A Holistic Approach to Wireless Design Through Physics Based Simulations
Large-Scale Modeling
Set-up
Place an antenna at the desired location in the city geometry and choose the directivity pattern. This example uses an omnidirectional dipole pattern. The frequency is 5 [GHz]. Create a grid of points above the terrain where the Poynting vector is to be calculated.
Pathloss
Extract real part of the Poynting vector at every one of the points and perform regression to obtain pathloss exponent and pathloss at 1 [m]. In this example, the pathloss exponent is -2.76. The free-space power decay has a pathloss exponent of -2.
Shadowing
Estimate the standard deviation of the zero-mean Poynting vector data and fit it to a normal distribution. In this example, the shadowing standard deviation is 7.47 [dB].
Small-Scale Modeling
Set-up
Create a set-up with a single-antenna transmitter and a single-antenna receiver. Place them at desired locations in the city. In this example we use two Hertzian dipoles, one as a transmitter and one as a receiver. The carrier frequency is chosen to be 5 [GHz] with a channel bandwidth of 100 [MHz].
Power Delay Profile (PDP)
Calculate PDP in [dBW] and plot it vs delay in microseconds. From the PDP we infer that the channel has a frequency flat response with main signal tap coming at a delay of approximately 0.3 microseconds. Since electromagnetic waves in free space propagate at the speed of light, c, the distance between the transmitter and the receiver can be calculated to be 90 [m].
Normalized PDP
Normalize the PDP such that the total channel power is one and each tap represents a fraction of the total power. Its clear that the main tap is at least 10dB above the second largest tap.
Localization
Antenna Array
Create a receiver with a 16-element uniform linear Hertzian dipole array and a transmitter with a single-antenna Hertzian dipole.
Placement
Place a receiver at an elevation with respect to the transmitter.
Post-Processing
Obtain the channel vector and compute a 1D Discrete Fourier Transform (DFT) of the channel vector. Plot the magnitudes of the multipath components vs the angle of arrival to pick out the strongest multipath. From the plot we see that the transmitter is at 112 degrees with respect to the receiver which could be verified from the set-up (see picture above).