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Continuous-Time Equivalents of Welch Bound Equality Sequences

Published: 01 September 2005 Publication History

Abstract

The theory developed on the sequence optimization for equal-power code-division multiple-access (CDMA) systems is generalized in this paper. Unlike previous works, where discrete-time or vector channel models are predominantly employed, the overloaded channels are modeled as strictly band-limited, continuous-time multiple-access channels corrupted by additive white Gaussian noise (AWGN). After being posed as a multiple-input/single-output (MISO) joint transmitter and receiver optimization problem with the total mean-squared error (MSE) as the objective functional to be minimized, the variational problem is solved by using a frequency-domain approach. It is shown that there exist continuous-time equivalents of Welch bound equality (CTE-WBE) sequences as the jointly optimum transmit waveforms and that the matched filters are the jointly optimum receivers. The user capacity of the band-limited channels is characterized by a necessary and sufficient condition for the admissibility of users into the system in terms of the channel load, the received signal-to-noise ratio, and the signal-to-interference-plus-noise ratio (SINR) requirement. It is also shown that CTE-WBE sequences achieve the lower bound on the continuous-time equivalent of total squared correlation (CTE-TSC).

Cited By

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  • (2018)An optimal orthogonal overlay for a cyclostationary legacy signalIEEE Transactions on Communications10.1109/TCOMM.2010.05.09000158:5(1557-1567)Online publication date: 13-Dec-2018
  • (2012)Welch bound for bandlimited and timelimited signalsProceedings of the 7th international conference on Sequences and Their Applications10.1007/978-3-642-30615-0_25(269-278)Online publication date: 4-Jun-2012
  • (2006)Chip-asynchronous version of welch boundProceedings of the 4th international conference on Sequences and Their Applications10.1007/11863854_31(351-363)Online publication date: 24-Sep-2006

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Published In

cover image IEEE Transactions on Information Theory
IEEE Transactions on Information Theory  Volume 51, Issue 9
September 2005
372 pages

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IEEE Press

Publication History

Published: 01 September 2005

Author Tags

  1. Code-division multiple-access (CDMA)
  2. Welch bound equality (WBE) sequences
  3. frequency-division multiple-access (FDMA)
  4. joint transmitter and receiver optimization
  5. time-division multiple-access (TDMA)
  6. total squared correlation
  7. user capacity

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Cited By

View all
  • (2018)An optimal orthogonal overlay for a cyclostationary legacy signalIEEE Transactions on Communications10.1109/TCOMM.2010.05.09000158:5(1557-1567)Online publication date: 13-Dec-2018
  • (2012)Welch bound for bandlimited and timelimited signalsProceedings of the 7th international conference on Sequences and Their Applications10.1007/978-3-642-30615-0_25(269-278)Online publication date: 4-Jun-2012
  • (2006)Chip-asynchronous version of welch boundProceedings of the 4th international conference on Sequences and Their Applications10.1007/11863854_31(351-363)Online publication date: 24-Sep-2006

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