Performance bounds for turbo-coded modulation systems

We apply the standard union bound to turbo-coded modulation systems with maximum-likelihood decoding. To illustrate the methodology, we explicitly derive the bounds for the 2-bits/s/Hz 16 QAM system. Generalization of this bound to other turbo-coded modulation systems is straightforward. As in the case of the standard union bound for turbo codes, we expect these bounds to be useful for rather large values of signal-to-noise ratios, i.e., signal-to-noise ratios for which the code rate is smaller than the corresponding cutoff rate. The bound is based on “uniform interleaving” just as its counterpart for standard turbo coding. The derived bound provides a tool for comparing coded modulation schemes having different component codes, interleaver lengths, mappings, etc., using maximum-likelihood decoding. It is also useful in studying the effectiveness of various suboptimal decoding algorithms. The bounding technique is also applicable to other coded-modulation schemes such as serially concatenated coded modulation     

Performance bounds for turbo-coded multiple antenna systems

We derive performance bounds for turbo-coded systems with transmit and receive antenna diversity. The bounds are derived by limiting the conditional union bound before averaging over the fading process. It is demonstrated that this approach provides a tight upper bound on the error probability of the turbo-coded multiple antenna systems. We also describe a method for deriving the weight-enumerating function of turbo-coded multiple antenna systems in order to take into account the presence of transmit and receive antenna diversity. Examples of the bounds are presented to illustrate their usefulness.     

Performance bounds for optimum multiuser DS-CDMA systems

In this letter we estimate the bit error probability (BEP) of optimum multiuser detection for synchronous and asynchronous code division multiple access (CDMA) systems on Gaussian and fading channels. We first compute an upper bound and a lower bound on the bit error probability for a given spreading code, then average the bounds over a few thousand sets of spreading codes. These bounds are obtained from a partial distance spectrum. On Gaussian channels, the upper bound converges to the lower bound at moderate to large signal-to-noise ratios. However, on fading channels the upper bound does not converge, hence we present our results for the lower bound only. The numerical results show that: 1) the BEP of a 31-user CDMA system with binary random spreading codes of length 31 is only two to four times higher than the BEP of the single user system; 2) the number of users that can be accommodated in an asynchronous CDMA system is larger than the processing gain; and 3) optimum multiuser detection outperforms linear detection (e.g., the decorrelating detector) by about 2.8 to 5.7 dB     

Performance bounds for power control supported DCA-algorithms inhighway micro cellular radio systems

To achieve a high spectrum efficiency in cellular radio systems, the radio resource allocation algorithms have to be adaptive to the actual traffic and interference situation. The focus of the paper is on performance bounds of a cellular radio system using dynamic channel assignment (DCA) combined with power control (PC). A trivial upper bound on the performance is identified. The bound is given by the performance of a hypothetical system which is able to use all channels simultaneously in all cells. A lower bound on the performance is derived from a theoretical PC supported DCA-algorithm. For a highway micro cellular system and a deterministic propagation model, numerical results show that the lower and upper bounds are tight. That is, the results indicate that it is possible to use all channels in all cells simultaneously and still provide an acceptable signal-to interference ratio in all assigned communication links     

Performance bounds for adaptive estimation

The performance of adaptive state estimators for linear dynamic systems is investigated. The adaptive state estimates are formed under the assumption that the unknown system parameter belongs to a finite set and is thus readily implementable. It is shown that, for the true parameter value in a prescribed region in the parameter space, the corresponding a posteriori probablity (or weighting coefficient in the adaptive estimator) converges exponentially in the vth mean (v > 1) and almost surely to unity. The analysis is based on the asymptotic per sample formula for the Kullback information function, which is derived in this paper. The significance of the analysis for applications is also examined.     

Performance bounds for VDE-SAT R-Mode

There has been growing interest within the satellite navigation community in the possibility of delivering positioning and timing services from existing or emerging constellations of Low-Earth Orbit communication satellites. At the same time, the international maritime community has been investigating the potential use of communication signals transmitted from shore-based stations for positioning—a concept commonly referred to as ‘ranging mode’, or R-Mode. The driving force for these developments is the desire to reduce the reliance on traditional Global Navigation Satellite Systems (GNSS). One of the technologies being considered for use in R-Mode is the evolution of the Automatic Identification System (AIS) known as the Very High Frequency Data Exchange System (VDES). VDES has a terrestrial and a satellite component. The feasibility of using terrestrial VDES transmissions for ranging was studied in a previous publication by the authors. This paper builds on the previous study and extends its results to the satellite component of VDES. Statistical bounds on the ranging error are derived for all downlink waveforms currently being considered for use in satellite VDES and for several custom-designed transmission formats. The analysis supports the feasibility of using both the existing and custom waveforms in ranging applications and points to related trade-offs that will need to be considered in the design of satellite VDES R-Mode systems.     

Performance bounds for linear MMSE receivers in CDMA systems with partial channel knowledge

In code division multiple access (CDMA) systems employing linear adaptive receivers, the detector is typically estimated directly from the received signals, based on some partial knowledge about the system, e.g., signature waveforms of one or several users. We derive the Cramer-Rao lower bounds on the covariances of the estimated linear detectors, under three different assumptions on the mechanism for estimating the detectors, namely, a) finite-alphabet-based (FA) blind detectors, b) constant-modulus-based (CM) blind detectors, and c) second-order-moments-based (SO) blind detectors. These bounds translate into the upper bounds on the achievable signal-to-interference-plus-noise ratio (SINR) by the corresponding adaptive receivers. The results are asymptotic in nature, either for high signal-to-noise ratio (SNR) or for large signal sample size. The effects of unknown multipath channels on these performance bounds are also addressed. Numerical results indicate that while the existing subspace blind or group-blind detectors perform close to the SINR bound for the SO detectors, the SINR bounds for the FA and CM detectors are significantly higher, which suggests potential avenues for developing more powerful adaptive detectors by exploiting more structural information from the system.     

Performance bounds for flow control protocols

We discuss a simple conceptual framework for analyzing the flow of data in integrated services networks. The framework allows us to easily model and analyze the behavior of open loop, rate based flow control protocols, as well as closed loop, window based flow control protocols. Central to the framework is the concept of a service curve element, whose departure process is bounded between the convolution of the arrival process with a minimum service curve and the convolution of the arrival process with a maximum service curve. Service curve elements can model links, propagation delays, schedulers, regulators, and window based throttles. The mathematical properties of convolution allow us to easily analyze complex configurations of service curve elements to obtain bounds on the end-to-end performance. We demonstrate this by examples, and investigate tradeoffs between buffering requirements, throughput, and delay, for different flow control strategies     

Performance bounds for multistep prediction-based blindequalization

Blind equalization attempts to remove the interference caused by a communication channel without using any known training sequences. Blind equalizers may be implemented with linear prediction-error filters (PEFs). For many practical channel types, a suitable delay at the output of the equalizer allows for achieving a small estimation error. The delay cannot be controlled with one-step predictors. Consequently, multistep PEF-based algorithms have been suggested as a solution to the problem. The derivation of the existing algorithms is based on the assumption of a noiseless channel, which results in zero-forcing equalization. We consider the effects of additive noise at the output of the multistep PEF. Analytical error bounds for two PEF-based blind equalizers in the presence of noise are derived. The obtained results are verified with simulations. The effect of energy concentration in the channel impulse response on the error bound is also addressed     

Performance bounds for space-time trellis codes

We derive the union bound for space-time trellis codes over quasi-static fading channels. We first observe that the standard approach for evaluating the union bound yields very loose, in fact divergent, bounds over the quasi-static fading channel. We then develop a method for obtaining a tight bound on the error probability. We derive the union bound by performing expurgation of the standard union bound. In addition, we limit the conditional union bound before averaging over the fading process. We demonstrate that this approach provides a tight bound on the error probability of space-time codes. The bounds can be used for the case when the fading coefficients among different transmit/receive antenna pairs are correlated as well. We present several examples of the bounds to illustrate their usefulness.     

Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data

This paper on performance analysis of parameter estimation is motivated by a practical consideration that the data length is finite. In particular, for time-varying systems, we study the properties of the well-known forgetting factor least-squares (FFLS) algorithm in detail in the stochastic framework, and derive upperbounds and lowerbounds of the parameter estimation errors (PEE), using directly the finite input-output data. The analysis indicates that the mean square PEE upperbounds and lowerbounds of the FFLS algorithm approach two finite positive constants, respectively, as the data length increases, and that these PEE upperbounds can be minimized by choosing appropriate forgetting factors. We further show that for time-invariant systems, the PEE upperbounds and lowerbounds of the ordinary least-squares algorithm both tend to zero as the data length increases. Finally, we illustrate and verify the theoretical findings with several example systems, including an experimental water-level system.     

Distortion bounds for vector quantizers with finite codebook size

Upper and lower bounds are presented for the distortion of the optimal N-point vector quantizer applied to k-dimensional signals. Under certain smoothness conditions on the source distribution, the bounds are shown to hold for each and every value of N, the codebook size. These results extend bounds derived in the high-resolution limit, which assume that the number of code vectors is arbitrarily large. Two approaches to the upper bound are presented. The first, constructive construction, achieves the correct asymptotic rate of convergence as well as the correct dependence on the source density, although leading to an inferior value for the constant. The second construction, based on a random coding argument, is shown to additionally achieve a value of the constant which is much closer to the best known result derived within the asymptotic theory. Lower bound results derived in the correspondence are again shown to possess the correct asymptotic form and yield a constant which is almost indistinguishable from the best value achieved in the asymptotic regime. Finally, application of the results to the problem of source coding yields upper bounds on the distortion rate function for a wide class of processes     

Performance bounds for trellis-coded modulation on time-dispersivechannels

The performance of trellis-coded modulation (TCM) on additive white Gaussian noise channels is well understood, and tight analytical bounds exist on the probability of the Viterbi decoder making a decision error. When a channel is also time-dispersive, the performance of TCM systems has been studied mainly by simulation. However, simulation is limited to symbol error probabilities greater than 10^-6 and is not a particularly useful tool for designing codes. Tight analytical bounds on the error probability of TCM on time-dispersive channels are required for a more thorough study of performance. Moreover, the design of good codes and optimum metrics for time-dispersive channels requires tight analytical bounds. In this paper we derive analytical upper bounds, which, although requiring numerical techniques for tractable evaluation, are tight for a wide range of time-dispersive channel conditions. The bounds are based on a union bound of error events that leads to a summation of pairwise error probabilities, which are themselves upper bounded     

Quantization error bounds for hybrid control systems

A useful quantization error bound is obtained for hybrid digital-analog control systems. The error is bounded by a time-varying function that becomes zero if the digital computer has no time or ordinate quantization error. The error bound may either converge or diverge depending on the magnitudes involved. The analysis is valid for a hybrid computerization of a linear time-varying system. Sharp results for the constant coefficient case are presented.     

Performance bounds of a multiple-step paging strategy in future universal mobile telecommunication systems

In future mobile telecommunications, due to the huge number of users and the specific functions that support mobility, a significant amount of signaling load will have to be carried by the finite capacity of the radio link. Hence, methods aiming at radio link signaling load reduction are welcome. In this paper we propose and analyze a method that saves paging signaling load by exploiting information related to the terminal location during the most recent interaction between the terminal and the network. The penalty paid is extra processing power and extra paging delays. An analytical model is developed so as to describe the performance versus traffic intensity and mobility conditions. The performance of the proposed paging scheme is investigated, and it is shown that the method operates well even in the worst case, which is the high user mobility conditions. Possible extensions of the method, which exploit information related to the mobility degree of each individual user or information characterizing the mobility conditions in a certain location area, are also proposed.This paper has been partially funded by CEC through the RACE 2066 Mobile Network (MONET) project. The paper does not present the views of the project as a whole, but those of the authors.     

Performance of vector perturbation multiuser MIMO systems with limited feedback

This paper considers the multiuser multiple-input multiple-output (MIMO) Rayleigh fading broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via a multiuser technique known as vector perturbation. We propose lattice-theoretic and rate-distortion based approaches to analyze the performance of these systems, taking into account the practical restrictions imposed by limited feedback and training. We show that performance is primarily determined by the ratio between the number of users and the number of transmit antennas. We then propose a new practical low-complexity low-rate feedback scheme, and show that the performance approaches the ideal rate-distortion based scheme.     

Bonferroni-type bounds for CDMA systems with nonuniform signalling

This letter develops Bonferroni-type lower and upper bounds of the bit-error-rate (BER) performance for the optimal multiuser detector of code-division multiple access (CDMA) systems with nonuniform signalling. The bounds are shown to be very tight for all signal-to-noise ratios. The bounds are also tighter than the Verdu's bounds of the maximum-likelihood (ML) multiuser detector for the case of uniform signalling.     

Cramer-Rao bounds for estimating range, velocity, and directionwith an active array

We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model. Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional (3-D) array with isotropic sensors in spatially white noise and show that it is a function of the array geometry only through the “moments of inertia” of the array. The volume of the confidence region for the target's location is proposed as a measure of accuracy. For this measure, we show that the highest (and lowest) target location accuracy is achieved if the target lies along one of the principal axes of inertia of the array. Finally, we compare the location accuracies of several array geometries     

Performance bounds on image registration

Registration is a fundamental step in image processing systems where there is a need to match two or more images. Applications include motion detection, target recognition, video processing, and medical imaging. Although a vast number of publications have appeared on image registration, performance analysis is usually performed visually, and little attention has been given to statistical performance bounds. Such bounds can be useful in evaluating image registration techniques, determining parameter regions where accurate registration is possible, and choosing features to be used for the registration. In this paper, Crame/spl acute/r-Rao bounds on a wide variety of geometric deformation models, including translation, rotation, shearing, rigid, more general affine and nonlinear transformations, are derived. For some of the cases, closed-form expressions are given for the maximum-likelihood (ML) estimates, as well as their variances, as space permits. The bounds are also extended to unknown original objects. Numerical examples illustrating the analytical performance bounds are presented.     

Interference bounds in power controlled systems

Capacity in a code-division multiple access (CDMA) cellular system is often referred to in terms of the maximum number of users that can be supported within a carrier to interference ratio above a specified quality threshold. This paper presents a simple analysis showing that the total mean interference in the reverse channel, in a multi-tier scenario of a CDMA system with power control, is finite regardless of the number of surrounding tiers. Riemann-Hurwitz analysis is introduced in order to obtain upper and lower interference bounds