The geometry of the capacity region for CDMA systems with general power constraints

Access-control strategies and rational pricing in code-division multiple-access (CDMA) systems need exact knowledge of the available transmission capacity and its limiting boundaries. We use the term "capacity region" to specify the set of user-transmission demands that can be supported at the desired quality of service (QoS). In this paper, we investigate the geometrical properties of the capacity region for a fixed number of users in a CDMA radio network under general QoS characteristics and general power constraints. It turns out that, under very mild assumptions, the capacity region is convex, and has an appealing monotonicity property. As a side result, we develop an elementary theory for characterizing the existence of solutions to systems of linear equations with nonnegative elements, analogous to Perron-Frobenius' theory, but bypassing irreducibility.     

Direct sequence CDMA power control, interleaving, and coding

The authors develop and analyze models of power control that consider other aspects of code-division multiple access (CDMA) systems, such as interleaving and coding on the land mobile radio channel. The orientation is that a power control scheme keeps the received powers at the base station almost equal, and the performance degradation incurred if the powers are not exactly equal will be quantified. In doing so, the authors consider the performance implications of control latency and a maximum speech delay constraint. Because of positive correlations between the fading channel amplitudes, the effectiveness of the combination of interleaving and coding in combating the effects of power variations due to slow Rayleigh fading is reduced. It is shown that power control and interleaving/coding are most effective in complementary parameter regions, thus providing a degree of robustness for both fast and slow Rayleigh fading     

Uplink capacity optimization by power allocation for multimedia CDMA networks with imperfect power control

A closed-form capacity quasi-optimal power allocation scheme is presented for the uplink of multimedia code-division multiple-access (CDMA) systems with randomized received signal-to-interference ratio (SIR) resulted from the errors of power control. The optimality in capacity comes from that this scheme provides class-dependent SIR margins subject to the constraint of differentiated outage requirements. The statistics of signal under imperfect power control is modeled as lognormal random variable. The objective of capacity maximization is formulated as the minimization of total average received powers since the capacity of a CDMA system is interference limited. Under this model, we first derive the necessary conditions that a capacity-optimal power allocation should satisfy. By using conservative bounds, we provide a closed-form approximate solution to this optimization problem. This approximate solution provides nearly the same admissible region for multimedia traffic under imperfect power control as the accurate solution (the optimal one) does. The closed-form quasi-optimal power allocation scheme proposed in this paper is just based on this approximate solution. By numerical example we verify our analysis and show that great capacity gain (e.g., 92% as a maximum in the example) can be achieved by our scheme over its counterpart.     

Combined multidimensional signaling and transmit diversity forhigh-rate wide-band CDMA

Multidimensional signaling is newly designed to provide a diversity gain of order 2 using two transmit antennas in uplink transmission of wide-band CDMA (W-CDMA) while achieving high and multiple data rates at the same time. The rate can be easily changed on the slot basis in a frame transmission by adapting the order of multidimensional signaling to the incoming traffic. The multidimensional signaling of order zero simply reduces to conventional multicode scheme, so there exists a tradeoff between rate and complexity. Also, the use of multidimensional signaling results in far reduced envelope variations at the maximum rate. With the transmit diversity, the uplink signal-to-interference ratio (SIR) will be further stabilized to meet the requirements of multimedia traffic. Statistics of interferences are characterized in terms of their second- and fourth-order moments from which diversity gain is theoretically verified. For realistic multipath fading channels, considering both equal and unequal average path powers, the average probability of symbol error is obtained in compact form, in which the two schemes, multidimensional signaling with and without transmit diversity are compared, and then with nonmulticode scheme in view of the bit error rate (BER). Numerical and simulation results show that the multidimensional signal with transmit diversity provides a significant gain over that with no diversity, and furthermore outperforms nonmulticode scheme subject to the same signal energy per bit and chip rate     

CDMA systems in fading channels: admissibility, network capacity,and power control

We study the admissibility and network capacity of imperfect power-controlled code-division multiple access (CDMA) systems with linear receivers in fading environments. In a CDMA system, a set of users is admissible if their simultaneous transmission does not result in violation of any of their quality-of-service (QoS) requirements; the network capacity is the maximum number of admissible users. We consider a single-cell imperfect power-controlled CDMA system, assuming known received power distributions. We identify the network capacities of single-class systems with matched-filter (MF) receivers for both the deterministic and random signature cases. We also characterize the network capacity of single-class systems with linear minimum-mean-square-error (MMSE) receivers for the deterministic signature case. The network capacities can be expressed uniquely in terms of the users' signal-to-interference ratio (SIR) requirements and received power distributions. For multiple-class systems equipped with MF receivers, we find a necessary and sufficient condition on the admissibility for the random signature case, but only a sufficient condition for the deterministic signature case. We also introduce the notions of effective target SIR and effective bandwidth, which are useful in determining the admissibility and hence network capacity of an imperfect power-controlled system     

Performance analysis of CDMA with imperfect power control

The standard correlation receiver for code-division multiple access (CDMA) systems is susceptible to the near-far problem. Power control techniques attempt to overcome near-far effects by varying transmitted power levels to ensure that all signals are received with equal power levels. Since these algorithms cannot perfectly compensate for power fluctuations in a mobile communications channel, the capacity of the system is reduced for a given bit-error rate (BER). This paper examines the performance of a CDMA system using imperfect power control by extending analytical techniques that account for multiple access interference. Single cell capacity is compared with systems employing perfect power control     

On antenna design and capacity analysis for the forward link of amultibeam power controlled satellite CDMA network

This paper deals with the problem of rigorously analyzing the forward link behavior of a power controlled CDMA-based satellite multibeam communication system. For the first time, the complete system links equations are expressed in a compact matrix form so that they can be solved simultaneously, thus leading to an exact problem solution. In particular the effect of actual antenna beam patterns, overlapping satellites interference, users location, conventional and linear blind minimum output energy (MOE) CDMA detectors are accounted for by comprehensive system analysis. Under simplified yet realistic system assumptions, the proposed technique allows us to derive the key satellite antenna parameters. It is shown that for power controlled CDMA satellite networks, the key antenna figure of merit is the average gain and the so-called antenna inverse average interference-to-carrier ratio rather than the more intuitive average carrier-to-interference ratio. It is shown that under simplified system assumptions, these parameters can be used to compute simple yet accurate one-dimensional system link budget. Also, by means of a simplified system analysis, the antenna beam overlapping point capacity impact is determined. Furthermore, results about system capacity and outage probability for a practical personal communication satellite network are presented with and without adopting an advanced CDMA MOE single-user detector. The MOE advantages in terms of capacity increase for a given outage probability are shown to be substantial when the system loading is appreciable, even assuming perfect power control     

Unified framework for the analysis and design of linear uplink power control in CDMA systems

In this work, it is proposed a unified framework to design and analyze uplink distributed power control schemes over flat-fading channels from a control theory perspective. The effects of linear detectors and round trip delays are explicitly characterized in this study. First, the optimal solution to the power minimization problem under signal to interference-noise ratio (SINR) restrictions is reviewed, where sufficient conditions for its existence are presented that depends on the detection strategy. Four different linear detection schemes are studied in this work: Matched Filter, Decorrelator, MMSE and Projector. Specifically, two special cases are analyzed with respect to the spreading codes properties: uniform cross-correlation and orthogonal codes, and under both conditions an explicit expression for the central solution is obtained. Nevertheless, one drawback of the central solution is its lack of robustness against channel estimation errors, transport delays and noise. Hence, it is proposed closed-loop control laws with linear power assignment which are capable of provide robustness to these channel effects. It is then presented that under certain conditions, stable feedback loops can be obtained considering SINR quantification, transmission and processing delays, and the resulting closed-loop power solutions tend to the central ones. Finally, it is illustrated that the selection of the linear detectors does not affect the resulting closed-loop dynamics, but the uplink transmission power in steady-state. An exhaustive simulation evaluation is included to validate the mathematical analysis presented for open and closed-loop solutions.     

Capacity and power control for CDMA microcells

Capacity and power control issues are considered for urban CDMA microcells that operate on channels characterized by log-normal shadowing and Nakagami fading. The effects of fading on the desired and interfering signals, variations in the shadow standard deviation, imperfect power control, and the requiredE _b /N _o for satisfactory link operation are investigated. It is shown that the reverse channel is relatively insensitive, and the forward channel very sensitive, to shadow and fading variations. Power control error is shown to significantly degrade reverse channel capacity. Twobiased forward channel power control strategies are introduced to enhance existing unbiasedbalancing forward channel power control algorithms.This research has been supported by BNR Inc.     

DS/CDMA closed-loop power control with adaptive algorithm

Closed-loop power control in the reverse link of a DS/CDMA system is analysed. The transmitter/receiver based on IS-95 and the radio propagation channel under mobile communication environments are modelled and a new power control algorithm is proposed. This algorithm utilises the burst error characteristics of the channel and can be directly applied to the current IS-95 system. The new power control algorithm, with respect to the SIR (signal to interference ratio), increases the service quality, and finally, enhances the system capacity     

Simulation of CDMA system performance with feedback power control

The authors present a summary of the results of a study on CDMA feedback power control in multipath fading radio channels. The signal and interference statistics after power control are presented for a simulated radio system which includes multiple base stations. It is shown that often used analyses based on perfect average power control lead to optimistic capacity results because interference is underestimated by 1-2 dB.<>     

基于CDMA系统的加速功率控制和多用户检测

本文中的算法是交织了一个固定点功率控制算法,该算法是利用以多用户检测MMSE为标准的Aitken's过程加速的.通过应用于MMSE滤波器的扩展Steffensen算法,得自关于Lipshitz常量的一个下限.Lipshitz常量是用来保证所提算法的收敛性.此算法体现了渐进二次收敛,是以牛顿方法为基准.最后给出了仿真结果.     

Outer loop power control in CDMA satellite systems with on-board power constraints

This paper aims at clarifying the role of the outer loop power control for CDMA satellite systems with on-board power constraints. If the inner loop of the power control is perfect, the channel turns into a AWGN channel and there is no need of the outer loop. In satellite CDMA systems, due to the longer propagation delay with respect to a terrestrial system, the inner loop of power control is only partly able to track power variations due to fast fading. Moreover, the Rice factor, which characterizes the channel statistics, can widely vary even if the user does not move but just because of the change of the elevation angle. Because of that, a wide range of target SNIR (and larger than in typical terrestrial systems) may be necessary to get the same BER performance. Therefore, the outer loop power control turns out to be essential to minimize the dynamic of the power link margins and avoid capacity degradations induced by the systematic use of static link margins. A semi-analytical model for the capacity evaluation has been developed, which is specifically intended for the power-limited satellite-to-mobile link with multi satellite reception. We found that the capacity gain with respect to a pure SNIR-based strategy (i.e., only inner loop) can reach the 40% of the total capacity in a single reception scheme. A smaller, but still noticeable capacity gain of the order of 20 - 30% is observed in presence of satellite diversity. Therefore, any dimensioning of CDMA satellite systems should not neglect this component of the power control.     

Optical CDMA with time hopping and power control for multimedia networks

Optical code-division multiple access (OCDMA) for high-speed multimedia transmission is proposed and its performance is investigated. The proposed system introduces time hopping to vary transmission bit rate and power control to control transmission signal performance, which allows various signals with different desired rate and performance. An expression for the bit error rate (BER) of the proposed system is derived and numerical results are shown. An optical power selector (OPS) coupled with a hard limiter are also proposed to improve system performance. The OPS is a device to transmit the instantaneous maximum optical power among input signals. The OPS combined with the optical hard limiter reduces the interference from simultaneous users which results in an improved BER. BER is theoretically derived and numerical results for some parameters are shown. We show that the proposed system significantly improves BER and is an attractive scheme for future multimedia networks.     

宽带CDMA网络非理想功率控制下的CAC策略

针对多媒体业务的CAC(call admission control)策略,给出了宽带CDMA(code division multiple access)网络中非理想功率控制下和外小区干扰因子对系统容量的影响分析.针对语音、视频和数据等多媒体业务的QoS(quality of service)要求,给出了一种基于QoS保证的CAC策略.仿真结果表明,非理想功率控制对系统容量有显著的影响,该策略能有效地保证不同业务的QoS需求,并明显地提高系统资源利用率.     

Symmetric capacity and signal design for L-out-of-Ksymbol-synchronous CDMA Gaussian channels

We consider the symbol-synchronous Gaussian L-out-of-K code-division multiaccess channel, and obtain the capacity region and the upper and lower bounds to the symmetric capacity. The capacity region is found to be the same with or without frame synchronism. The lower bound depends on the signature waveforms through the eigenvalues of the SNR-weighted crosscorrelation matrix. We find a sufficient condition for the signature waveform set to maximize this lower bound and give an algorithm to construct a set of signature waveforms satisfying the sufficient condition     

Forward-link soft-handoff in CDMA with multiple-antenna selection and fast joint power control

We consider forward-link soft-handoff with multiple antenna selection and fast joint power control at high data rates in a cellular code-division multiple-access network, where signals are directed to a mobile station (MS) from antennas located at the same or different base stations. The total power transmitted to any mobile is divided among the active antennas selected according to the momentary channel conditions so as to maximize the signal-interference ratio at each MS. Multiple-antenna selection is used to mitigate the effects of both short- and long-term fading, and achieve the best soft-handoff with respect to system capacity and complexity. To achieve capacity gains with soft-handoff, we derive optimum handoff thresholds corresponding to the optimum handoff region in different cell environments. Numerical results demonstrate that under high Doppler spread and large handoff-delay conditions, the proposed soft-handoff employing two transmit antennas and the optimum handoff threshold achieves a significant gain in microcell environments, but not in macrocell environments.     

Ratioed power and rate control for CDMA wireless networks

We propose in this paper the ratioed power and rate control (RPRC) algorithm to satisfy the requirements of both the data rate and the signal quality. During the execution of the RPRC algorithm, only the representative user in each cell adjusts its power level according to certain distributed power control algorithm, and the ratio of the power level for the non‐representative user to that for the representative user is kept constant. When the RPRC algorithm is finished, the power levels for all users remain unchanged and the transmission rate is determined by the available rate. We show that the RPRC algorithm can be used for allocating the bandwidth of each cell and achieving the required rate of each user. Furthermore, simulation results reveal that the RPRC algorithm results in larger throughput and finds a feasible power set faster than the other algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimum power control for CDMA with deterministic sequences in fading channels

We specify the capacity region for a power-controlled, fading code-division multiple-access (CDMA) channel. We investigate the properties of the optimum power allocation policy that maximizes the information-theoretic ergodic sum capacity of a CDMA system where the users are assigned arbitrary signature sequences in a frequency flat-fading environment. We provide an iterative waterfilling algorithm to obtain the powers of all users at all channel fade levels, and prove its convergence. Under certain mild conditions on the signature sequences, the optimum power allocation dictates that more than one user transmit simultaneously in some nonzero probability region of the space of all channel states. We identify these conditions, and provide an upper bound on the maximum number of users that can transmit simultaneously at any given time. Using these properties of the sum capacity maximizing power control policy, we also show that the capacity region of the fading CDMA channel is not in general strictly convex.