Multiuser Constrained Water-Pouring for Continuous-Time Overloaded Gaussian Multiple-Access Channels

• Published in: IEEE transactions on information theory Vol. 54; no. 4; pp. 1437 - 1459
• Main Author: Cho, Joon Ho
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; AWGN; Bandwidth; Channels; Code division multiplexing; Code-division multiple-access (CDMA); Communication channels; Constraints; Design optimization; Electric noise; Equivalence; Exact sciences and technology; Feedback; Fourier transforms; Frequency division multiaccess; frequency-division multiple-access (FDMA); Gaussian; Information theory; Information, signal and communications theory; joint transmitter and receiver optimization; linear minimum mean-squared error (LMMSE) receivers; Mean square errors; Multiaccess communication; Normal distribution; Optimization; Pulse modulation; Radiocommunications; Signal to noise ratio; Signatures; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; tight frame; Transmission and modulation (techniques and equipments); Transmitters; Transmitters. Receivers; water-pouring; Waveforms; Welch bound equality (WBE) sequences; joint transmitter and receiver optimization; Optimal systems; Fourier transformation; AWGN; Necessary and sufficient condition; Wireless telecommunication; Frequency division multiple access; Transmitter; Continuous time; Optimization; Mean square error; linear minimum mean-squared error (LMMSE) receivers; Multiple access; Gaussian channel; tight frame; Frequency domain method; Welch bound equality (WBE) sequences; Overload; Optimal solution; Code-division multiple-access (CDMA); Code division multiple access; water-pouring; Signal to interference plus noise ratio; Multiple channel; frequency-division multiple-access (FDMA)
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2008.917724

In this paper, signature waveforms and signal powers are jointly optimized for multiuser communications over strictly bandlimited, continuous-time, overloaded channels corrupted by additive white Gaussian noise (AWGN). The total signal power is minimized subject to general asymmetric signal-to-interference-plus-noise ratio (SINR) constraints at the output of linear minimum mean-squared error (LMMSE) receivers. Using vectorized Fourier transform (VFT) technique, the optimal solutions as well as a necessary and sufficient condition for the existence of a feasible solution are derived in the frequency domain. It turns out that every optimal solution performs the same as the optimal frequency-division multiple-access (FDMA) system. A geometric procedure called multiuser constrained water-pouring is developed to construct every possible optimal solution, of which profiles of signal power and equivalent bandwidth are, respectively, the same as those of signal power and physical bandwidth of the optimal FDMA system. It is shown that orthogonal signature waveforms are assigned to oversized users and continuous-time equivalents of generalized Welch bound equality (CTE-GWBE) sequences are assigned to non-oversized users.