It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multiple-input multiple-output (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schur-concave and Schur-convex functions. Once the optimal structure of the transmit-receive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closed-form expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peak-to-average ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel water-filling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.

Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.

/pdf/a-tutorial-on-geometric-programming-47sdznbzxw.pdf

A tutorial on geometric programming

Ad hoc wireless networks enable new and exciting applications, but also pose significant technical challenges. In this article we give a brief overview of ad hoc wireless networks and their applications with a particular emphasis on energy constraints. We then discuss advances in the link, multiple access, network, and application protocols for these networks. We show that cross-layer design of these protocols is imperative to meet emerging application requirements, particularly when energy is a limited resource.

Design challenges for energy-constrained ad hoc wireless networks

In wireless cellular or ad hoc networks where Quality of Service (QoS) is interference-limited, a variety of power control problems can be formulated as nonlinear optimization with a system-wide objective, e.g., maximizing the total system throughput or the worst user throughput, subject to QoS constraints from individual users, e.g., on data rate, delay, and outage probability. We show that in the high Signal-to- interference Ratios (SIR) regime, these nonlinear and apparently difficult, nonconvex optimization problems can be transformed into convex optimization problems in the form of geometric programming; hence they can be very efficiently solved for global optimality even with a large number of users. In the medium to low SIR regime, some of these constrained nonlinear optimization of power control cannot be turned into tractable convex formulations, but a heuristic can be used to compute in most cases the optimal solution by solving a series of geometric programs through the approach of successive convex approximation. While efficient and robust algorithms have been extensively studied for centralized solutions of geometric programs, distributed algorithms have not been explored before. We present a systematic method of distributed algorithms for power control that is geometric-programming-based. These techniques for power control, together with their implications to admission control and pricing in wireless networks, are illustrated through several numerical examples.

/pdf/power-control-by-geometric-programming-2799lyyh3b.pdf

Power Control By Geometric Programming

We propose a new method of power control for interference-limited wireless networks with Rayleigh fading of both the desired and interference signals Our method explicitly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair We establish several results for this type of problem We establish tight bounds that relate the outage probability caused by channel fading to the signal-to-interference margin calculated when the statistical variation of the signal and interference powers is ignored This allows us to show that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (ie, minimal) outage probability We show that the problems of minimizing the transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP) A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by interior-point methods We also give a fast iterative method for finding the optimal power allocation to minimize the outage probability

/pdf/optimal-power-control-in-interference-limited-fading-4dn1xx7gmt.pdf

Optimal power control in interference-limited fading wireless channels with outage-probability specifications

We consider a wireless multimedia CDMA system, where the different mobiles transmit at different rates. We devise a method of simultaneously optimizing the power and rate at which the different terminals transmit for achieving their required quality of service (QoS). The QoS is defined to be the effective data rate which is different from the transmission rate. Optimization of power enhances battery life and optimization of data transmission rates facilitates in building cheaper and power efficient mobile systems. The joint optimization problem is formulated so that for a specified QoS, the total power transmitted by all the mobiles, and the sum of the transmitting rates of different mobiles can be minimized. The optimization problem is shown to be a non-linear and non-convex problem, but is solved to get a globally optimal solution using geometric programming. Results show that with optimized rates and powers, we can obtain better QoS than that obtained by present systems which use higher power.

https://ieeexplore.ieee.org/iel5/7047/18971/00876498.pdf

S. Kandukuri

Papers

Optimal power control in interference-limited fading wireless channels with outage-probability specifications

Simultaneous rate and power control in multirate multimedia CDMA systems