Chris T. K. Ng

Linear Precoding in Cooperative MIMO Cellular Networks with Limited Coordination Clusters

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 users message is only routed to those that participate in the users 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.

Capacity Gain From Two-Transmitter and Two-Receiver Cooperation

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.

Distortion Minimization in Gaussian Layered Broadcast Coding With Successive Refinement

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.

Transmitter cooperation in ad-hoc wireless networks: does dirty-paper coding beat relaying?

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.

The impact of CSI and power allocation on relay channel capacity and cooperation strategies

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 decode-and- 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.

Transmit Signal and Bandwidth Optimization in Multiple-Antenna Relay Channels

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.

Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement

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.

Recursive Power Allocation in Gaussian Layered Broadcast Coding with Successive Refinement

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.

Joint coding and scheduling optimization in wireless systems with varying delay sensitivities

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.

Capacity and Power Allocation for Transmitter and Receiver Cooperation in Fading Channels

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.