Maximum likelihood channel estimation of flat Rayleigh multiuser CDMA channels

Coherent detection in CDMA mobile radio is desirable but non-trivial. Recent attempts to find a better coherent detection scheme utilise embedded reference symbols on the CDMA uplink for estimating the channel impulse response where both conventional matched filter and multi-user detection are employed*. The use of coherent detection is also crucial to multiple access interference suppression schemes. This is because the gain in capacity is negated without coherent detection and this gain is contingent upon the accuracy of the channel estimates, as we have found in our work on successive serial-parallel cancellation. The channel estimation process in asynchronous CDMA system is complicated by the multiple access interference (MAI) which is due to the reference symbols and/or data symbols of other users. Accurate channel estimation is therefore dependent on the removal of the MAI. Much work has been done in the area of CDMA channel estimation for multi-user CDMA systems. A guard band may be introduced to overcome the degrading effect of MAI arising from the data symbols of other users in the quasi- synchronous channels' and employed in conjunction with the application of successive parallel cancellation on the reference symbols. The decorrelating detector is able to remove the MAI completely and is also a form of maximum likelihood estimator. It has also been employed for channel estimation in conjunction with a successive serial cancellation scheme for data symbols in a quasi-synchronous channels and in synchronous channels.Maximum likelihood channel estimation has also been applied to both synchronous CDMA satellite and mobile radio systems. In reference, the authors extended the work done by Ruprecht for single user channel estimation to multi-users channel estimations for multi-path satellite channels. Maximum likelihood estimation is similar to least square estimation when the noise is both white and Gaussian and the estimate obtained is both unbiased and efficient. However, the main drawback of using maximum likelihood estimation stems from the noise enhancement or signal-to-noise ratio (SNR) degradation property when ordinary spreading codes with non-zero side-lobes are used [2][10][13]. Such noise enhancement or SNR degradation decreases the accuracy of the channel estimates. In this discourse, we will first characterise the degradation for Gold codes as they are commonly used for the spreading sequences of both data and reference bits, and also as the actual degradation has not been published. We will show that the SNR degradation increases with the number of users in the channel. This is followed by the analysis and simulation of the noise enhancement effect, in terms of mean square error (MSE) , when Gold codes are used for maximum likelihood quasi-synchronous channels estimation where three successive embedded reference bits are used. The use of three reference symbols is to ensure that there is no MA1 effect on the centre reference bits arising from the data bits in the channels. We will then compare the results obtained for Gold codes with the results of SNR degradation and noise enhancement when a single pseudo-noise (PN) or self-orthogonal PN code is used. The performance of channel estimation using successive serial cancellation with perfect ranking knowledge will be used as a bench marker. The effect of doppler fading rates on maximum likelihood estimation are also shown. The use of self-orthogonal PN codes for channel estimation, which are a two-level non-binary spreading code whose auto-correlation function does not have side lobes, was first proposed by Clark for narrow- band mobile radio system. The use of either PN or self-orthogonal PN codes for CDMA channels would nevertheless impose a tighter timing requirement for the up-link transmissions. This paper is organised as follows; Section 2 presents the system model with respect to the transmitter model and the maximum likelihood channel estimator model, while section 3 presents the simulation and analytical results. Section 4 contains the concluding remarks.*In this channel the embedded reference bits of all users are within a bit period of one another.