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Chapter 9. Time-Scale and Dispersive Pro... > 9.2 Narrowband Channel Characterizat... - Pg. 381

9.2 Narrowband Channel Characterization 381 9.2 NARROWBAND CHANNEL CHARACTERIZATION 9.2.1 Narrowband Spreading Function An LTV channel H can be characterized by a kernel representation that is based on the time-varying impulse response h(t, ) of the channel, as discussed in Chapter 1 (Kailath, 1959; Zadeh & Desoer, 1963). A narrowband LTV channel can cause time shifts and frequency or Doppler shifts on the transmitted signal s(t). This time-frequency spreading of the signal can be quantified using the narrowband spreading function (SF) based representation, that has been widely used, specifically for radar signal design (Vakman, 1968), pulse shaping in multicarrier communications (B olcskei, ¨ Duhamel, & Hleiss, 1999; Haas & Belfiore, 1997; Kozek & Molisch, 1998; Matz, Schafhuber, Gr ochenig, Hartmann, & Hlawatsch, 2007), and wireless channel modeling (Giannakis & Tepedelen- ¨ lioglu, 1998; Sayeed & Aazhang, 1999; Ye & Papandreou-Suppappola, 2006). Using the narrowband SF, S H ( , ), the (noise free) received signal, r(t) = (H s)(t) = - - S H ( , )s(t - )e j2 t d d (9.1) can be physically interpreted in terms of the time-shift operation s(t - ) = (S s)(t) and the frequency-