On the Optimal Sequences and Total Weighted Square Correlation of Synchronous CDMA Systems in Multipath Channels

Texas Univ., San Antonio
IEEE Transactions on Vehicular Technology (Impact Factor: 2.06). 08/2007; DOI: 10.1109/TVT.2007.897235
Source: IEEE Xplore

ABSTRACT We generalize the total square correlation and the total weighted square correlation (TWSC) for a given signature set used in synchronous code division multiple access (S-CDMA) systems. We define the extended TWSC measure for multipath channels in the presence and the absence of the colored noise. The main results of this paper are the following: 1, the necessary and sufficient conditions of the received Gram matrix to maximize the sum capacity in the presence of multipath; 2, the conditions on the channel such that the received multipath sequences in the presence of the colored noise are Welch bound equality (WBE) sequences; 3, a decentralized method for obtaining generalized WBE sequences that minimize the TWSC in the presence of multipath and colored noise. Using this method, the optimal sequences, which achieve sum capacity for overloaded S-CDMA systems, in the presence of multipath are obtained. Numerical examples that illustrate the mathematical formalism are also included.

1 Bookmark
  • [Show abstract] [Hide abstract]
    ABSTRACT: We investigate the capacity of finite-input finite-output discrete memoryless channels (DMC) whose channel matrix is n × n square and furthermore is assumed to be nonsingular with n linearly independent real eigenvectors. For any given DMC with such a channel matrix, we characterize the mutual information in terms of its eigenvalues. Our main result, obtained by using the method of Lagrange multipliers, is to derive an analytic expression for the capacity, depending on the eigenvectors and the eigenvalues of the invertible channel matrix. In particular, by using the inverse eigenvalue problem, we characterize the capacity of (2, 2) channels, with invertible channel matrices, in terms of lower and upper bounds that exist in the literature. In addition, numerical examples are provided, and probability of error is discussed.
    Information Sciences and Systems (CISS), 2010 44th Annual Conference on; 04/2010
  • [Show abstract] [Hide abstract]
    ABSTRACT: A comparison of the optimal power allocation for a Gaussian vector channel subject to sum power constraint under water filling principle and inverse eigenvalue problem is given. We focus on the overloaded multipath DS - CDMA systems when the channel information is known at both transmitter and receiver. We generalize the sum of power constraint for each cell by considering p-norm matrices, and we provide numerical and graphical results for an overloaded CDMA cell in the presence and the absence of the multipath fading.
    Sarnoff Symposium, 2009. SARNOFF '09. IEEE; 05/2009
  • [Show abstract] [Hide abstract]
    ABSTRACT: Levenshtein improved the Welch bound on aperiodic correlation by weighting the cyclic shifts of the sequences over complex roots-of-unity. Although many works have been concerned on meeting the Welch bound with equality, no such effort has been reported for the Levenshtein bound. We show that the Levenshtein bound with equality is met if and only if the non-trivial aperiodic correlations have identical amplitude for all time-shifts, and the sequences form a novel class of complementary set whose aperiodic correlation is defined as the conventional aperiodic correlation modulated by a simplex weighting vector.
    Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on; 01/2012