Random Signature Research Articles

Linear MMSE multiuser receivers: MAI conditional weak convergence and network capacity

We explore the performance of minimum mean-square error (MMSE) multiuser receivers in wireless systems where the signatures are modeled as random and take values in complex space. First we study the conditional distribution of the output multiple-access interference (MAI) of the MMSE receiver. By appealing to the notion of conditional weak convergence, we find that the conditional distribution of the output MAI, given the received signatures and received powers, converges in probability to a proper complex Gaussian distribution that does not depend on the signatures. This result indicates that, in a large system, the output interference of the MMSE receiver is approximately Gaussian with high probability, and that systems with MMSE receivers are robust to the randomness of the signatures. Building on the Gaussianity of the output interference, we then take the quality of service (QoS) requirements as meeting the signal-to-interference ratio (SIR) constraints and identify the network capacity of single-class systems with random spreading. The network capacity is expressed uniquely in terms of the SIR requirements and received power distributions. Compared to the network capacity corresponding to the optimal signature allocation, we conclude that at the cost of transmission power, the gap between the network capacity corresponding to optimal signatures and that corresponding to random signatures can be made arbitrarily small. Therefore, from the viewpoint of the network capacity, systems with MMSE receivers are robust to the randomness of signatures.

Analysis of acoustic dot echo signature over an Antarctic ice shelf: the possible remote sensing of Antarctic petrels

Data from a monostatic acoustic radar operating at British Antarctic Survey's Halley station on a coastal Antarctic ice shelf show a band of small target echoes at an altitude of 700–1000 m during spring 1991. Statistical analysis of the echo signature show that the targets are spread more evenly in the horizontal than would be expected for a random signature, whilst the local distribution in the vertical is Gaussian. Similar echo signatures have been observed previously, and are attributed to birds, bats or insects: the Antarctic data are also consistent with bird targets, but the case is not proven. No birds have been observed directly, but at 700 m they would be barely visible to the naked eye. The nearest nesting area with suitably large numbers of birds (Antarctic petrels, Thalassoica antarctica) is a few hundred kilometres away. Estimates of velocity and target density imply that the Halley site would need to be specially favoured by the colony for their acoustic signature to be observed in such numbers, but such might be the case due to the presence of perennial coastal open water to the west of the station.

On the reliability of a class of system identification techniques: insights from bootstrap theory

The estimation of structural damping from systems with unknown input can be particularly challenging but is vital to furthering the understanding of energy dissipation in structural motions. The random decrement technique and spectral analysis are commonly invoked system identification schemes for this problem. Although there is well-established theory regarding the bias and variance errors of power spectra and random decrement signatures, the theoretical error formulae give only approximate indications of errors inherent to the estimated dynamic properties. This study addresses this through a bootstrap approach to assess the quality of system identification by providing surrogate estimates of damping and natural frequency to generate useful statistics and confidence intervals.

A statistical analysis of random polyphase signature sequences in multipath fading DS-CDMA channels

Direct sequence code division multiple access (DS-CDMA) communication systems using random polyphase sequences with coherent reception in multipath fading channels are considered. By examining the asymptotic characteristics of the multiple access interference and multipath interference, we show that the DS-CDMA system performance with random m p -phase sequences of m p ⩾3 is better than that with random binary sequences in multipath fading environment.

Stochastic wave field solution of the 2D elastic wave equation based on the random Fourier–Stieltjes increments

An analytical solution of the stochastic wave equation is presented to model 2D heterogeneous geological environments. In the formulation, a plane-harmonic seismic wave propagates in a medium having random elastic properties in the horizontal and vertical directions. The 2D random field representation is introduced in the stiffness properties of the medium by assuming it has log-normal probability density functions. The constitutive stress and displacement laws with the momentum balance equation for total stress yield a partial differential equation, which is developed using a perturbation approach by assuming a 2D random geological medium having material heterogeneity randomly distributed in the horizontal ( x) and vertical ( z) directions. The method yields a double integral representation of the displacement wave vector based on the Green's tensor and the Fourier–Stieltjes increments. The double integral is reduced to one integral representation by removing the singularities. The final form of the integral is used to construct the stochastic wave field displacement components expressed in terms of a single integral that is appropriate for calculations. This paper also describes a numerical approach that predicts the stochastic wave field used to test the applicability of the theory by simulating a 2D randomly heterogeneous geological medium. Synthetic vertical and horizontal component seismograms based on this random medium indicate a decrease in wave amplitude and wave broadening effects at different depths of the random velocity images. The results suggest that the attenuation and dispersion of waves traveling between two wells are caused by the presence of scatterers observed in the 2D random velocity distribution. Large scatterers produce strong reflections that are observed in the random horizontal wave field seismograms. In general, the random wave field seismograms show characteristic seismic signatures that are associated with the structural distribution of the heterogeneities. In particular, random wave field signatures associated with heterogeneous low velocity zones are observed in the simulations. This kind of signature has been observed in crosswell data recorded at the Gypsy test site in Oklahoma.

On error probabilities of DS-CDMA systems with arbitrary chip waveforms

The error probabilities of asynchronous DS-CDMA systems using random signature sequences depend on the number of users, the processing gain and the chip waveforms employed. The exact calculation of the error probabilities is computationally difficult and therefore approximations and bounds are more commonly used. In this article, the improved Gaussian approximation proposed by Holtzman (1992) is extended to include arbitrary chip waveforms. Comparisons to the exact calculation and the standard Gaussian approximation are also made to evaluate the accuracy of the improved Gaussian approximation.

Multicell uplink spectral efficiency of coded DS-CDMA with random signatures

A simple multicell uplink communication model is suggested and analyzed for optimally coded randomly spread direct sequence code-division multiple access (DS-CDMA). The model adheres to Wyner's (1994) infinite linear cell-array model, according to which only adjacent-cell interference is present, and characterized by a single parameter 0/spl les//spl alpha//spl les/1. The discussion is confined to asymptotic analysis where both the number of users and the processing gain go to infinity, while their ratio goes to some finite constant. Single cell-site processing is assumed and four multiuser detection strategies are considered: the matched-filter detector, optimum detection with adjacent-cell interference treated as Gaussian noise, the linear minimum mean square error (MMSE) detector and a detector that performs MMSE-based successive interference cancellation for intracell users with linear MMSE processing of adjacent-cell interference. Spectral efficiency is evaluated under three power allocation policies: equal received powers (for all users), equal rates, and a maximal spectral efficiency policy. Comparative results demonstrate how performance is affected by the introduction of intercell interference, and what is the penalty associated with the randomly spread coded DS-CDMA strategy. Finally, the effect of intercell time-sharing protocols as suggested by Shamai and Wyner (1997) is also examined, and a significant system performance enhancement is observed.

On the use of the autocorrelation function to identify the damage in the side shell of a ship's hull

When structural damage occurs, the dynamic characteristics of the structure changes correspondingly. This can be used to detect damage occurrence. In this paper, an autocorrelation function was utilized to identify damage in the side shell of ship structures using a combination of experimental and numerical studies. A stiffened plate was used to model the side shell of a ship structure. The damage was simulated by a cut in the longitudinal near the transverse member. The cut was made using a hacksaw. An experimental study using modal testing methods was carried out to measure the random response time history of the undamaged and damaged stiffened plate model. The random response time history was used to obtain its autocorrelation function and its random decrement signature. The autocorrelation function was then compared with the random decrement signature. Finite element models were developed for the stiffened plate, in the undamaged and damaged conditions. The random responses of the model were used to obtain the autocorrelation functions. The autocorrelation functions obtained numerically were compared to the ones obtained experimentally. The results indicate that the autocorrelation functions can be used to identify the occurrence of damage in the stiffened plate model.

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.

Linear multiuser receivers in random environments

We study the signal-to-interference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in "random directions." Such a random environment may arise in a DS-CDMA system with random signature sequences, or in a system with antenna diversity where the randomness is due to channel fading. Assuming that such random directions can be tracked by the receiver, the resulting SIR performance is a function of the directions and therefore also random. We study the asymptotic distribution of this random performance in the regime where both the number of users K and the number of degrees of freedom N in the system are large, but keeping their ratio fixed. Our results show that for both the decorrelator and the minimum mean-square error (MMSE) receiver, the variance of the SIR distribution decreases like 1/N, and the SIR distribution is asymptotically Gaussian. We compute closed-form expressions for the asymptotic means and variances for both receivers. Simulation results are presented to verify the accuracy of the asymptotic results for finite-sized systems.

Information capacity of a random signature multiple-input multiple-output channel

A closed-form expression for information capacity of the random signature multiple input multiple-output channel is given. A direct calculation of the capacity is provided additional to the proof involving the capacity of minimum mean-square-error systems provided by Verdu and Shamai (see IEEE Trans. Inform. Theory, vol.45, p.622-40, 1999).

Asynchronous multiple-access interference suppression and chip waveform selection with aperiodic random sequences

A linear decentralized receiver capable of suppressing multiple-access interference (MAI) for asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems with aperiodic random signature sequences is proposed. Performance bounds on this receiver are also obtained. Using them as performance measures, the problem of chip waveform selection in DS-CDMA systems with the proposed receiver under the near-far scenario is investigated. In particular, the performance of several practical chip waveforms is compared. An LMS-type adaptive algorithm is developed to obtain the parameters needed in the receiver, which only requires the signature sequence and coarse timing information of the desired user.

A multicarrier CDMA system with adaptive subchannel allocation for forward links

Multicarrier transmission schemes have been introduced into code-division multiple access (CDMA) systems to gain advantages for high data rate transmission. One of the methods is to transmit identical narrowband direct-sequence (DS) waveforms in parallel over a number of subchannels using frequency diversity. In this paper, we propose a multicarrier CDMA system with an adaptive subchannel allocation method for forward links. In the proposed system, instead of identical DS waveforms being transmitted over a number of subchannels in parallel, each user's DS waveform is transmitted over the user's favourite subchannel which has the largest fading amplitude among all the subchannels. We analyze the performance characteristics of the system when orthogonal and random signature sequences are used. The proposed system is shown to have performance gain over the conventional multicarrier CDMA system. We also investigate how the performance is influenced when the signal is not perfectly allocated into the best subchannel.

Overlapping M-ary frequency shift keying spread-spectrum multiple-access systems using random signal sequences

A multiple-access spread-spectrum communication system using binary frequency shift keying (BFSK) or M-ary frequency shift keying (MFSK) and noncoherent demodulation is considered. In contrast to previous work typically assuming that the frequency shift keying (FSK) tones are nonoverlapping after direct-sequence (DS) spreading, here we consider a spread-spectrum multiple-access (SSMA) system under the assumption that the DS spread signals of different FSK tones are only orthogonal over the information symbol duration. Consequently, the frequency band of a spread FSK tone may be fully or partially overlapping with the other spread signals. An estimate of the variance of the multiple-access interference is obtained by assuming that the phase angles and time delays of the received signals are mutually independent random variables, provided that random signature sequences are employed for spreading. On the basis of the above assumptions, the bit error rate (BER) of our DS spread-spectrum multiple-access (DS-SSMA) and that of our hybrid DS slow frequency-hopping spread-spectrum multiple-access (DS-SFH SSMA) systems using FSK modulation is analyzed, when the channel impairments are constituted by a combination of additive white Gaussian noise (AWGN) and multiple-access interference. From our analysis and the numerical results, we concluded that, for a given system bandwidth and for a certain value of M, the system's BER performance can be optimized by controlling the amount of overlapping and that the systems with optimized overlapping outperformed the systems using no overlapping.

Optimum near-far resistance for dual-rate DS/CDMA signals: random signature sequence analysis

Optimum near-far resistance is studied for synchronous dual-rate DS/CDMA systems. Three multirate access schemes are considered: multicode (MC) access where high-rate users multiplex their data bits onto multiple codes and form a single-rate system; variable spreading length (VSL) access where the spreading lengths of signature sequences are inversely proportional to users' data rates; and variable chipping rate (VCR) access where the chipping rates of the signature sequences are proportional to users' data rates. In order to remove the influence of signature sequences in the comparison of the three schemes, random signature sequences are assumed. Optimum mar-far resistance is then averaged over all possible realizations. Two types of code sets are considered for the VSL system: general random codes and random repetition codes. Bounds and approximations are provided for the average optimum near-far resistance. Analytical results show that the performance depends on the access schemes and the data rate of the users. The results for the VSL scheme with general random codes are extended for performance evaluation of systems with signature sequences which span many symbol intervals.

On the average near-far resistance for MMSE detection of direct sequence CDMA signals with random spreading

The performance of a near-far-resistant, finite-complexity, minimum mean squared error (MMSE) linear detector for demodulating direct sequence (DS) code-division multiple access (CDMA) signals is studied, assuming that the users are assigned random signature sequences. We obtain tight upper and lower bounds on the expected near-far resistance of the MMSE detector, averaged over signature sequences and delays, as a function of the processing gain and the number of users. Since the MMSE detector is optimally near-far-resistant, these bounds apply to any multiuser detector that uses the same observation interval and sampling rate. The lower bound on near-far resistance implies that, even without power control, linear multiuser detection provides near-far-resistant performance for a number of users that grows linearly with the processing gain.

Generalized Random Decrement Method for Analysis of Vibration Data

The Random Decrement method used in system identification for analysis of random vibration data is considered from a rigorous mathematical perspective. It is shown that the Random Decrement signature deviates from the system free vibration curve of an associated linear system, unless the corresponding input excitation is white. The error induced by approximating the system excitation by a white noise process is examined. Further, a generalized Random Decrement signature is introduced; it is used to estimate efficiently the auto-correlation function of an ergodic Gaussian random process. Several examples are discussed to elucidate the theoretical developments.

Performance comparison of a slotted ALOHA DS/SSMA network and a multichannel narrow-band slotted ALOHA network

Throughput, delay, and stability for two slotted ALOHA packet radio systems are compared. One system is a slotted direct-sequence spread-spectrum multiple-access (DS/SSMA) network where each user employs a newly chosen random signature sequence for each bit in a transmitted packet. The other system is a multiple-channel slotted narrow-band ALOHA network where each packet is transmitted over a randomly selected channel. Accurate packet success probabilities for the code-division multiple-access (CDMA) system are computed using an improved Gaussian approximation technique which accounts for bit-to-bit error dependencies. Average throughput and delay results are obtained for the multiple-channel slotted ALOHA system and CDMA systems with block error correction. The first exit time (FET) is computed for both systems and used as a measure of the network stability. The CDMA system is shown to have better performance than the multiple-channel ALOHA system in all three areas.

Accurate CDMA BER calculations with low computational complexity

An accurate approximation for calculating bit error rates in direct sequence code division multiple access (CDMA) radio systems using binary phase shift keyed (BPSK) signaling is presented. All interfering users are assumed to employ random signature sequences, but the desired signal can be structured with either a random or a deterministic spreading code. Bit error probabilities are given for signals having carrier phase or chip offsets that are either deterministic or random. Computational complexity of all calculations is O(1).

Analysis of an Approximate Decorrelating Detector

In this paper an approximate decorrelating detector is analyzed on the basis of a first order approximation to the inverse crosscorrelation matrix of signature waveforms. The approximation is fairly accurate for systems with low crosscorrelations and is exact in the two-user synchronous case. We present an exact as well as approximate analysis of the bit-error-rate performance of this detector on a channel that is subject to flat fading, and also specifically for the case of random signature waveforms. The detector outperforms the conventional matched filter receiver in terms of BER. The approximate decorrelator (while not being near-far resistant like the decorrelating detector) is fairly robust to imperfections in power control. Power trade-off regions are identified which characterize the significant advantage that the approximate decorrelator provides over the matched filter receiver. The reduced complexity of the approximate decorrelator and performance gains over the conventional matched filter makes it a viable alternative for implementation in practical CDMA systems, in particular in those where the signature waveforms span many symbol intervals.