We consider a single cell uplink in which many devices randomly transmit a data payload to the base station. Given a fixed latency constraint per device, we propose a time and frequency slotted random access scheme with retransmissions, which when necessary, are Chase combined at the receiver. We analyze the proposed setting at constant SNR. We characterize the scaling of random access throughput versus the latency, by optimizing the number of retransmissions and the number of frequency bins. For infinite block length (IBL), we conclude that at low SNR devices should completely share the time and frequency resources. For high SNR, however, the number of frequency bins should scale with altered load, and the slot duration for each retransmission is determined by the outage tolerance. Since infinite packet sizes are not possible, we extend our model to the finite block length (FBL) regime and characterize the gap versus the IBL regime. We also provide some new results for FBL capacity to bound the probability of outage. The proposed random access model gives an upper bound for the total uplink traffic that can be successfully decoded for a single receive antenna given the latency constraint, and provides insights for 5G cellular system design.
Because ideal interference cancellation is not realizable in practice, especially for a large number of devices, reference @cite_10 characterizes the throughput of a suboptimal but more practical random access system where both the time and frequency domains are slotted. The receiver uses conventional single-user detection which demodulates a desired user's data stream by treating other users' interfering signals as noise, and as a simplifying assumption, the analysis uses Shannon capacity to approximate the SINR threshold for a failed transmission. This approximation leads to an optimistic bound on the throughput, and it becomes exact in the limit of infinite coding block lengths.
@cite_10
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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. In a cognitive radio scenario, we consider a single secondary user (SU) accessing a multichannel system. The SU senses the channels sequentially to detect if a primary user (PU) is occupying the channels and stops its search to access a channel if it offers a significantly high throughput. The optimal stopping rule and power control problem is considered. The problem is formulated as an SU's throughput-maximization problem under power, interference, and packet delay constraints. We first show the effect of the optimal stopping rule on packet delay and then solve this optimization problem for both the overlay system, where the SU transmits only at the spectrum holes, and the underlay system, where tolerable interference (or tolerable collision probability) is allowed. We provide closed-form expressions for the optimal stopping rule and show that the optimal power control strategy for this multichannel problem is a modified waterfilling approach. We extend the work to a multi-SU scenario and show that when the number of SUs is large, the complexity of the solution becomes smaller than that of the single-SU case. We discuss the application of this problem in typical networks where packets simultaneously arrive and have the same departure deadline. We further propose an online adaptation policy to the optimal stopping rule that meets the packets' hard-deadline constraint and, at the same time, gives higher throughput than the offline policy. The performance benefits of two interference cancellation methods, successive interference cancellation (SIC) and joint detection (JD), in wireless ad hoc networks are compared within the transmission capacity framework. SIC involves successively decoding and subtracting out strong interfering signals until the desired signal can be decoded, while higher-complexity JD refers to simultaneously decoding the desired signal and the signals of a few strong interferers. Tools from stochastic geometry are used to develop bounds on the outage probability as a function of the spatial density of interferers. These bounds show that SIC performs nearly as well as JD when the signal-to-interference ratio (SIR) threshold is less than one, but that SIC is essentially useless for SIR thresholds larger than one whereas JD provides a significant outage benefit regardless of the SIR threshold. A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.