10−5 10−4 10−3 10−2 10−1
Signal to Noise Ratio E
b/N0 [dB]
BER
M = 8, N = 64, K = 18, L = 4, fdT = 0.01
7−stage PIC for chip−synchronous system 7−stage PIC for chip−asynchronous system
Figure 4.13:Chip-synchronism vs. chip-asynchronism.
4.5
Conclusions
BER performance of the multistage PIC scheme is theoretically analyzed in this chapter. We use the Central Limit Theorem to model MAI and ISI as Gaussian random processes. Comparison with the simulated results shows that the analysis is fairly accurate. A simplified method is also presented using only the mean and variance of SINR, leading to accurate approximations.
A close agreement is seen between analysis and simulation in most cases except for low BER (below 10−4). The analysis tends to over estimate MAI
in very lightly loaded systems, and under estimate MAI in very heavily loaded system. Considering the fact that the target BER for an uncoded system is usually above 10−4, our analytical results are quite satisfactory.
The presented analytical method provides an effective measure to predict BER performance and system capacity for the PIC scheme under investi- gation.
The PIC convergence property and multipath diversity gains are stud- ied analytically. It is shown that the multistage PIC receiver effectively removes interference, the variance of MAI is reduced to asymptotic values with only a few stages of cancellation. It is also shown that multipath di- versity gains can be achieved by the subsequent coherent stages rather than the first noncoherent stage. Interference cancellation and coherent combin- ing are important techniques to combat MAI and multipath propagation.
presence of unequal power among different paths are examined using the analytical approach. The study shows that the PIC is near-far resistant. It can be used in practical systems even when strict power control is hard to obtain. We also learned that the PIC scheme achieves the best performance in presence of equal power among different diversity branches.
Chapter
5
ESTIMATION OF FADING CHANNELS
The performance of a communication system depends largely on its ability to retrieve an accurate measurement of the underlying channel. In this chapter, we present joint approach to data detection and channel estima- tion. The purpose of channel estimation is to enable M -ary orthogonal sig- nals to be demodulated coherently and a Rake receiver to use a maximum ratio combining (MRC) scheme. For data detection, we mainly consider the use of interference cancellation technique which is suitable for CDMA sys- tems with long codes. Different channel estimation schemes are evaluated and compared in terms of mean square error (MSE) of the channel esti- mation and the bit error rate (BER) performance. Based on our analysis and numerical results, some recommendations are made on how to choose appropriate channel estimators in practical systems.
5.1
Introduction
In addition to multiple access interference (MAI), CDMA systems also suffer from multipath fading. Mobile radio communication channels are time-varying channels. They are characterized by the presence of both delay and Doppler spread. Depending on the delay spread and the data rate, the channel may be approximately flat fading or frequency-selective fading. The latter one produces intersymbol interference (ISI). The received signal includes multiple versions of the transmitted waveform which are attenuated and delayed in time.
Accurate knowledge (or good estimate) of the underlying channel is es- sential for mitigating interference and the effect of multipath and fading. If the channel estimates are not reliable, the performance of algorithms such
as multiuser detectors and coherent Rake receivers degrade significantly. Channel estimation consequently is an important issue in mobile commu- nications and good channel estimates have a very important impact on the overall performance of the system.
Several channel estimators, e.g., subspace-based estimators, and maxi- mum likelihood estimators have been proposed, e.g., in [37, 38]. The au- thors only considered the use of short spreading codes. However, current and next generation CDMA systems use long spreading codes whose pe- riod is much larger than the symbol duration. For long code CDMA, sev- eral attempts have been made in obtaining channel estimates. In [39], a subspace-based algorithm for blind channel estimation of a synchronous CDMA downlink was proposed. It was shown that the estimation accuracy can be increased considerably using a decision feedback approach. However, a time invariant multipath channel was assumed in [39]. The time-varying nature of the fading channel prohibits the use of subspace algorithm, since the received signal is not constrained to any particular subspace if channel parameters are time-varying.
The estimation of channel parameters in a DS-CDMA system with M -ary orthogonal modulation, which is the main concern of this thesis, has been the subject of study in several papers (see, for instance, [16, 18, 19, 40]). The maximum likelihood (ML) channel estimator for long code CDMA systems over time-varying multipath channels was employed in [19]. In [16], a blind channel estimation strategy based on an adaptive Wiener fil- tering approach that yields unbiased channel estimates and low estimation variance for CDMA system using random codes was proposed. In [18, 40], it was shown that the channel parameters can be estimated with a maxi- mum correlator output. Furthermore, the estimated parameters are used for the interference canceler with coherent detection, which results in an increase in system capacity.
Recall that the received signal vector is formed as r = Ah+n. The task of a channel estimator is to estimate the fading vector h given the received observation r and the transmitted data. Depending on the form of the data that can be retrieved, channel estimation can be either decision directed or pilot aided. The former uses decision feedback loops and utilizes the decisions on the transmitted signals ˆAto extract the channel coefficients. The second approach makes the use of pilot symbols or channels (A is known in this case). The use of pilots simplifies channel estimation with the penalty of wasting channel resources. In this chapter, we focus on the first approach and make an extensive investigation on different alternatives for estimating time-varying multipath Rayleigh fading channels in absence of pilot symbols.
We take an integrated approach such that channel estimation is coupled with data detection. All the channel estimators are decision-directed and can work in conjunction with the coherent data detection (interference