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Register a new userSum Capacity Bounds and Design of Suboptimal Codes for Asynchronous CDMA Systems
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Added by
Shayan Dashmiz
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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In this paper, we study two issues in asynchronous communication systems. The first issue is the derivation of sum capacity bounds for finite dimensional asynchronous systems. In addition, asymptotic results for the sum capacity bounds are obtained. The second issue is the design of practical suboptimal codes for binary chip asynchronous CDMA systems that become optimal for high Signal-to-Noise (SNR) ratios. The performance of such suboptimal codes is also compared to Gold and Optical Orthogonal codes. The conclusion is that the proposed suboptimal codes perform favorably compared to other known codes for high SNR asynchronous systems and perform more or less the same as the other codes for the low SNR values.
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Totally asynchronous code-division multiple-access (CDMA) systems are addressed. In Part I, the fundamental limits of asynchronous CDMA systems are analyzed in terms of spectral efficiency and SINR at the output of the optimum linear detector. The focus of Part II is the design of low-complexity implementations of linear multiuser detectors in systems with many users that admit a multistage representation, e.g. reduced rank multistage Wiener filters, polynomial expansion detectors, weighted linear parallel interference cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay distribution on CDMA with suboptimum linear receiver structures are investigated. Recursive expressions for universal weight design are given. The performance in terms of SINR is derived in the large-system limit and the performance improvement over synchronous systems is quantified. The considerations distinguish between two ways of forming discrete-time statistics: chip-matched filtering and oversampling.
We derive simplified sphere-packing and Gilbert--Varshamov bounds for codes in the sum-rank metric, which can be computed more efficiently than previous ones. They give rise to asymptotic bounds that cover the asymptotic setting that has not yet been considered in the literature: families of sum-rank-metric codes whose block size grows in the code length. We also provide two genericity results: we show that random linear codes achieve almost the sum-rank-metric Gilbert--Varshamov bound with high probability. Furthermore, we derive bounds on the probability that a random linear code attains the sum-rank-metric Singleton bound, showing that for large enough extension fields, almost all linear codes achieve it.
This paper investigates the H2 and H-infinity suboptimal distributed filtering problems for continuous time linear systems. Consider a linear system monitored by a number of filters, where each of the filters receives only part of the measured output of the system. Each filter can communicate with the other filters according to an a priori given strongly connected weighted directed graph. The aim is to design filter gains that guarantee the H2 or H-infinity norm of the transfer matrix from the disturbance input to the output estimation error to be smaller than an a priori given upper bound, while all local filters reconstruct the full system state asymptotically. We provide a centralized design method for obtaining such H2 and H-infinity suboptimal distributed filters. The proposed design method is illustrated by a simulation example.
Spectral efficiency for asynchronous code division multiple access (CDMA) with random spreading is calculated in the large system limit allowing for arbitrary chip waveforms and frequency-flat fading. Signal to interference and noise ratios (SINRs) for suboptimal receivers, such as the linear minimum mean square error (MMSE) detectors, are derived. The approach is general and optionally allows even for statistics obtained by under-sampling the received signal. All performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit. It turns out that synchronizing users on a chip level impairs performance for all chip waveforms with bandwidth greater than the Nyquist bandwidth, e.g., positive roll-off factors. For example, with the pulse shaping demanded in the UMTS standard, user synchronization reduces spectral efficiency up to 12% at 10 dB normalized signal-to-noise ratio. The benefits of asynchronism stem from the finding that the excess bandwidth of chip waveforms actually spans additional dimensions in signal space, if the users are de-synchronized on the chip-level. The analysis of linear MMSE detectors shows that the limiting interference effects can be decoupled both in the user domain and in the frequency domain such that the concept of the effective interference spectral density arises. This generalizes and refines Tse and Hanlys concept of effective interference. In Part II, the analysis is extended to any linear detector that admits a representation as multistage detector and guidelines for the design of low complexity multistage detectors with universal weights are provided.
The optimal spectral efficiency and number of independent channels for MIMO antennas in isotropic multipath channels are investigated when bandwidth requirements are placed on the antenna. By posing the problem as a convex optimization problem restricted by the port Q-factor a semi-analytical expression is formed for its solution. The antennas are simulated by method of moments and the solution is formulated both for structures fed by discrete ports, as well as for design regions characterized by an equivalent current. It is shown that the solution is solely dependent on the eigenvalues of the so-called energy modes of the antenna. The magnitude of these eigenvalues is analyzed for a linear dipole array as well as a plate with embedded antenna regions. The energy modes are also compared to the characteristic modes to validate characteristic modes as a design strategy for MIMO antennas. The antenna performance is illustrated through spectral efficiency over the Q-factor, a quantity that is connected to the capacity. It is proposed that the number of energy modes below a given Q-factor can be used to estimate the degrees of freedom for that Q-factor.
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