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: 1.98). 08/2007; 56(4):2063 - 2072. DOI: 10.1109/TVT.2007.897235
Source: IEEE Xplore


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.

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    • "For asynchronous CDMA systems, Mow found that the maximum worst-case signal-to-noise ratio (SNR) is achieved if and only if the WBE sequences form a complementary sequence [25], [21]. Since then, a lot of works have been concerned on the WBE sequences [26]-[30]. In [31], Liu and Guan have shown that the Levenshtein bound can be met with equality by the weighted-correlation complementary sequences. "
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    ABSTRACT: Levenshtein improved the famous Welch bound on aperiodic correlation for binary sequences by utilizing some properties of the weighted mean square aperiodic correlation. Following Levenshtein's idea, a new correlation lower bound for quasi-complementary sequence sets (QCSSs) over the complex roots of unity is proposed in this paper. The derived lower bound is shown to be tighter than the Welch bound for QCSSs when the set size is greater than some value. The conditions for meeting the new bound with equality are also investigated.
    Full-text · Article · Jan 2014 · IEEE Transactions on Information Theory
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    • "However , if the users are located in signal spaces, which are orthogonal to each other, then that number of users, which are experiencing higher interference, cannot have a higher contribution to the total interference in the system. This statement was proved in the context of CDMA systems in [16]. "
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    ABSTRACT: The global optimization of sensor locations and a sensitivity analysis based on the minimization of interferences due to wireless communications between sensors are studied in the presence of additive white Gaussian noise (AWGN). We used a Gram matrix approach for robust determination of sensor locations by minimizing the interferences (maximizing the signal strength) among sensors for engine health monitoring systems. In order to solve the problem of optimum placement, an iterative algorithm for maximizing the determinant of the Gram matrix is proposed and implemented. The sensitivity criterion proposed in this paper is the spectral number of the Frobenius norm of the Gram matrix associated with sensor readings. We derived the necessary conditions under which the number of sensors and the optimal sensor locations will remain unchanged when the data measured for sensitivity analysis is affected by AWGN. Our theoretical results are verified by simulations providing details concerning numerical implementations.
    Full-text · Article · Jan 2008 · Journal on Advances in Signal Processing
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    • "In the theoretical context of TSC optimized signature sets that are real (or complex) valued, one may consider the early work of Welch [1] followed by representative works in [2]-[13]. Findings in [1]-[13] constitute only pertinent performance bounds for digital communication systems with digital signatures . Recently, new bounds on the TSC of binary signature sets were presented [14] that led to minimum-TSC optimal binary signature set designs for almost all 1 signature lengths and set sizes [14]-[16]. "
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    ABSTRACT: We develop a binary signature design procedure to scale upwards overloaded minimum total-squared-correlation (TSC) binary signature sets. The quality of the design is measured against the recently published binary TSC bounds.
    Full-text · Article · Dec 2007 · IEEE Communications Letters
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