1. The AT&T Wireless owns the spectrum with 15MHz in Brooklyn. A cell-planning engineer divides the region into 280 cells.

a. For an AMPS system, the available spectrum to a cell is 15MHz/ 7 . If a channel requites 30KHz, how many channels he can provide in the entire Brooklyn region?

b. For a GSM system, the available spectrum to a cell is 15MHz/ 4 . If a channel requires 25KHz, how many channels he can provide in the entire Brooklyn region?

c. For a CDMA system, each cluster is a cell and each channel requites 1.25MHz. However, 25 channels can share an 1.25MHz bandwidth in each cell. How many channels he can provide in the entire Brooklyn region?

2. Walsh codes wi and wi: PN codes ci and cj:

W_i(n)w_j(n)=Nδ_ij             E{c_i(n)c_j(n)} = Nδ_ij

Define new combined codes

a_ii(n)= w_i(n)c_i(n)            a_ij(n) = w_i(n)c_i(n)

a_ji(n)= w_j(n)c_i(n)           a_jj(n)= w_j(n)c_j(n)

Find

A_ij(n)a_ij(n)          and  E{a_ij(n)a_ij(n)}

3. The minimum Eb/No (bit energy over noise energy) per user in the downlink of a synchronized CDMA system is 2. The spectral efficiency is lchip/sec/Hz. The bandwidth of the available spectrum is 2MHz. Data rate per user is lkbit/sec/user. The chip energy for MI Nu goers (i.e. including interferences hut excluding noise) received by the user (at distance-n meters) is E/(riA4) Joule where E is the unknown total power transmitted by the base station (measured at r-lm). The power spectrum density of Gaussian white noise No received the user is 10^(-12) Joule (watt/Hz)). Note that Nu is the number of users and r, is the distance (in meters) between the iN user and the base station. Here, the users are not having the same distance from the base station.

a. If E10 Joules, what are the maximum coverage distance r and the corresponding processing gain N for Nu=100?

b. If the maximum coverage distance r=1000 meters, what are the minimum E (in Joules) and the corresponding processing gain N for Nu=100?

c. If E=1 Joules and the maximum coverage distance r=1000 meters, what are the maximum Nu and corresponding processing gain N?

d. If E=10 Joules and the maximum coverage distance r=1000 meters, what are the maximum Nu and corresponding processing gain N?

4. a. The data rate of an asynchronous CDMA system is Skbpts. The bandwidth is I MHz. What is the processing gain? What is the chip duration?

b. For an environment that the maximum channel delay spread of 6 psec, what is the maximum number of fingers in a rake receiver?

c. How many peaks can be obtained by a rake receiver if the channel impulse response is h(r)= a#0 -Id

[a1]= [0,9,8,7,6,5,7,3,2,4]

[t1]=[0,0.49,0.8,2.3,2.6,2.65,2.87,4.3,4.42,5.9],u sec

d. Can you use a rake receiver in a synchronous CDMA system? Explain your answer.

e). Can you use an equalizer in an asynchronous CI)MA system? Explain your reason.