ADAPTIVE INTERFERENCE SUPPRESSION IN MULTIUSER DS-CDMA SYSTEMS

Abstract

During the last two decades, direct-sequence code-division multiple-access (DSCDMA) technique has received a considerable interest in mobile and personal communication systems, and will play an important role in future wireless communication systems. In DS-CDMA systems a number of users share a common channel bandwidth, in which the users are distinguished from one another by superimposing a distinct pseudo random code sequence. The code sequence, which is known at the receiver, spreads the bandwidth of the data signal and also provides the multiple access capability. All users can transmit at the same time and are allocated the entire frequency spectrum for transmission, in contrast to frequency-division multiple-access (FDMA) and time-division multiple-access (TDMA) techniques. Hence, the detector receives signal composed of the sum of the signals of all users, which overlap in time and frequency. In practice, the interfering signals are not truly orthogonal to the desired signal, due to the random time offsets of the received signals. Hence the orthogonality property of the codes will not be achieved at the receiver, which results in the production of the multiple access interference (MAI). The MAI is a factor which limits the capacity and performance of DS-CDMA systems. Additionally, due to the propagation mechanism, the received signal from a user close to the base station will be stronger than that received from another user located far from the base station. Hence, a close user will dominate the distant users and reliable reception in this situation is not possible. This is called the near far problem and a possible solution to this is to use power control: such that all users will achieve the same power at the base station. The conventional matched-filter receiver output contains contributions from the MAI. Thus, even if the receiver thermal noise level goes to zero, the error probability of the conventional receiver exhibits a non-zero floor because of the MAI. Moreover, under the near-far situation, the weak signal will be overwhelmed by the MAI. The MAI and the near-far problem can be overcome by the use of multiuser detection (MUD) techniques. In MUD, the receiver jointly detects all signals in order to mitigate the non-orthogonal properties of the received signals. MUD has been a topic of extensive research interest since 1986 when Verdu formulated an optimum MUD based on the maximum likelihood sequence detection (MLSD). However, the complexity of the optimal detector is exponential in the number of active users, which has motivated the design of a number of suboptimal multiuser detectors with lower computational complexity. Amongst the linear suboptimal detectors, which apply a linear transform to the output of the matched filters to remove the MAI, is the linear minimum mean square error (MMSE) detector. It minimizes the mean square error between the actual and the estimated data bit, and possesses a linear computational complexity in the number of users. Adaptive interference suppression techniques are analogous to adaptive equalization of dispersive channels by virtue of the analogy between MAI and intersymbol interference (ISI). The adaptive MMSE receiver eliminates the use of the matched filter bank and can be implemented using a tapped delay line filter. It directly processes samples of the received signal at the chip interval without the explicit knowledge of the MAI. However, it requires the knowledge of the timing of the desired user as well as the knowledge of the training sequence of symbols transmitted by the desired user. In this work, adaptive multiuser detection techniques based on the MMSE error criterion have been considered for the adaptation and demodulation of DS-CDMA signals to solve the problems inherited in both conventional and non-adaptive detection techniques. The main issues considered in this work are to develop adaptive algorithms with low computational n complexity which are near-far resistant. They may be adapted blindly and without the knowledge of the timing of the desired user (i.e. with lower requirement for side information). A comparative study of the adaptation techniques using the least mean square (LMS), normalized LMS (NLMS) and recursive least squares (RLS) algorithms based on the MMSE criterion has been considered for the interference suppression in DS-CDMA systems. Different performance measures (such as the probability of error, convergence rate, near-far resistance, capacity, computational complexity and signal to interference ratio) have been used for the assessment of the performance of the various algorithms. A number of examples have been simulated to illustrate the performance comparison of these algorithms. It is well known, that the RLS algorithm possesses much faster convergence rate as compared to LMS algorithm, however the RLS algorithm requires larger number of computations, (0[N ]), as compared to LMS, (0[N]). To reduce the computational complexity, we have proposed and implemented a novel block algorithm for the adaptation and demodulation of DS-CDMA signals. The block algorithm possesses fast convergence rate which is comparable to the RLS algorithm, while requiring computational complexity comparable to that of the LMS algorithm. Simulation has been performed to compare the performance of the proposed block algorithm with the LMS and RLS algorithms for interference suppression and demodulation ofDS-CDMA signals. We have next proposed the use of the Kalman filter (KF) for the adaptation and interference suppression ofDS-CDMA signals. A motivation for using the KF is that it is the best linear unbiased estimator and is optimal in the MMSE sense. Moreover, the KF is usually formulated using the state-space approach, which contains the necessary information about the system. A number of examples have been simulated which show its improved in performance compared to the algorithms mentioned above. A drawback of the KF algorithm is that it requires the knowledge of the noise variance and like RLS, is prone to numerical instability due to the use of finite word-length arithmetic for calculating the Riccati difference equation. To solve this problem, the state-error correlation matrix is factorized into two square-root matrices and unitary transformations are used to update the matrix at each iteration. We have considered the use of the square-root KF (SQRT-KF) algorithm for the interference suppression and demodulation of DS-CDMA signals and implemented the system using both Givens rotations and Householder transformations. Simulations have been performed, to compare its performance with the conventional KF algorithm, which show better numerical stability but at the expense of increased computational complexity. To deal with the problems of instability in the RLS algorithm periodic re-initialization has been proposed in the literature. However, this requires the use of a training sequence periodically, which will result in decrease in the rate of transmission of the system. To remedy this problem, algorithms based on matrix factorization of the input auto-correlation matrix using orthogonal transformations have been derived and investigated. The resulting algorithms are less sensitive to round off errors, and, moreover can be efficiently mapped into systolic array structure for parallel implementation. Also, the computation of the leastsquares weight vector of the adaptive filtering algorithm may be accomplished by working directly with the incoming data matrix via the matrix factorization and decomposition rather than working with the (time-averaged) correlation matrix of the input data as in the RLS algorithm. Therefore, we have proposed the use of the QR-decomposition technique based on the recursive modified Gram-Schmidt (RMGS) algorithm for the adaptation and interference suppression of DS-CDMA signals. It requires lower computational complexity as compared to RLS, KF, SQRT-KF and other QR-RLS algorithms based on Givens rotations or IV Householder transformations. An attractive feature of the RMGS algorithm is that it can be set for parallel implementation, realized in a highly modular structure using systolic arrays such that using N-parallel processors will reduce the computational complexity to 0[N] per processor. It is worth mentioning that the RMGS-based algorithm does not involve the computationally expensive square roots as in the QR-RLS algorithms. An improved error feedback version of the RMGS algorithm (RMGSEF) is more efficient and has even better numerical properties as compared to the RMGS algorithm. Results show that the RMGSEF algorithm is near-far resistant, possesses the same convergence as the RLS algorithm and has improved numerical stability. The performance of the DS-CDMA receiver based on the RMGS algorithm has also been studied in a multipath fading dispersive environment. Simulations show that the proposed RMGS algorithm performs much better compared to LMS algorithm in a multipath fading dispersive environment and possesses lower error floor. The implementation of the adaptive MMSE receiver, considered so far, requires the knowledge of training sequence of the desired user during initial adaptation, and then switching to the decision directed mode during actual data transmission. Moreover, a fresh training sequence may also be required when the receiver loses synchronization due to deep fades or due to the interference from a strong interferer entering the network. However, in some applications, the use of training sequences may be impractical. Therefore, there is a need for adaptive receivers which do not require training sequence during the adaptation mode (i.e. blind). Blind algorithms using subspace estimation approach through either eigen value or singular-value decomposition of the data matrix are either computationally expensive, for adaptive applications, or suffer from relatively slow convergence rate. Blind equalization based on the Bussgang technique uses a soft decision (non-linear function) at the output of the detector in contrast to the MMSE detector. The constant modulus algorithm (CMA) is considered as the most successful and the simplest higher-order statistics (HOS) based algorithm among the Bussgang family of blind equalization algorithms. It chooses a linear receiver that minimizes the deviation of the receiver output from a constant modulus. However, its cost function includes a number of local minima. The constrained blind minimum output energy (MOE) detector for the interference suppression in DS-CDMA systems minimizes the mean output energy of the detector. It requires the knowledge of the spreading sequence of the desired user and its cost function does not include any local minima, which ensures global convergence. Based on the attractive features of the RMGS algorithm, we have derived and implemented a novel blind adaptive RMGS-based MOE algorithm for the adaptation and interference suppression in DS-CDMA systems. A number of numerical examples have been simulated which show that the convergence rate of the blind RMGS algorithm is much faster than that of the CMA and blind MOE-based LMS algorithm. Parallel implementation of the blind RMGS algorithm via systolic arrays, using Nparallel processors, will reduce the computational complexity to 0[N] per processor. The implementation of the MMSE receiver in DS-CDMA systems, considered so far, requires the knowledge of the timing of the desired user. This knowledge is used to successfully suppress MAI as well as to demodulate the desired user data bits. Therefore, in the literature there has been considerable effort devoted towards the development of time delay estimators for DS-CDMA systems. The commonly used sliding correlator technique for time delay estimation (TDE) fails in a near far environment. Delay acquisition using the MUSIC estimator based on subspace decomposition, in DS-CDMA systems, is shown to be near far resistant, however, its complexity is 0[N ]. Moreover, a poor performance is achieved when the number of users is unknown and large. Joint data detection and parameter estimation using the extended KF (EKF) has also been proposed earlier. Although, the vi algorithm is near far resistant and could be used in the tracking mode, it requires the initial parameter estimates of all users to be known and is computationally expensive. In this work, we have considered two techniques for TDE in DS-CDMA systems, which can be used during both the initialization and tracking modes. The first method is based on cross-correlating the MMSE weights vector, obtained by the RMGS algorithm, with the desired user spreading sequence. The estimated delay is specified by the location of the maximum value of the crosscorrelation peak. This method is shown to be near far resistant but it requires an all one training sequence, or alternatively, the adaptive filter has to be of length 2N taps. In the second technique, estimate of the time delay is obtained by running N-parallel adaptive MMSE algorithms at N-hypothetical values of the delay (equal to multiples of the chip period). This technique is near far resistant and it can also be used for both the initialization and tracking modes. A number of examples have been simulated to evaluate the performance of these techniques in both initialization and tracking modes. Lastly a novel blind adaptive DS-CDMA receiver for interference suppression, which does not require any side information except the desired user's spreading sequence, has been implemented.