## Multiuser Detection and Channel Estimation for DS-CDMA Systems

Erlanger Berichte aus der Informations- und Kommunikationstechnik,
Erlangen, 2003.

### Abstract

In this thesis, the performance of receiver algorithms for mobile communications systems is studied which apply DS-CDMA or CDMA as multiple-access technique as well as multiple transmit and/or receive antennas. Starting from the general multiple-input/multiple-output (MIMO) relation these systems can be described by, the system performance is evaluated during the investigations from an information theoretic point of view as well as in terms of the bit error ratios attainable by means of different receiver schemes.

Focusing on the uplink of mobile communications systems, i.e., the transmission from the mobile user(s) to a common base station, after introduction of a simplified MIMO system model for transmission over multipath fading channels which allows analytical tractability, we start by investigating the spectral efficiency attainable in MIMO systems employing CDMA. Thereby, we distinguish two scenarios - on the one hand decentralized transmission where the multiple inputs are generated by spatially separated users being equipped with multiple transmit antennas, and on the other hand centralized transmission where the inputs are the signals propagated from the antennas of a single user.

Regarding the case of perfect channel knowledge only at the receiver, it is well-known that for joint decoding at the receiver the spectral efficiency of a MIMO system is maximized by choosing rotationally invariant complex-valued transmit signals. In addition, the spectral efficiency; rises with the number of transmit signals. This situation changes when applying instead suboptimum receiver algorithms based on single user decoding. In fact, the MIMO system becomes interference limited if rotationally invariant complex-valued transmit signals are used and the number of MIMO system inputs exceeds the number of MIMO system outputs. However, employing instead real-valued modulation schemes in combination with widely linear filtering this problem can be solved in part and the performance of systems with decentralized transmission is improved for large signal-to-noise ratios. In addition, we find that the interference limitation can be overcome completely if each user knows its own propagation channel state and utilizes this information for transmit signal generation.

Since the availability of channel state information at the transmitter is limited in nowadays systems and can therefore not be used in order to increase the system performance, we investigate in the major part of this work the performance achievable in the uplink of mobile communications systems when DS-CDMA is used instead of CDMA. This is motivated by the fact that DS-CDMA has been chosen as access technique for 3rd generation mobile communications systems which is among others due to the possibility to recover the information sequences sent by distinct users even with suboptimum, low complexity receivers.

Being interested in the information theoretic limits attainable with different receiver schemes for a DS-CDMA system, random spreading sequences are presupposed and the large system limit is considered for the sake of analytical tractability. That is, the system performance is studied under the assumption that the spreading factor approaches infinity while the system load, being defined as the ratio of the number of users to the spreading factor, is fixed. This allows the application of so-called random matrix theory.

Assuming perfect channel knowledge at the receiver it turns out that for system loads less than unity the application of linear interference suppression filters is sufficient in order to attain each desired spectral efficiency. While these receivers operate still far away from the Shannon bound, the gap can be closed by applying not only linear interference suppression but also successive interference cancellation. In addition, using real-valued data symbols instead of complex-valued ones, it is shown that the system performance equals that of a transmission with complex-valued data symbols but at halved system load in the asymptotic limit. Moreover, regarding the question how spatial diversity provided by multiple transmit antennas shall be used, it turns out that the spectral efficiency grows with the number of antennas available to each user if the optimum system load is chosen.

However, this situation changes dramatically if perfect channel knowledge is not given at the receiver anymore and the path weights have to be estimated explicitly. This is due to the fact that severe multiuser interference affects the channel estimation if DS-CDMA is employed leading to significant channel estimation errors. Calculating the attainable spectral efficiencies if estimated path weight coefficients are used to adjust the interference suppression filters, we find that it is now prefereable in a wide range to restrict the number of transmit antennas per user to one.

Equipped with this theoretical insight we propose in a final part of this work feasible multiuser detection algorithms which are based on the principles of iterative soft decision interference cancellation. We show that by an appropriate design of the multiuser interference suppression filters and decision metrics a close to optimum performance in terms of bit error ratio can be achieved for perfect channel knowledge as well as for explicit channel estimation at the receiver. Furthermore, we provide semianalytical algorithms which allow the justification of simplifying assumptions made in the design of different receiver components for the sake of feasibility. In addition, since these semianalytical algorithms closely approximate the actual receiver performance for parameters of practical interest, they can even be used for prediction of the attainable system performance.