Transmit and Receive Signal Models
Introduction:
Propagation models are mainly developed for UHF (0.3-3GHz) and VHF (3-30GHz) bands. These frequency bands are quite favorable for wireless system operation due to propagation characteristics and small antenna size.
Transmit and Receive Signal:
- All transmitted and received signals are real because of that modulators are built using oscillators that generate real sinusoids
- We model the transmitted signal as
s (t)=R{u(t)e^{j2πfct}}
=R {u (t)} cos (2πfct) −j {u (t)} sin (2πfct)
= x (t) cos (2πfct) − y (t) sin (2πfct),
u(t) is called the complex envelope or complex lowpass equivalent signal of s(t).
The received signal will have a similar form
r (t) =R {v(t)e^{j2πfct}}
Where complex baseband signal v(t) will depend on the channel through which s(t) propagates
- The received signal may have a Doppler shift of f_{D} = v cos θ/λ associated with it, where θ is the arrivalangle of the received signal relative to the direction of motion, v is the receiver velocity towards the transmitter in the direction of motion, and λ = c/fc is the signal wavelength.
- The Doppler shift results from the fact that transmitter or receiver movement over a short time interval Δt causes a slight change in distance
Δd = vΔtcos θ
- The phase change due to this path length difference is
Δφ = 2πvΔtcos θ/λ
- The Doppler frequency is then obtained from the relationship between signal frequency and phase:
Linear path loss of the channel as the ratio of transmit power to receive power
In dB
The dB path gain is defined as the negative of the dB path loss:
P_{G} = −P_{L} =10 log10 (Pr/Pt) dB which is generally a negative number