Finite-step algorithms for constructing optimal CDMA signature sequences

A description of optimal sequences for direct-spread code-division multiple access (DS-CDMA) is a byproduct of recent characterizations of the sum capacity. This paper restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite-step algorithms from matrix theory. It proposes a new one-sided algorithm that is numerically stable and faster than previous methods

Optimal CDMA signatures: a finite-step approach

A description of optimal sequences for direct-sequence code division multiple access is a byproduct of recent characterizations of the sum capacity. The paper restates the sequence design problem as an inverse singular value problem and shows that it can be solved with finite-step algorithms from matrix analysis. Relevant algorithms are reviewed and a new one-sided construction is proposed that obtains the sequences directly instead of computing the Gram matrix of the optimal signatures

CDMA signature sequences with low peak-to-average-power ratio via alternating projection

Several algorithms have been proposed to construct optimal signature sequences that maximize the sum capacity of the uplink in a direct-spread synchronous code division multiple access (CDMA) system. These algorithms produce signatures with real-valued or complex-valued entries that generally have a large peak-to-average power ratio (PAR). This paper presents an alternating projection algorithm that can design optimal signature sequences that satisfy PAR side constraints. This algorithm converges to a fixed point, and these fixed points are partially characterized

Designing structured tight frames via an alternating projection method

Tight frames, also known as general Welch-bound- equality sequences, generalize orthonormal systems. Numerous applications - including communications, coding, and sparse approximation- require finite-dimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems (IEPs), which includes the frame design problem. To apply this method, one needs only to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is the fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate that alternating projection is an effective tool for frame design, the paper studies some important structural properties in detail. First, it addresses the most basic design problem: constructing tight frames with prescribed vector norms. Then, it discusses equiangular tight frames, which are natural dictionaries for sparse approximation. Finally, it examines tight frames whose individual vectors have low peak-to-average-power ratio (PAR), which is a valuable property for code-division multiple-access (CDMA) applications. Numerical experiments show that the proposed algorithm succeeds in each of these three cases. The appendices investigate the convergence properties of the algorithm

Construction of equiangular signatures for synchronous CDMA systems

Welch bound equality (WBE) signature sequences maximize the uplink sum capacity in direct-spread synchronous code division multiple access (CDMA) systems. WBE sequences have a nice interference invariance property that typically holds only when the system is fully loaded, and, to maintain this property, the signature set must be redesigned and reassigned as the number of active users changes. An additional equiangular constraint on the signature set, however, maintains interference invariance. Finding such signatures requires equiangular side constraints to be imposed on an inverse eigenvalue problem. The paper presents an alternating projection algorithm that can design WBE sequences that satisfy equiangular side constraints. The proposed algorithm can be used to find Grassmannian frames as well as equiangular tight frames. Though one projection is onto a closed, but non-convex, set, it is shown that this algorithm converges to a fixed point, and these fixed points are partially characterized

Efficient Radio Resource Allocation Schemes and Code Optimizations for High Speed Downlink Packet Access Transmission

An important enhancement on the Wideband Code Division Multiple Access (WCDMA) air interface of the 3G mobile communications, High Speed Downlink Packet Access (HSDPA) standard has been launched to realize higher spectral utilization efficiency. It introduces the features of multicode CDMA transmission and Adaptive Modulation and Coding (AMC) technique, which makes radio resource allocation feasible and essential. This thesis studies channel-aware resource allocation schemes, coupled with fast power adjustment and spreading code optimization techniques, for the HSDPA standard operating over frequency selective channel. A two-group resource allocation scheme is developed in order to achieve a promising balance between performance enhancement and time efficiency. It only requires calculating two parameters to specify the allocations of discrete bit rates and transmitted symbol energies in all channels. The thesis develops the calculation methods of the two parameters for interference-free and interference-present channels, respectively. For the interference-present channels, the performance of two-group allocation can be further enhanced by applying a clustering-based channel removal scheme. In order to make the two-group approach more time-efficient, reduction in matrix inversions in optimum energy calculation is then discussed. When the Minimum Mean Square Error (MMSE) equalizer is applied, optimum energy allocation can be calculated by iterating a set of eigenvalues and eigenvectors. By using the MMSE Successive Interference Cancellation (SIC) receiver, the optimum energies are calculated recursively combined with an optimum channel ordering scheme for enhancement in both system performance and time efficiency. This thesis then studies the signature optimization methods with multipath channel and examines their system performances when combined with different resource allocation methods. Two multipath-aware signature optimization methods are developed by applying iterative optimization techniques, for the system using MMSE equalizer and MMSE precoder respectively. A PAM system using complex signature sequences is also examined for improving resource utilization efficiency, where two receiving schemes are proposed to fully take advantage of PAM features. In addition by applying a short chip sampling window, a Singular Value Decomposition (SVD) based interference-free signature design method is presented

Generalized Finite Algorithms for Constructing Hermitian Matrices with Prescribed Diagonal and Spectrum

In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of the matrix. They perform this feat by applying a sequence of (N-1) or fewer plane rotations, where N is the dimension of the matrix. Both the Bendel-Mickey and the Chan-Li algorithms are special cases of the proposed procedures. Using the fact that a positive semidefinite matrix can always be factored as \mtx{X^\adj X}, we also provide more efficient versions of the algorithms that can directly construct factors with specified singular values and column norms. We conclude with some open problems related to the construction of Hermitian matrices with joint diagonal and spectral properties