. For a wireless network where (potential) interferers form a Poisson point process and use ALOHA for channel access, we calculate the joint success and outage probabilities of n transmissions over a reference link. The results are based on the diversity polynomial, which captures the temporal interference correlation. The joint outage probability is used to determine the diversity gain (as the SIR goes to infinity), and it turns out that there is no diversity gain in simple retransmission schemes, even with independent Rayleigh fading over all links. We also determine the complete joint SIR distribution for two transmissions and the distribution of the local delay, which is the time until a repeated transmission over the reference link succeeds.
A separate line of work focuses on the local delay , which is the time it takes for a node to connect to a nearby neighbor. The local delay, introduced in @cite_8 and further investigated in @cite_2 @cite_1 , is a sensitive indicator of correlations in the network. In @cite_6 the two lines of work are combined and approximate joint temporal statistics of the interference are used to derive throughput and local delay results in the high-reliability regime. In @cite_7 , the mean local delay for ALOHA and frequency-hopping multiple access (FHMA) are compared, and it is shown that FHMA has comparable performance in the mean delay but is significantly more efficient than ALOHA in terms of the delay variance.
@cite_7 @cite_8 @cite_1 @cite_6 @cite_2
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The capacity of wireless networks is fundamentally limited by interference. However, little research has focused on the interference correlation, which may greatly increase the local delay (namely the number of time slots required for a node to successfully transmit a packet). This paper focuses on the question whether increasing randomness in the MAC, specifically frequency-hopping multiple access (FHMA) and ALOHA, helps to reduce the effect of interference correlation. We derive closed-form results for the mean and variance of the local delay for the two MAC protocols and evaluate the optimal parameters that minimize the mean local delay. Based on the optimal parameters, we identify two operating regimes, the correlation-limited regime and the bandwidth-limited regime. Our results reveal that while the mean local delays for FHMA with N sub-bands and for ALOHA with transmit probability p essentially coincide when p=1 N, a fundamental discrepancy exists between their variances. We also discuss implications from the analysis, including an interesting mean delay-jitter tradeoff, and convenient bounds on the tail probability of the local delay, which shed useful insights into system design. We study a slotted version of the Aloha Medium Access (MAC) protocol in a Mobile Ad-hoc Network (MANET). Our model features transmitters randomly located in the Euclidean plane, according to a Poisson point process and a set of receivers representing the next-hop from every transmitter. We concentrate on the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise (SINR) larger than some threshold. We analyze the local delays in such a network, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers. The analysis depends very much on the receiver scenario and on the variability of the fading. In most cases, each node has finite-mean geometric random delay and thus a positive next hop throughput. However, the spatial (or large population) averaging of these individual finite mean-delays leads to infinite values in several practical cases, including the Rayleigh fading and positive thermal noise case. In some cases it exhibits an interesting phase transition phenomenon where the spatial average is finite when certain model parameters (receiver distance, thermal noise, Aloha medium access probability) are below a threshold and infinite above. To the best of our knowledge, this phenomenon, which we propose to call the wireless contention phase transition, has not been discussed in the literature. We comment on the relationships between the above facts and the heavy tails found in the so-called "RESTART" algorithm. We argue that the spatial average of the mean local delays is infinite primarily because of the outage logic, where one transmits full packets at time slots when the receiver is covered at the required SINR and where one wastes all the other time slots. This results in the "RESTART" mechanism, which in turn explains why we have infinite spatial average. Adaptive coding offers another nice way of breaking the outage RESTART logic. We show examples where the average delays are finite in the adaptive coding case, whereas they are infinite in the outage case. For communication between two neighboring nodes in wireless networks, the local delay is defined as the time it takes a node to successfully transmit a packet. Previous research focuses on the local delay in static or infinitely mobile Poisson networks with ALOHA. In this paper, we extend the local delay results to Poisson networks with finite mobility. The results obtained show that mobility helps reduce the local delay. Bounds of the local delay in mobile Poisson networks are derived for different mobility and transmission models. The phase transition that marks the jump of the local delay from finite to infinite is also characterized. Communication in decentralized wireless networks is limited by interference. Because transmissions typically last for more than a single contention time slot, interference often exhibits a strong statistical dependence over time that results in temporally correlated communication performance. The temporal dependence in interference increases as user mobility decreases and or the total transmission time increases. We propose a network model that spans the extremes of temporal independence to long-term temporal dependence. Using the proposed model, closed-form single hop communication performance metrics are derived that are asymptotically exact in the low outage regime. The primary contributions are (i) deriving the joint temporal statistics of network interference and showing that it follows a multivariate symmetric alpha stable distribution; (ii) utilizing the joint interference statistics to derive closed-form expressions for local delay, throughput outage probability, and average network throughput; and (iii) using the joint interference statistics to redefine and analyze the network transmission capacity that captures the throughput-delay-reliability tradeoffs in single hop transmissions. Simulation results verify the closed-form expressions derived in this paper and we demonstrate up to 2× gain in network throughput and reliability by optimizing certain parameters of medium access control layer protocol in view of the temporal correlations. Communication between two neighboring nodes is a very basic operation in wireless networks. Yet very little research has focused on the local delay in networks with randomly placed nodes, defined as the mean time it takes a node to connect to its nearest neighbor. We study this problem for Poisson networks, first considering interference only, then noise only, and finally and briefly, interference plus noise. In the noiseless case, we analyze four different types of nearest-neighbor communication and compare the extreme cases of high mobility, where a new Poisson process is drawn in each time slot, and no mobility, where only a single realization exists and nodes stay put forever. It turns out that the local delay behaves rather differently in the two cases. We also provide the low- and high-rate asymptotic behavior of the minimum achievable delay in each case. In the cases with noise, power control is essential to keep the delay finite, and randomized power control can drastically reduce the required (mean) power for finite local delay.