A. Busboom

Efficient implementation of linear multiuser detectors for asynchronous CDMA systems by linear interference cancellation

The decorrelating and the linear, minimum mean-squared error (MMSE) detector for asynchronous code-division multiple-access communications are ideally infinite memory-length detectors. Finite memory approximations of these detectors require the inversion of a correlation matrix whose dimension is given by the product of the number of active users and the length of the processing window. With increasing number of active users or increasing length of the processing window, the calculation of the inverse may soon become numerically very expensive. In this paper, we prove that the decorrelating and the linear MMSE detector can both be realized by linear multistage interference cancellation algorithms with ideally an infinite number of stages. It will be shown that depending on the signal-to-noise ratio, the number of active users, and the choice of the cancellation algorithm, only a few stages are necessary to obtain the same BER performance as with the ideal detectors. The computational costs for one stage of a linear interference cancellation algorithm are essentially given by one matrix-vector multiplication. Thus, the computational complexity can be reduced considerably. Since each stage introduces a time delay equivalent to the bit duration, the number of stages also determines the detection delay. Because a few stages are sufficient, this approach can also be used to obtain receiver structures with low memory consumption and detection delay.

Coded aperture imaging with multiple measurements

In coded aperture imaging, only aperture arrays consisting of (0, 1) elements are physically realizable. If multiple coded images are obtained with different aperture masks and the resulting detector images are suitably combined, a larger variety of aperture arrays, such as multilevel, complex-valued, vector-valued, or complementary arrays becomes applicable. We present a general theory of coded aperture imaging with multiple measurements. An image reconstruction scheme from the coded images is described that results in a maximum signal-to-noise ratio. Also, the design of sets of aperture arrays is addressed and explicitly solved for several important cases. It is shown how known classes of correlation arrays can be beneficially applied to coded aperture imaging.

Uniformly Redundant Arrays

Uniformly Redundant Arrays (URAs) are two–dimensional binary arrays with constant sidelobes of their periodic autocorrelation function. They are widely agreed upon to be optimum mask patterns for coded aperture imaging, particularly in imaging systems with a cyclic coded mask. In this paper, a survey of all currently known construction methods for URAs is given and the sizes and open fractions of the arrays resulting from each construction method are pointed out. Alternatives to URAs for situations in which a URA does not exist, are discussed.

Adaptive multi-rate multi-code CDMA systems

To support variable data-rates multi-code code-division multiple-access (MC-CDMA) systems have been proposed for mobile communications. They allow the support of variable source data-rates by variation of the set of spreading-sequences assigned to each user. The impact of the sequence-design on the system performance is considered. For the antifading capability and the multiuser interference performance measures are derived. We describe sequence-sets which are almost optimum with respect to these parameters and which allow each user to change its data-rate without affecting the other users.

Binary arrays with perfect odd-periodic autocorrelation

Arrays with good autocorrelation functions are required for coded aperture imaging. A generalized folding procedure is derived that permits the construction of arrays with good correlation properties from well correlating sequences for many array sizes. This synthesis method is applied to the construction of approximately square binary arrays with a single zero element and perfect odd-periodic autocorrelation functions. In addition, new binary arrays with constant sidelobes of their periodic autocorrelation functions (uniformly redundant arrays) can be generated with the generalized folding method.

Spreading sequences for zero-forcing DS-CDMA multiuser detectors

In the past, different multiuser detectors for asynchronous code-division multiple-access communications have been proposed, many of them may be characterized as zero-forcing detectors, e.g., the decorrelation detector. We show that linear interference cancellation schemes are asymptotically zero-forcing which means that they are equivalent to the decorrelating detector if the number of stages approaches infinity. These detectors have been found to be superior to the conventional matched filter detector. However, the design of spreading sequences optimized especially for these receivers has not been considered up to now. Usually, spreading sequences are designed to have a low peak correlation parameter. Pursley (1977) has shown that the average interference parameter (AIP) is an important design parameter since it is related to the average signal-to-interference ratio of the conventional receiver. In this paper, we consider the construction of spreading sequences for zero-forcing multiuser detectors that are optimal in the sense of performance and near-far resistance. It is shown that sequences with a low AIP are near-optimal. This, again, stresses the importance of the AIP for the design of spreading sequences for CDMA systems employing any kind of receiver. Numerical examples indicate that by using optimized sequences the average signal-to-noise ratio (SNR) can be improved by about 1-2 dB for lengths of interest in applications.

Combinatorial design of near-optimum masks for coded aperture imaging

In coded aperture imaging the attainable quality of the reconstructed images strongly depends on the choice of the aperture pattern. Optimum mask patterns can be designed from binary arrays with constant sidelobes of their periodic autocorrelation function, the so-called URAs. However, URAs exist for a restricted number of aperture sizes and open fractions only. Using a mismatched filter decoding scheme, artifact-free reconstructions can be obtained even if the aperture array violates the URA condition. A general expression and an upper bound for the signal-to-noise ratio as a function of the aperture array and the relative detector noise level are derived. Combinatorial optimization algorithms, such as the great deluge algorithm, are employed for the design of near-optimum aperture arrays. The signal-to-noise ratio of the reconstructions is predicted to be only slightly inferior to the URA case while no restrictions with respect to the aperture size or open fraction are imposed.

Implementation of linear multiuser detectors for asynchronous CDMA systems by linear interference cancellation algorithms

The decorrelating and the linear, minimum mean-squared error (MMSE) detectors for asynchronous code-division multiple-access communications are ideally infinite memory-length detectors. Finite memory approximations of these detectors require the inversion of a correlation matrix whose dimension is given by the product of the number of active users and the length of the processing window. With increasing number of active users or increasing length of the processing window, the calculation of the inverse may soon become numerically very expensive. In this paper, we show that by applying iterative algorithms for the inversion of the correlation matrix in the frequency domain, linear multiuser detectors can be implemented with low complexity, low memory consumption and small detection delay.

MISMATCHED FILTERING OF PERIODIC AND ODD-PERIODIC BINARY ARRAYS

Arrays with good correlation properties are required for coded-aperture imaging, as well as for other applications of two-dimensional signal processing. Since binary arrays with perfect periodic autocorrelation functions exist for only a few sizes, mismatched filtering is discussed. Mismatched filtering entirely suppresses any sidelobes of the periodic autocorrelation function at the expense of a slightly reduced signal-to-noise ratio. New construction methods for binary arrays are presented for which this loss, with respect to periodic or odd-periodic correlation, converges to zero with an increasing array size.

Adaptive receivers for mobile DS-CDMA communication systems

We investigate the performance of adaptive receivers for mobile DS-CDMA communication systems. Adaptive filters are known to effectively cope with both multiuser interference and multipath propagation in the case of static channels. A time-variant channel can be assumed static if the variations of the channel are slow compared with the convergence rate of the adaptive algorithm. However, in mobile communication where channels change very rapidly, this assumption is not valid. Therefore, we investigate the tracking performance of adaptive receivers in a mobile environment with realistic parameters. Different algorithms and receiver structures are compared. The results indicate that the convergence speed of the LMS algorithm is too slow. The NLMS yields good results if the velocity of the mobile is slow. The RLS yields good results if the number of users is relatively small. We propose a new adaptive multiuser receiver structure which allows one to increase the number of users.