# 计算机通信代写｜Department of Systems and Computer Engineering Wireless Communications (SYSC 4607) Computer Simulation Laboratory Lab 1

**Objectives **

This laboratory experiment consists of fifive parts. In part 1, we examine the effffect of directional antennas on the received power under 2-ray model. In Part 2, we study the cellular coverage and the effffect of path loss and shadowing parameters on the coverage. In Part 3,we examine macrodiversity through multiple base station reception and the effffect of correlation of the received signals on the outage performance. In Part 4, we study the accuracy of Nakagami approximation for Ricean fading.

**1 Two-ray Model **

The two-ray model is commonly used when there is a LOS path and a single dominant path reflflecting from the ground. Read Section 2.4.1 of the textbook for detailed information on this model. Consider a transmitter and a receiver with antenna heights given in Figure 1.

The carrier frequency is *f**c *= 900MHz. The gain of the LOS path and the reflflected path is denoted by *G**l *and *G**r*, respectively.

***Q1****. **Consider two functions of *d*: *y*1(*d*) = 1*/d*2 and *y*2(*d*) = 1*/d*4 . Verify that if *y*1 and *y*2 are measured in dB, i.e., 10 log10(*.*), and the distance is measured in logarithmic scale (i.e. log10(*d*)), each function corresponds to a straight line. Find the slopes of these two lines in dB/decade.

***Q2****. **Calculate the critical distance *d**c *and log10 *d**c *for the given parameter values.

***Q3****. **Following the explanation in page 36 of the textbook, plot the piecewise linear model for the received power in dBm (10 log10 *P**r*) versus the log of distance (log10 *d*) if the transmit power is normalized such that for very small distances the plot starts at 0 dBm.

***Q4****. **Express both the phase difffference (∆*φ*) between the two paths and the received power *P**r *in terms of *h**r*, *h**t *, *d*, *f**c*, *G**l *, *G**r*, and *P**t *(give the exact expression, not the approximation).

Assume that the ground reflflection coeffiffifficient *R *is *−*1.

***Q5****. **Write a MATLAB program that plots the phase difffference ∆*φ *between the two received signal components (from *Q4) versus log10(*d*).

**Objectives **

This laboratory experiment consists of fifive parts. In part 1, we examine the effffect of directional antennas on the received power under 2-ray model. In Part 2, we study the cellular coverage and the effffect of path loss and shadowing parameters on the coverage. In Part 3,we examine macrodiversity through multiple base station reception and the effffect of correlation of the received signals on the outage performance. In Part 4, we study the accuracy of Nakagami approximation for Ricean fading.

**1 Two-ray Model **

The two-ray model is commonly used when there is a LOS path and a single dominant path reflflecting from the ground. Read Section 2.4.1 of the textbook for detailed information on this model. Consider a transmitter and a receiver with antenna heights given in Figure 1.

The carrier frequency is *f**c *= 900MHz. The gain of the LOS path and the reflflected path is denoted by *G**l *and *G**r*, respectively.

***Q1****. **Consider two functions of *d*: *y*1(*d*) = 1*/d*2 and *y*2(*d*) = 1*/d*4 . Verify that if *y*1 and *y*2 are measured in dB, i.e., 10 log10(*.*), and the distance is measured in logarithmic scale (i.e.log10(*d*)), each function corresponds to a straight line. Find the slopes of these two lines in dB/decade.

***Q2****. **Calculate the critical distance *d**c *and log10 *d**c *for the given parameter values.

***Q3****. **Following the explanation in page 36 of the textbook, plot the piecewise linear model for the received power in dBm (10 log10 *P**r*) versus the log of distance (log10 *d*) if the transmit power is normalized such that for very small distances the plot starts at 0 dBm.

***Q4****. **Express both the phase difffference (∆*φ*) between the two paths and the received power *P**r *in terms of *h**r*, *h**t *, *d*, *f**c*, *G**l *, *G**r*, and *P**t *(give the exact expression, not the approximation).

Assume that the ground reflflection coeffiffifficient *R *is *−*1.

***Q5****. **Write a MATLAB program that plots the phase difffference ∆*φ *between the two received signal components (from *Q4) versus log10(*d*).

values of *G**r*? Discuss and explain your answer.

**Q12****. **In the light of your ∆*φ *plot, explain the changes of the received power versus distance in the four plots.

**2 Cellular Coverage **

In a cellular network, cell coverage area of a base station is defifined as the average area within a cell where the received power from the base station is above a given minimum value (*P**min*).

Under path loss only, coverage region is a circular disc centered at the base station. However,the shape of the coverage region is random under path loss and lognormal shadowing.

***Q1****. **Consider a microcell with radius *R*. Let the average received power at cell boundary be *P*¯ *r*(*R*). The minimum desired power level is *P**min *and the shadowing standard deviation is *σ**ψ**dB *. Write an expression for the cell coverage percentage.

***Q2****. **Simplify the expression in *Q1 if *P**min *= *P*¯ *r*(*R*).

***Q3****. **In microcells, path loss exponents *γ *usually range from 2 to 6, and shadowing standard deviation *σ**ψ**dB *typically ranges from 4 to 12. Assuming *P**min *= *P*¯ *r*(*R*), write a MATLAB program to plot the coverage area as a function of *γ *and *σ**ψ**dB *. For both *γ *and *σ**ψ**dB *use a step size of 0*.*1 in the corresponding intervals. (*Hint*: You can use function “normcdf” of MATLAB.)

**Q4****. **Using your MATLAB program, plot the cell coverage percentage as a function of *γ *and *σ**ψ**dB *.

**Q5****. **Which combinations of *γ *and *σ**ψ**dB *give the best percentage of coverage area and the worst percentage of coverage area? Explain and justify your answers.

**Q6****. **What is the percentage of coverage area when these parameters are in the middle of their respective ranges?

**3 Macrodiversity through Multiple Base Stations **

In order to improve the performance of cellular systems, multiple base stations can receive the signal transmitted from a given mobile unit and combine these multiple signals either by selecting the strongest one or summing the signals together, perhaps with some optimized weights. This typically increases SNR and reduces the effffects of shadowing. Similarly a mobile unit can combine the signals transmitted from multiple base stations. Combining of signals received from multiple base stations is called macrodiversity. In this part, we explore the benefifits of macrodiversity. (Diversity will be covered in more detail later in the course).

Consider a mobile at the midpoint between two base stations in a cellular network. The received signals (in dBW) from the base stations are given by

*P**r,*1 = *W *+ *Z*1*, *

*P**r,*2 = *W *+ *Z*2*, *

where *Z*1 and *Z*2 are *N*(0*, σ*2 ) variables. We defifine outage with macrodiversity to be the event that **both ***P**r,*1 and *P**r,*2 fall below a threshold *T*.

***Q1****. **Interpret the terms *W*, *Z*1, *Z*2 in *P**r,*1 and *P**r,*2.

***Q2****. **If *Z*1 and *Z*2 are independent, show that the outage probability is given by

*P**out *= [*Q*(∆*/σ*)]2 *, *

where ∆ = *W **− **T *is the fade margin at the mobile’s location.