# Simulating a SISO Ring Model

We simulate the SISO Ring Model described previously by varying the transmit receive separation from 50m to 500m. Keeping the ring radius fixed at 20m the angular spread of the channel decreases as the receiver moves away from the transmitter.

It is observed that the power level of the received signal fluctuates as the distance ‘d’ is varied. However, after a certain critical distance (around 250 m) the power vs distance curve approaches a straight line.

# Simulating a SISO Ring Model

A Ring Model is a well known spatial channel model. It models the propagation channel as an unobstructed transmitter and a receiver surrounded by a ring of reflectors. The distance between the transmitter and receiver is usually much larger than the radius of the ring. The reflectors are distributed uniformly around the ring. This model is useful for modeling a scenario where a base station is located at sufficient altitude and is unobstructed whereas the mobile station is at ground level and is surrounded by a bunch of reflectors.

Ring Model

Given below is the MATLAB code for a SISO Ring Model consisting of eight reflectors distributed uniformly around the ring.

```%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Et]=ring_mod0(d,r,B)
Et=0;
for phi=0:pi/4:(2*pi)-(pi/4);
R=sqrt((d-r*cos(phi))^2+(r*sin(phi))^2);
E=exp(-i*B*(r+R))/(r+R);
Et=Et+E;
end
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
```

# Simulating a MIMO Ring Model

A Ring Model is a well known spatial channel model. It models the propagation channel as an unobstructed transmitter and a receiver surrounded by a ring of reflectors. The distance between the transmitter and receiver is usually much larger than the radius of the ring. The reflectors are distributed uniformly around the ring. This model is useful for modeling a scenario where a base station is located at sufficient altitude and is unobstructed whereas the mobile station is at ground level and is surrounded by a bunch of reflectors.

Given below is the MATLAB code that calculates the composite signal (from nth Tx element to mth Rx element) at the receiver for a MIMO channel composed of eight reflectors.

```%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Et]=ring_mod2(d,r,psi,l,B,alpha,a)
Et=0;
for phi=0:pi/4:(2*pi)-(pi/4);
R_=sqrt((d-l*cos(psi)-r*cos(phi))^2+(r*sin(phi)-l*sin(psi))^2);
r_=sqrt((r*cos(phi)-a*cos(alpha))^2+(r*sin(phi)-a*sin(alpha))^2);
E=exp(-i*B(r_+R_))/(r_+R_);
Et=Et+E;
end
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%```