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Asymptotic error rates in third-generation wireless systems
Abstract
The introduction of the so-called third-generation wireless communication system, also known as UMTS or IMT-2000, is a large-scale revolution in telecommunications. It uses a technique called code division multiple access (CDMA). An advanced algorithm to improve the performance of such a CDMA system is called hard-decision parallel interference cancellation and was studied by van der Hofstad and Klok for a rather basic model. We extend many of their results to a more realistic model, where different users transmit at different powers and where additive noise is present.
... In that paper, large deviation techniques are used to prove properties of the exponential rate and the BEP. In [7] and [11], various results have been proven for the HD-PIC sys- tem. ...
... In this paper, we start by repeating results of one-stage and multi-stage HD-PIC of [7] and [11]. We extend these results to values of the processing gain and the number of users that are comparable using Chernoff bounds. ...
We study a multiuser detection system for code-division multiple access (CDMA). We show that applying multistage hard-decision parallel interference cancellation (HD-PIC) significantly improves performance compared to the matched filter system. In (multistage) HD-PIC, estimates of the interfering signals are used iteratively to improve knowledge of the desired signal. We use large deviation theory to show that the bit-error probability (BEP) is exponentially small when the number of users is fixed and the processing gain increases. We investigate the exponential rate of the BEP after several stages of HD-PIC. We propose to use the exponential rate of the BEP as a measure of performance, rather than the signal-to-noise ratio (SNR), which is often not reliable in multiuser detection models when the system is lightly loaded. We show that the exponential rate of the BEP remains fixed after a finite number of stages, resulting in an optimal hard-decision system. When the number of users becomes large, the exponential rate of the BEP converges to (log 2)/2 $1/4. We provide guidelines for the number of stages necessary to obtain this asymptotic exponential rate. We also give Chernoff bounds on the BEPs. These estimates show that the BEPs are quite small as long as k = o(n/log n) when the number of stages of HD-PIC is fixed, and even exponentially small when k = O(n) for the optimal HD-PIC system, and where k is the number of users in the system and n is the processing gain. Finally, we extend the results to the case where the number of stages depends on k in a certain manner. The above results are proved for a noiseless channel, and we argue that we expect similar results in a noisy channel as long as the two-sided spectrum of the noise decreases proportionally to n.
... However, we believe that many of our results extend to the situation where the powers are allowed to be different and there is noise in such a way that it is not dominant. For example, this situation was studied in [16] for HD-PIC and s = 2. See also [17]. The HD-PIC and SD-PIC results that we have used in this paper extend to a large extent to the setting where the powers are allowed to be different in the noiseless setting (see [7], [12]). ...
In this correspondence, we study a lightly loaded code-division multiple-access (CDMA) system with and without multistage hard- and soft-decision parallel interference cancelation (HD-PIC and SD-PIC). Throughout this paper we will only consider the situation of a noiseless channel, equal powers and random spreading codes. For the system with no or a fixed number of steps of interference cancelation, we give a lower bound on the maximum number of users such that the probability for the system to have no bit-errors converges to one. Moreover, we investigate when the matched filter system, where parallel interference cancelation is absent, has bit errors with probability converging to one. This implies that the use of HD-PIC and SD-PIC significantly enhances the number of users the system can serve
We derive approximations for the probability of a bit error for a code division multiple access (CDMA) system with one-stage soft decision parallel interference cancellation. More precisely, we derive the exponential rates, Jk with cancellation and Ik without cancellation, of a CDMA system with k users and processing gain equal to n as n → ∞. Whereas the rates Ik follow explicitly from Cramér's theorem, the rates Jk are given in terms of an optimization problem that can be evaluated numerically. We prove that Jk > Ik for k ≥ 3, which shows that interference cancellation is effective. For the case without interference cancellation, we investigate the second order (Bahadur-Rao) asymptotics. For the case with interference cancellation, we can obtain second order asymptotics only for k = 3. Together the limits provide excellent approximations for the probability of a bit error in a wide range of interest.
The third-generation (3G) mobile communication system uses a technique called code division multiple access (CDMA), in which multiple users use the same frequency and time domain. The data signals of the users are distinguished using codes. When there are many users, interference deteriorates the quality of the system. For more efficient use of resources, we wish to allow more users to transmit simultaneously, by using algorithms that utilize the structure of the CDMA system more effectively than the simple matched filter (MF) system used in the proposed 3G systems. In this paper, we investigate an advanced algorithm called hard-decision parallel interference cancellation (HD-PIC), in which estimates of the interfering signals are used to improve the quality of the signal of the desired user. We compare HD-PIC with MF in a simple case, where the only two parameters are the number of users and the length of the coding sequences. We focus on the exponential rate for the probability of a bit-error, explain the relevance of this parameter, and investigate how it scales when the number of users grows large. We also review extensions of our results, proved elsewhere, showing that in HD-PIC, more users can transmit without errors than in the MF system.
Consider a Gaussian multiple-access channel shared by K users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms. The uncoded probability of error achievable by optimum multiuser detectors is investigated. It is shown that the K -user maximum-likelihood sequence detector consists of a bank of single-user matched filters followed by a Viterbi algorithm whose complexity per binary decision is O(2^{K}) . The upper bound analysis of this detector follows an approach based on the decomposition of error sequences. The issues of convergence and tightness of the bounds are examined, and it is shown that the minimum multiuser error probability is equivalent in the Iow-noise region to that of a single-user system with reduced power. These results show that the proposed multiuser detectors afford important performance gains over conventional single-user systems, in which the signal constellation carries the entire burden of complexity required to achieve a given performance level.
Third Generation Mobile Communication Systems Improving the performance of the third generation wireless communication systems
- R Prasad
- W Mohr
- W R Konhäuser
- M J Klok
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communication systems. Adv. Appl. Probab., 36, 1046–1084.
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- F Den Hollander
den Hollander, F. (2000) Large Deviations, Fields Inst. Monogr. 14. Providence, RI: American
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