In fifth generation (5G) cellular systems with massive MIMO, coherent hybrid beamforming with phased arrays can be used to achieve high beamforming gain with low system complexity. Typically, hybrid beamforming systems require beam training between the base station (BS) and mobile users to optimize the beamforming coefficients, which causes extra overhead. For avoiding this overhead, long-term beamforming methods are considered to design beams that do not frequently change to serve a specific region over a long period. A framework is hence necessary to acquire the user distribution and apply it for beam design. However, in the absence of beam training, standard localization schemes usually require external assistance or incur extra measurement cost. We propose a framework called Beamforming with Iterative Traffic Sensing (BITS), which alternately infers the active user distribution based on celllevel sum network spectral efficiency and optimizes the beams accordingly. The sum network spectral efficiency can be readily measured during data transmission periods with no extra communication overhead. Simulation results show quick and significant performance improvement when we infer the user distribution with sparsity using Key Performance Indicators (KPIs) that are available to the BS and iteratively improve the beamforming.

This letter provides a theoretical analysis for the static beamforming problem when the base station is equipped with two antennas. It is assumed that the base station cannot change the beamforming vector dynamically due to hardware restrictions. The objective is to find the static beamforming vector that maximizes network utility when long-term information about the user location is available. Non-linear optimization techniques are used to find the solution of the problem for two different network utility functions: average SNR and average rate. Numerical results are provided to support the analysis.

Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications. We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop wireless packet erasure broadcast channels. We capture the delay sensitivities across different types of network applications using a class of delay metrics based on the norms of packet arrival times. With these delay metrics, we establish a unified framework to characterize the rate and delay requirements of applications and to optimize system parameters. In the single receiver case, we demonstrate the trade-off between average packet delay, which we view as the inverse of throughput, and maximum inorder inter-arrival delay for various system parameters. For a single broadcast channel with multiple receivers having different delay constraints and feedback delays, we jointly optimize the coding parameters and time-division scheduling parameters at the transmitter. We formulate the optimization problem as a Generalized Geometric Program (GGP). This approach allows the transmitter to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints. In the case where the receivers are served by multiple non-interfering wireless broadcast channels, the same optimization problem is formulated as a Signomial Program, which is NP-hard in general. We provide approximation methods using successive formulation of geometric programs and show the convergence of approximations.

An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared-error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

In a multiple-antenna relay channel, the full-duplex cut-set capacity upper bound and decode-and-forward rate are formulated as convex optimization problems. For half-duplex relaying, bandwidth allocation and transmit signals are optimized jointly. Moreover, achievable rates based on the compress-and-forward strategy are presented using rate-distortion and Wyner-Ziv compression schemes.

This paper studies the asymptotic properties of amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-hop relay channels, where the source terminal (ST), relay terminal (RT) and destination terminal (DT) are equipped with a number of correlated antennas and there is a direct link between the ST and DT. The analysis is based on the Kronecker correlated fading model where the correlation properties of the MIMO channel are modeled at the transmitter and receiver ends separately. Our first main contribution is the derivation of the asymptotic mutual information expressions for the MIMO-AF relay channel for any given signaling input distributions (not necessarily Gaussian) in the large-system regime, which is particularly relevant if practical modulation schemes are used. In addition to the formula that uses joint optimal decoding (JOD) at the DT, we also obtain the asymptotic result for a more practical system which performs separate detection and decoding (SDD) (i.e., spatial detection followed by a temporal error-correction decoder). Another major contribution of this paper is an efficient algorithm that can compute the optimal source covariance matrix and the relay precoding matrix to maximize the asymptotic mutual information of the MIMO-AF relay system if channel covariance information (CCI) is known at the ST and RT.

This paper presents an empirical study of the achievable data rates of network multiple-input multiple-output (MIMO) techniques including zero-forcing (ZF), zero-forcing dirty paper coding (ZF-DPC) and dirty paper coding (DPC) using actual 4-by-4 indoor wireless channel measurements at 3.5 GHz. Their performances are contrasted with those of conventional techniques, in which either the base stations are not coordinated (NC), or their interference is avoided using frequency division (FD) multiplexing. The measurements were taken in aisle-to-office and large unobstructed hall scenarios. The study of these results reveals that, at high signal-to-noise ratios (SNRs), DPC and ZF-DPC can yield more than a three-fold increase in attainable data rates when compared to NC and FD. The gains obtained using ZF are smaller, but still significant. At low SNRs the system is noise-(rather than interference-) limited, and only DPC exhibits gains. The evaluations in this paper also show that collaborative systems such as DPC can benefit from interference-prone environments to yield increased transmission capacity. With regard to the propagation channel, the classical log-normal plus Rayleigh/Ricean fading model, with parameters fitted to the scenario type, was found to be good at predicting the statistics of the achievable data rates of all the strategies considered.

In a cooperative multiple-antenna downlink cellular network, maximization of a concave function of user rates is considered. A new linear precoding technique called soft interference nulling (SIN) is proposed, which performs at least as well as zero-forcing (ZF) beamforming. All base stations share channel state information, but each user's message is only routed to those that participate in the user's coordination cluster. SIN precoding is particularly useful when clusters of limited sizes overlap in the network, in which case traditional techniques such as dirty paper coding or ZF do not directly apply. The SIN precoder is computed by solving a sequence of convex optimization problems. SIN under partial network coordination can outperform ZF under full network coordination at moderate SNRs. Under overlapping coordination clusters, SIN precoding achieves considerably higher throughput compared to myopic ZF, especially when the clusters are large.

A wireless packet network is considered in which each user transmits a stream of packets to its destination. The transmit power of each user interferes with the transmission of all other users. A convex cost function of the completion times of the user packets are minimized by optimally allocating the users' transmission power subject to their respective power constraints. It is shown that, at all ranges of SINR, completion time minimization can be formulated as a convex optimization problem and hence can be efficiently solved. When channel knowledge is imperfect, robust power control is considered based on the channel fading distribution subject to outage probability constraints. The problem is shown to be convex when the fading distribution is log-concave in exponentiated channel power gains; e.g., when each user is under independent Rayleigh, Nakagami, or log-normal fading.

A transmitter without channel state information wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the number of channel uses per source symbol tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity.

The cooperative dirty paper coding (DPC) rate region is investigated in a two-transmitter two-receiver network with full channel state information available at all terminals. The transmitters cooperate by first exchanging messages over an orthogonal cooperation channel, then they mimic a broadcast channel (BC) and jointly perform DPC to send to the two independent receivers. The allocation of network power and bandwidth between the data and the cooperation channel is studied to characterize the cooperative DPC rate region. First, the optimal sum power allocation for a multiple access channel (MAC) is presented. Then through an application of the MAC-BC capacity duality, the cooperative DPC rate region is evaluated under different bandwidth allocation assumptions. Cooperative DPC outperforms non-cooperative time-division (TD) only when the cooperation channel is strong, since the joint-encoding capacity gain is negated by the overhead of message exchanges in a weak cooperation channel. Moreover, the cooperative capacity advantage over TD is more pronounced at the maximum sum rate point than when the rate vector is skewed toward one of the users.

Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decodeand- forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.

A transmitter without channel state information wishes to send a delay-limited Gaussian source over a slowly fading channel that has a finite number of discrete fading states. The source is coded in layers, with each layer successively refining the description in the previous one. These coded source layers are then superimposed and simultaneously transmitted to the receiver. The receiver decodes the layers that are supported by the realization of the channel, and combines the descriptions in the decoded layers to reconstruct the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the given number of source layers. For two layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For multiple layers, the overall expected distortion can be written as a set of recurrence relations, and the minimum expected distortion is found by recursively applying the two-layer optimization procedure at each recurrence step.

We consider transmission of a Gaussian source over a Gaussian relay channel, where the relay terminal has access to correlated side information. We propose several cooperative joint source-channel coding strategies that utilize both the broadcast nature of the wireless transmission and/or the availability of the correlated side information at the relay, and compare these to distortion lower bounds obtained by the cut-set arguments. In general, the best performing scheme depends on the correlation among the source and the relay signals, and the average link qualities. We illustrate that the strategies introduced in this paper perform very close to the lower bound in most cases.

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. In the limit of a continuum of infinite layers, the optimal power distribution that minimizes the expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. In the optimal power distribution, as SNR increases, the allocation over the higher layers remains unchanged; rather the extra power is allocated towards the lower layers. On the other hand, as the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the power distribution that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.

Capacity improvement from transmitter and receiver cooperation is investigated in a two-transmitter, two-receiver network with phase fading and full channel state information (CSI) available at all terminals. The transmitters cooperate by first exchanging messages over an orthogonal transmitter cooperation channel, then encoding jointly with dirty-paper coding. The receivers cooperate by using Wyner-Ziv compress-and-forward over an analogous orthogonal receiver cooperation channel. To account for the cost of cooperation, the allocation of network power and bandwidth among the data and cooperation channels is studied. It is shown that transmitter cooperation outperforms receiver cooperation and improves capacity over noncooperative transmission under most operating conditions when the cooperation channel is strong. However, a weak cooperation channel limits the transmitter cooperation rate; in this case, receiver cooperation is more advantageous. Transmitter-and-receiver cooperation offers sizable additional capacity gain over transmitter-only cooperation at low signal-to-noise ratio (SNR), whereas at high SNR transmitter cooperation alone captures most of the cooperative capacity improvement.

Capacity gain from transmitter and receiver cooperation under channel fading are compared in a relay network where the cooperating nodes are close together. We assume a Rayleigh flat-fading environment in the high signal-to-noise ratio (SNR) regime where the transmitters only have channel distribution information (CDI) but not channel state information (CSI). When all nodes have equal average transmit power, we show that the decode-and-forward transmitter cooperation strategy is capacity-achieving and is superior to receiver cooperation. However, the compress-and-forward receiver cooperation strategy is shown to outperform transmitter cooperation when power is optimally allocated among the nodes. Furthermore, we show that cooperative systems provide resilience to channel fading. However, in a fading channel, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together. With respect to limits on cooperation, it is shown that in a large cluster of M cooperating nodes, transmitter cooperation without CSI at the transmitter (CSIT), or receiver cooperation under equal power allocation, provides no capacity gain in a static channel, and at most a constant capacity gain that fails to grow with M in a fading channel.

We compare the rate of a multiple-antenna relay channel to the capacity of multiple-antenna systems to characterize the cooperative capacity in different SNR regions. While it is known that in the asymptotic regime, at a high SNR or with a large number of cooperating nodes, cooperative systems lack full multiplexing gain, in this paper we consider cooperative capacity gain at moderate SNR with a fixed number of cooperating antennas. We show that up to a lower bound to an SNR threshold, a cooperative system performs at least as well as a MIMO system with isotropic inputs; whereas beyond an upper bound to the SNR threshold, the cooperative system is limited by its coordination costs, and the capacity is strictly less than that of a MIMO orthogonal channel. The SNR threshold depends on the network geometry (the power gain g between the source and relay) and the number of cooperating antennas M; when the relay is close to the source (g [unk] 1), the SNR threshold lower and upper bounds are approximately equal. As the cooperating nodes are closer, i.e., as g increases, the MIMO-gain region extends to a higher SNR. Whereas for a populous cluster, i.e., when M is large, the coordination-limited region sets in at a lower SNR.

We compare the rates of one-shot and iterative conferencing in a cooperative Gaussian relay channel. The relay and receiver cooperate via a conference, as introduced by Willems, in which they exchange a series of communications over orthogonal links. Under one-shot conferencing, decode-and-forward (DF) is capacity-achieving when the relay has a strong channel. On the other hand, Wyner-Ziv compress-and-forward (CF) approaches the cut-set bound when the conference link capacity is large. To contrast with one-shot conferencing, we consider a two-round iterative conference scheme; it comprises CF in the first round, and DF in the second. When the relay has a weak channel, the iterative scheme is disadvantageous. However, when the relay channel is strong, iterative cooperation, with optimal allocation of conferencing resources, outperforms one-shot cooperation provided that the conference link capacity is large. When precise allocation of conferencing resources is not possible, we consider iterative cooperation with symmetric conference links, and show that the iterative scheme still surpasses one-shot cooperation, albeit under more restricted conditions.

Capacity gain from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. When all nodes have equal average transmit power along with full channel state information (CSI), it is proved that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the nodes but only receiver phase CSI is available. In addition, when the nodes have equal average power with receiver phase CSI only, cooperation is shown to offer no capacity improvement over a non-cooperative scheme with the same average network power. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Moreover, it is shown that full CSI is essential in transmitter cooperation, while optimal power allocation is essential in receiver cooperation

We investigate capacity and achievable rates for transmitter cooperation schemes in ad-hoc wireless networks. In addition to cooperative dirty paper coding, we propose two new cooperative transmission techniques: time-division successive broadcasting and time-division relaying. We show that transmitter cooperation can significantly increase capacity, even if one of the cooperating nodes is halfway between the transmit and receive node clusters. However, the best form of cooperation depends on the relative geometry of the transmit and receive clusters. When the transmitters are close together, cooperative dirty paper coding achieves the highest rates. However, if one of the transmitters is relatively close to the receive cluster, cooperative broadcasting or relaying achieves higher rates than dirty paper coding. That is because, at large separations, the exchange of messages between the transmitters required for dirty paper coding consumes a substantial amount of power. We show that in most cases transmitter cooperation provides a substantial capacity improvement over noncooperative techniques, especially under an equal rate constraint.