Discrete time-scale characterization of wideband time-varying systems

Cooperative Communication over Multi-Scale and Multi-Lag Wireless Channels

“…Therefore, according to the wavelet theory, we sample the multi-scale and multi-lag plane in a dyadic lattice as shown in Fig. 1 [10,29].…”

“…For wideband channels, on the other hand, each propagation path experiences a distinct Doppler scale, hence the term, multi-scale, multi-lag channel. For both types of wideband and narrowband time-varying channels, so-called canonical channel models have been proposed [8][9][10][11], limiting the number of channel coefficients required to represent the channel.…”

“…For wideband time-varying channels a canonical model has been proposed in [9][10][11], which is also dubbed as the scale-lag canonical model. This model has been adopted for direct sequence spread spectrum (DSSS) communication systems [11] to develop a scale-lag RAKE receiver to collect the diversity inherent in the multi-scale multi-lag channel.…”

“…In addition, this model has spurred the use of wavelet signaling due to the fact that when the wavelets are "matched" to the scale-lag model, the receiver structure is greatly simplified -the signals corresponding to different scale-lag branches of the model are orthogonal when a single wavelet pulse is transmitted. The single pulse case is examined in paper [10]. Multi-scale multi-lag wavelet signaling is possible as well [12], [13], although inter-scale and inter-delay interference results.…”

“…This scale-lag diversity is better described by the wavelet transform than the conventional time-frequency representation for the narrowband linear time-varying (LTV) system, and is so called the wideband LTV representation [10,11]. Wideband LTV representation has been proven and verified for many applications in terms of high data rate wireless communications [14][15][16][17], high-speed underwater acoustic communications [18][19][20], vehicle-to-vehicle (V2V) wideband communication systems [21,22], and radar/sonar systems [23].…”