Project - Please use Matlab to complete.

Project Goal: This project examines the design of a realistic pulse shape to be used with linear modulation that will meet a spectral emissions mask.

A spectral emissions mask is given in Figure 16.17. This spectral emissions mask is the one used for GSM handsets. So this problem is one of great practical interest.

Consider a linear stream modulation having the form

Xz(t) = √(E_b)_k=1∑^K_b D_z(k)u(t-(k-1)T)

The design is further constrained in that the pulse, u(t), must not extend for longer than T_u = 40 us in time. Design a pulse shape that will satisfy Nyquist's criterion for an arbitrary constellation.

For the remainder of the project it is assumed that the pulse shape designed above is used with BPSK modulation. Any finite length pulse shape which achieves this spectral mask will have to produced some intersymbol interference (1S1) (i.e., Nyquist's criterion cannot exactly be met). Hence the matched filter demodulator given in Figure 16.18 will not be exactly optimal but can be made to be very close to optimal with a well designed pulse shape.

(a) Assume D_z(k) = 1, compute the worse case degradation for an arbitrary pulse shape to the bit error probability for the demodulator given in Figure 16.18. Specifically consider the case of the kth bit where k = K_b/2 where K_b is large and compute the effects of ISI. Identify the values of Dz(j), j ≠ k which achieve this worse case degradation for an arbitrary pulse shape with BPSK modulation.

(b) Design a pulse shape and corresponding symbol rate such that the worse case (over all ISI patterns) degradation to the effective Stilt is less than 0.26 dB and the spectral mask given in Figure 16.17 is met by the transmission. Grades will be assigned proportional to the achieved symbol rate (higher the better!). Anyone who beats the posted solution will get a bonus of 10 points for the project!

(c) Plot the transmitted complex envelope for the pulse shape that was designed in (b). Plot the real component of the matched filter output for a modulation sequence of (1- 111 - 11 - 1 - 1- 11) for your design. Identify the symbol time sampling points.