Log-Logarithmic Selection Resolution Protocols in a Multiple Access Channel

In this work, we investigate a three-user cognitive communication network where a primary two-user multiple access channel suffers interference from a secondary point-to-point channel, sharing the same medium. While the point-to-point channel transmitter—transmitter 3—causes an interference at the primary multiple access channel receiver, we assume that the primary channel transmitters—transmitters 1 and 2—do not cause any interference at the point-to-point receiver. It is assumed that one of the multiple access channel transmitters has cognitive capabilities and cribs causally from the other multiple access channel transmitter. Furthermore, we assume that the cognitive transmitter knows the message of transmitter 3 in a non-causal manner, thus introducing the three-user multiple access cognitive Z-interference channel. We obtain inner and outer bounds on the capacity region of the this channel for both causal and strictly causal cribbing cognitive encoders. We further investigate different variations and aspects of the channel, referring to some previously studied cases. Attempting to better characterize the capacity region we look at the vertex points of the capacity region where each one of the transmitters tries to achieve its maximal rate. Moreover, we find the capacity region of a special case of a certain kind of more-capable multiple access cognitive Z-interference channels. In addition, we study the case of full unidirectional cooperation between the 2 multiple access channel encoders. Finally, since direct cribbing allows us full cognition in the case of continuous input alphabets, we study the case of partial cribbing, i.e., when the cribbing is performed via a deterministic function.

This paper is eligible for the student paper award. This paper is classified under Information Theory. In this paper, we investigate a three-user cognitive communication network where a primary two-user Multiple Access Channel (MAC) suffers interference from a secondary point-to-point channel, sharing the same medium. While the secondary channel transmitter causes an interference at the primary MAC receiver, we assume that the primary channel transmitters do not cause any interference at the secondary receiver. It is assumed that one of the primary transmitters has cognitive capabilities and cribs causally from the other MAC transmitter. Furthermore, we assume that the cognitive transmitter knows the message of the secondary transmitter in a non-causal manner and we introduce three-user Multiple Access Cognitive Z-Interference Channel (MA-CZIC). We obtain inner and outer bounds on the capacity region of the three-user MA-CZIC for both strictly and non-strictly causal cribbing cognitive encoders.

In this paper, multiple access channels are considered in which user data rates increase with the signal-to-noise ratio (SNR). To account for channel estimation errors, a finite- SNR diversity-multiplexing tradeoff framework is formulated. The multiplexing gain is defined for each user as the ratio of the user's data rate to the capacity of an additive white Gaussian noise (AWGN) channel. For a set of user multiplexing gains, a finite-SNR diversity gain is defined by the slope of the common outage probability as a function of SNR for quasi-static fading. These definitions have been used in previous work to characterize a finite-SNR diversity-multiplexing tradeoff in multiple access channels and point-to-point multiantenna channels. Inner and outer bounds on the feasible rate region of a multiple access channel with channel estimation errors are used to obtain estimates of the common outage probability. The outage probability is then used to estimate the diversity gain as a function of user multiplexing gains and SNR. It is shown that a finite-SNR formulation is essential to characterizing the impact of channel estimation errors on the diversity-multiplexing tradeoff.

In this paper, we tackle decision fusion for distributed detection in a randomly-deployed clustered Wireless Sensor Networks (WSNs) operating over a non-ideal multiple access channels (MACs), i.e. considering Rayleigh fading, path loss and additive noise. To mitigate fading, we propose the distributed equal gain transmit combining (dEGTC) and distributed maximum ratio transit combining (dMRTC). The first and second order statistics of the received signals were analytically computed via stochastic geometry tools. Then the distribution of the received signal over the MAC are approximated by Gaussian and log-normal distributions via moment matching. This enabled the derivation of moment matching optimal fusion rules (MOR) for both distributions. Moreover, suboptimal simpler fusion rules were also proposed, in which all the CHs data are equally weighed, which is termed moment matching equal gain fusion rule (MER). It is shown by simulations that increasing the number of clusters improve the performance. Moreover, MOR-Gaussian based algorithms are better under free-space propagation whereas their lognormal counterparts are more suited in the ground-reflection case. Also, the latter algorithms show better results in low SNR and SN numbers conditions. We have proved that the received power at the CH in MAC is proportional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\lambda ^{2} R^{2})$</tex-math></inline-formula> and to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\lambda ^{2} \ln ^{2} R)$</tex-math></inline-formula> in the free-space propagation and the ground-reflection cases respectively, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> is SN deployment intensity and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R$</tex-math></inline-formula> is the cluster radius. This implies that having more clusters decreases the required transmission power for a given SNR at the receiver.

We consider the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> -relay Gaussian diamond network where a source node communicates to a destination node via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> parallel relays through a cascade of a Gaussian broadcast (BC) and a multiple access (MAC) channel. Introduced in 2000 by Schein and Gallager, the capacity of this relay network is unknown in general. The best currently available capacity approximation, independent of the coefficients and the SNRs of the constituent channels, is within an additive gap of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.3 N$ </tex-math></inline-formula> bits, which follows from the recent capacity approximations for general Gaussian relay networks with arbitrary topology. In this paper, we approximate the capacity of this network within 2 log <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> bits. We show that two strategies can be used to achieve the information-theoretic cut-set upper bound on the capacity of the network up to an additive gap of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(\log N)$ </tex-math></inline-formula> bits, independent of the channel configurations and the SNRs. The first of these strategies is simple partial decode-and-forward. Here, the source node uses a superposition codebook to broadcast independent messages to the relays at appropriately chosen rates; each relay decodes its intended message and then forwards it to the destination over the MAC channel. A similar performance can be also achieved with compress-and-forward type strategies (such as quantize-map-and-forward and noisy network coding) that provide the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.3 N$ </tex-math></inline-formula> -bit approximation for general Gaussian networks, but only if the relays quantize their observed signals at a resolution inversely proportional to the number of relay nodes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> . This suggests that the rule-of-thumb to quantize the received signals at the noise level in the current literature can be highly suboptimal.

In this paper, a generalized multiple access channel (MAC) model for secret key sharing between three terminals is considered. In this model, there are two transmitters and a receiver where all three terminals receive noisy channel outputs. In addition, there is a one-way public channel from the transmitters to the receiver. Each of the transmitters intends to share a secret key with the receiver by using the MAC and the public channel, where the transmitters are eavesdroppers with respect to each other. Two strategies for secret key sharing are considered, namely, the pregenerated key strategy and the two-stage key strategy. For both of them, inner and outer bounds of the secret key capacity region are derived. Furthermore, the effect of the public channel is discussed and the two strategies are compared. In both strategies, it is assumed that the channel outputs at the transmitters are only used for eavesdropping and not as inputs to the encoders. The effect of this assumption in the presence of the public channel is analyzed for some Gaussian MACs.

In this paper, we propose delay‐universal or ‘anytime’ code design for multiple access channels. The anytime characteristics of the proposed coding scheme are investigated asymptotically over two different multiple access channels. For the simplest multiple access channel, we derive the analytical delay‐exponent of the proposed code by using mathematical induction technique. Through comparison, we show that the analytical delay‐exponent matches with the delay‐exponent obtained from numerical results. Copyright © 2015 John Wiley &amp; Sons, Ltd.

We consider spatially coupled code ensembles over a multiple access channel. Convolutional LDPC ensembles are one instance of spatially coupled codes. It was shown recently that, for transmission over the binary erasure channel, this coupling of individual code ensembles has the effect of increasing the belief propagation threshold of the coupled ensembles to the maximum a-posteriori threshold of the underlying ensemble. In this sense, spatially coupled codes were shown to be capacity achieving. It was observed, empirically, that these codes are universal in the sense that they achieve performance close to the Shannon threshold for any general binary-input memoryless symmetric channels. In this work we provide further evidence of the threshold saturation phenomena when transmitting over a class of multiple access channel. We show, by density evolution analysis and EXIT curves, that the belief propagation threshold of the coupled ensembles is very close to the ultimate Shannon limit.

Channel state information (CSI) is important for achieving large rates in MIMO channels. However, in time-varying MIMO channels, there is a tradeoff between the time/energy spent acquiring channel state information (CSI) and the time/energy remaining for data transmission. This tradeoff is accentuated in the MIMO multiple access channel (MAC), since the number of channel vectors to be estimated increases with the number of users. Furthermore, the problem of acquiring CSI is tightly coupled with the problem of exploiting CSI through multiuser scheduling. This paper considers a block-fading MAC with coherence time <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> , n uncoordinated users-each with one transmit antenna and the same average power constraint, and a base station with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> receive antennas and no a priori CSI. For this scenario, a training-based communication scheme is proposed and the training and multiuser-scheduling aspects of the scheme are jointly optimized. In the high-SNR regime, the sum capacity of the non-coherent SIMO MAC is characterized and used to establish the SNR-scaling-law optimality of the proposed scheme. In the low-SNR regime, the sum-rate of the proposed scheme is found to decay linearly with vanishing SNR when flash signaling is incorporated. Furthermore, this linear decay is shown to be order-optimal through comparison to the low-SNR sum capacity of the non-coherent SIMO MAC. A by product of these SNR-asymptotic analyses is the observation that non-trivial scheduling (i.e., scheduling a strict subset of trained users) is advantageous at low SNR, but not at high SNR. The sum-rate and per-user throughput are also explored in the large- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> and large- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> regimes. Non-coherent capacity, training, multiple access channel, multiuser scheduling, opportunistic scheduling.

Non-orthogonal multiple access (NOMA) is a potential enabler for the development of 5G and beyond wireless networks. By allowing multiple users to share the same resource (time/frequency/code/space), NOMA can scale up the number of served users, increase the spectral efficiency, and improve user-fairness compared to existing orthogonal multiple access (OMA) techniques. The basic premise behind NOMA in a single-cell network is to reap the benefits promised by information theory for the downlink and uplink transmission of wireless systems, modeled respectively by the broadcast channel (BC) and multiple access channel (MAC). The capacity regions of the BC and MAC have been established several decades ago, and concurrent non-orthogonal transmission is the optimal transmission strategy in both cases. Unlike the single-cell setting, the capacity region of multi-cell wireless networks, commonly modeled by the interference channel (IC), is in general unknown. However, it is known that OMA is suboptimal. This chapter reviews what information theory promises and proposes for NOMA in single- and multi-cell networks with both single- and multi-antenna nodes. Furthermore, relevant physical layer security channel models are proposed and discussed.

We consider the distributed estimation of an unknown vector signal in a bandwidth constrained sensor network with a fusion center (FC). Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the FC. In this context, we design a linear decentralized estimation scheme (DES), where each sensor linearly encodes its observations before the transmission to the FC, which performs a minimum mean squared error (MMSE) estimation for the unknown vector signal based on the received messages. When the channels between sensors and the FC are orthogonal, it has been shown previously that the complexity of designing the optimal encoding matrices is NP-hard in general. In this paper, we study the optimal design of linear DES for the case of non- orthogonal multiple access channel (MAC) under both bandwidth and power constraints. We show that when the MAC between sensors and the FC is noiseless, the resulting problem has a closed-form solution, while in the noisy MAC case, the problem can be efficiently solved by semi-definite programming (SDP).

In this paper, we study upper and lower bounds on the achievable sum-rate of an uncorrelated multiple-input multiple-output (MIMO) multiple access channel (MAC) for Gaussian input signals and with channel estimation error at the receiver. We prove that the gap between the mutual information bounds does not exceed a certain value for arbitrary input covariance matrices and at any input transmit power. We also prove that in a MIMO MAC with uniform input power utilization over the transmit antennas, the gap between the mutual information bounds increases monotonically as the input power of each user increases. Furthermore, we show that the gap between the bounds is maximum when beamforming is applied at the transmitters of all users. We also derive the transmit directions that maximize the mutual information lower and upper bounds when delayed feedback is available from the receiver to the transmitters, and characterize the power allocation of this system in terms of its beamforming range. Numerical simulations are conducted to corroborate our theoretical results and quantify the effect of imperfect channel estimation.

Distributing data aggregation through multiple access channel (MAC) has been challenging in large wireless networks. In order to tackle the challenge, a computing over the MAC (CP-MAC) scheme has been proposed as a promising communication-computation integrated way for function-centric networks. In this paper, we analyze the performance of the CP-MAC scheme, compared with the traditional communication-computation separated way, i.e., a communicating over the MAC (CM-MAC) scheme. Function-centric wireless networks are considered, where the fusion center (FC) does not need the individual data of each node but only the target function. We begin with the ideal uniform-MAC scenarios, where the CP-MAC scheme is always better than the CM-MAC scheme. Then, practical non-uniform MAC scenarios are studied for both homogeneous networks with Rayleigh fading and heterogeneous networks with a different path loss. Closed-form expressions of the achievable function rate are provided using the asymptotic theory of ordered statistics. It is found that the CP-MAC scheme is not always superior to the CM-MAC scheme. Simulation results are provided to verify and illustrate our derived results.

In this paper, we study the two-user Gaussian fading Multiple Access Channel (MAC) with cooperative encoders. Two different scenarios are studied: the Gaussian fading MAC with a common message, and the Gaussian fading MAC with conferencing encoders. The throughput capacity region of these channels with partial Channel State Information (CSI) at the transmitters (CSIT) and perfect CSI at the receiver (CSIR) is established. For the Gaussian fading systems with only CSIR (transmitters have no access to CSIT), some numerical examples and simulation results are provided for Rayleigh fading models.

In this paper we consider transmit covariance matrix optimization and user ordering problem for successive zero-forcing (SZF) precoding for multiuser multiple-input multiple-output (MIMO) downlink, where base station as well as the mobile receivers are equipped with multiple antennas. With SZF, an optimization of sum rate maximizing transmit covariance matrices is necessary. A dirty paper coding (DPC) based transmit covariance matrix optimization algorithm has been recently proposed in [1]. The algorithm involves three steps: the dual multiple access channel (MAC) covariance optimization using sum power iterative water-filling [2], the MAC to broadcast channel (BC) covariance transformation [3] for DPC, and transformation of the DPC downlink covariance matrices to SZF matrices. Hence, that algorithm is computationally very complex, and may not be realizable in practice. In this paper, we propose a suboptimal but much simplified algorithm, which employs an iterative procedure similar to the MAC covariance optimization technique of [2], but does not involve multiple levels of covariance matrix transformations. Additionally, the optimized algorithm requires the optimization to be applied to all possible user orders. Hence, we propose a heuristic user ordering algorithm based on previously proposed user selection algorithms, so that the exhaustive search through all possible user orders is avoided without significant performance penalty. Simulation results show that proposed algorithm performs very close to the algorithm of [1] in low SNR regime.