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notes3 - ECE 562 Fall 2011 Complex Baseband Representation...

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ECE 562 Fall 2011 August 30, 2011 Complex Baseband Representation Channel Model for Point-to-Point Communications Point-to-point communications systems are well modeled using a bandpass additive noise channel model of the form shown in Figure 1. ˜ s ( t ) ˜ h ( t ) ˜ y ( t ) n ( t ) ˜ r ( t ) f c f c f | ˜ S ( f ) | Figure 1: Real bandpass channel model for point-to-point communications The message bearing signal ˜ s ( t ) is a real-valued bandpass signal whose spectrum is concentrated in the vicinity of some carrier frequency f c . Distortions introduced by the channel are characterized by a linear time invariant system with impulse response ˜ h ( t ), and frequency response ˜ H ( f ) concentrated around f c . The channel re- sponse ˜ h ( t ) may or may not be known at the receiver. In the simplest case, the response ˜ h ( t ) corresponds to a an ideal bandpass filter with bandwidth corresponding to that of the signal ˜ s ( t ). The additive noise process n ( t ) is usually idealized by White Gaussian Noise (WGN). The received signal ˜ r ( t ) is a real-valued bandpass process as well.
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