New Constructions of Codebooks Nearly Meeting the Welch Bound

Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks using generalized bent functions from [Formula: see text] to [Formula: see text], where [Formula: see text] is a prime and [Formula: see text] is a positive integer with [Formula: see text]. With this construction, we obtain two new families of codebooks nearly meeting the Welch bound. These codebooks have new parameters and could have a small alphabet size. In particular, a class of regular generalized bent functions from [Formula: see text] to [Formula: see text] is presented.

Robustness of Time Reversal versus All-Rake Transceivers in Multiple Access Channels

Time reversal (TR) is an effective solution in both single user and multiuser communications for moving complexity from the receiver to the transmitter, in comparison to traditional postfiltering based on Rake receivers. Imperfect channel estimation may, however, affect pre- versus postfiltering schemes in a different way; this paper analyzes the robustness of time reversal versus All-Rake (AR) transceivers, in multiple access communications, with respect to channel estimation errors. Two performance indicators are adopted in the analysis: symbol error probability and spectral efficiency. Analytic expressions for both indicators are derived and used as the basis for simulation-based performance evaluation. Results show that while TR leads to slight performance advantage over AR when channel estimation is accurate, its performance is severely degraded by large channel estimation errors, indicating a clear advantage for AR receivers in this case, in particular when extremely short impulsive waveforms are adopted. Results however also show a stronger non-Gaussianity of interference in the TR case suggesting that the adoption of a receiver structure adapted to non-Gaussian interference might tilt the balance towards TR.