Transmit and Receive Signal Models in 4G Wireless Communications

Transmit and Receive Signal Models in 4G Wireless Communications

4G Communications

Our models are developed mainly for signals in the UHF and SHF bands, from 0.3-3 GHz and 3-30 GHz, respectively. This range of frequencies is quite favorable for wireless system operation due to its propagation characteristics and relatively small required antenna size. We assume the transmission distances on the earth are small enough so as not to be affected by the earth’s curvature. All transmitted and received signals we consider are real. That is because modulators are built using oscillators that generate real sinusoids (not complex exponentials). While we model communication channels using a complex frequency response for analytical simplicity, in fact the channel just introduces an amplitude and phase change at each frequency of the transmitted signal so that the received signal is also real. Real modulated and demodulated signals are often represented as the real part of a complex signal to facilitate analysis. This model gives rise to the complex base-band representation of band-pass signals, which we use for our transmitted and received signals. More details on the complex base-band representation for band-pass signals and systems can be found in Appendix A.

We model the transmitted signal as

where u(t) = x(t) + j y(t) is a complex base-band signal with in-phase component x(t) =R{u(t)}, quadrature component y(t) = I{u(t)}, bandwidth Bu, and power Pu. The signal u(t) is called the complex envelope or complex low-pass equivalent signal of s(t). We call u(t) the complex envelope of s(t) since the magnitude of u(t) is the magnitude of s(t) and the phase of u(t) is the phase of s(t). This phase includes any carrier phase offset. This is a standard representation for band-pass signals with bandwidth B << fc, as it allows signal manipulation via u(t) irrespective of the carrier frequency. 

The power in the transmitted signal s(t) is   Pt = Pu/2.

The received signal will have a similar form:

where the complex base-band signal v(t) will depend on the channel through which s(t) propagates. In particular, as discussed in Appendix A, if s(t) is transmitted through a time invariant channel then  

v(t) = u(t) ∗ c(t), where c(t) is the equivalent low-pass channel impulse response for the channel. The received signal may have a Doppler shift of  fD= v cos θ/λ  associated with it, where θ is the arrival angle 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 (c = 3 × 108 m/s is the speed of light). The geometry associated with the Doppler shift is shown in Fig.1.2 . 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 = v Δt cos θ  that the transmitted signal needs to travel to the receiver. The phase change due to this path length difference is Δφ = 2πvΔt cosθ/λ. The Doppler frequency is then obtained from the relationship between signal frequency and phase

If the receiver is moving towards the transmitter, i.e. −π/2 ≤ θ ≤ π/2, then the Doppler frequency is positive, otherwise it is negative. We will ignore the Doppler term in the free space and ray tracing models when talking about them in the blog , since for typical vehicle speeds (75 Km/hr) and frequencies (around 1 GHz), it is on the order of 100 Hz .

Suppose s(t) of power Pt is transmitted through a given channel, with corresponding received signal r(t) of power Pr, where Pr is averaged over any random variations due to shadowing. 

We define the linear path loss of the channel as the ratio of transmit power to receive power:

We define the path loss of the channel as the dB value of the linear path loss or, equivalently, the difference in dB between the transmitted and received signal power:

In general the dB path loss is a non negative number since the channel does not contain active elements, and thus can only attenuate the signal. The dB path gain is defined as the negative of the dB path loss: 

PG = −PL = 10 log10(Pr/Pt) dB, which is generally a negative number. With shadowing the received power will include the effects of path loss and an additional random component due to blockage from objects.

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Transmit and Receive Signal Models in 4G wireless Communication channel,wireless Communications channel,

4G Communications,Transmit and Receive Signal Models in 4G wireless Communications channel

Transmit and Receive Signal Models in 4G wireless Communication channel,wireless Communication channel,

Transmit and Receive Signal Models in 4G wireless Communications channel,wireless Communications channel,

Transmit and Receive Signal Models in 4G wireless Communication channel in 4G communication,wireless Communication channel in 4G communication ,

Transmit and Receive Signal Models in 4G wireless Communications channel in 4G communications,wireless Communications channel in 4G communications,

Transmit and Receive Signal Models in 4G 4G wireless Communication channel,4G wireless Communication channel,