Prolate spheroidal functions: a general framework for MC-CDMA waveforms without time redundancy

Requests for higher data transmissions rates and systems performances in multiuser radio communications, needed for the future mobile generations or wireless local area networks, centered them in the focus of interest of investigations in signal processing area. When transmitting over mobile channel, two principal channel’s aspects have to be considered; its frequency selectivity and time dispersion. A modulation technique that can provide means for overcoming or at least minimizing those problems is Orthogonal Frequency Division Multiplex (OFDM). It converts frequency selective channel in a set of channels that experience flat fading. This is accomplished dividing whole channel’s bandwidth into a set of narrowband channels. Furthermore, carriers frequency of each channel are chosen the way that signals transmitted on them are orthogonal and with overlapping spectrum. This increases the system efficiency enabling more dense subcarriers frequencies selection. On the other hand, channels’ time dispersion causes signal spreading providing InterSymbol Interference (ISI) in the receiver. This channel aspect can be overcame if time redundancy between consecutive symbols is equal or greater than channel’s dispersion. Two kinds of redundancy are usual in OFDM: Cyclic Prefix (CP) and Zero Padding (ZP). First one leads directly to the multiplicative channel in frequency domain and simplified receivers, while the second one guarantees the channel invertibility but requires more sophisticated receivers[1, 2]. These approaches to the channel dispersion problem do eliminate ISI, but the cost is the reduction of the system transmission rate. When multiuser communications are considered, each user must have a signature uniquely associated with him in order to be separable from the rest of the users. Multiuser systems based on the combination of OFDM and Code Division Multiple Access (CDMA) principles are a challenging issue for researchers at the present. In these systems, mod-