Objective: To design and simulate binary baseband and passband communication systems in the presence of noise.

Description: Binary data is transmitted using antipodal rectangular pulses of duration T over an AWGN channel. The receiver is a correlation device followed by an threshold device. We also consider On-Off, Orthogonal and PSK modulation schemes.

Instructions

• I. Initialization: Copy the initialization files for the experiment into your Matlab working directory. Note that the initialization files have changed

  The following constants should be set by the startup file. Use who in the matlab workspace to check if the constants are all there. Some additional constants may also be set, but you may ignore them

  • T = 0.1s ------------Bit symbol duration
  • F_CARR = 2*pi*100 ------Carrier frequency (rad/sec)
  • A = 5----------------Pulse Height
  • T_SAMPLE = T/100 ----Sampling period used in Simulink
  • T_SIM = 100s ---------Total simulation time
  • N0 = 10 -------------AWGN spectral density.

• II. Generating Digital modulation
  1. The first step is to make a binary data source. Use the ece359lib/Rd Wksp block to get a random sequence of 0's and 1's. This block uses the randint function of matlab to generate random data at the rate of one bit every T seconds. The two bit values 0 and 1 are equiprobable.

  2. Depending on the value of the bit, we would like to choose from the two waveforms s0 and s1. First generate the waveform s0 using the following commands,

     taxis=linspace(0,T,100); % same as [0:T/100:T]
     s0 = A*ones(size(taxis)); % s0 has value A for t between 0 and T.
     
     s0 is the desired pulse of width T. Then, generate a signal which repeats the waveform s0 every T seconds. The Repeating Table block in ece359lib generates repeated copies of a signal of our choice(see the parameters of this block).
     Similarly (for antipodal signalling) generate a pulse which is the negative of s0, and call it s1. Use another Repeating Table block to generate a repeating signal corresponding to s1.
     To check the shape of the pulses, use the command check_s0s1

  3. Use the ece359lib/pulse modulator to select one of the two waveforms depending on the bit value. When the control port has input 0, stream 0 is passed to output. When the control port has input 1, stream 1 is passed to the output. Make connections to achieve the desired modulation.
  4. Using a scope, check if your modulator output is what you expect (you should see alternating signal levels of +A and -A).

• III. Channel and receiver
  
  1. Generate white Gaussian noise using the ece359lib/White Noise block. Set the sample time to T_SAMPLE. To get a noise spectral density of N0/2 you need to set the power of noise to N0/2 in the ece359lib/White Noise block. Add this noise to the signal using an adder block. Check that the noise PSD is indeed N0/2 using the ece359lib/PSD block.
  2. Demodulation involves multiplying the signal by s1-s0. Generate this difference (repeating table blocks produce s0 and s1) and use a multiplier to generate the product.
  3. This product needs to be integrated over the bit period T. Use the ece359lib/correlator block to integrate. Note that the integrator needs to be reset at the end of each bit period. The reset signal is given at the second port of the integrator. Use the ece359lib/Correlator Reset block to generate this reset signal (the parameters of this block are preset).
  4. The integrator output is to be compared with a threshold value. (What is the appropriate threshold value for the modulation scheme in use?) Subtract the threshold from the integrator output using a constant block and a subtractor. A decision device is given in ece359lib. You should be able to see how this device works.
  5. To measure the bit error rate use ece359lib/Error Meter. This device needs two inputs, the transmitted data stream and the received data stream (at the decision device output).
     Note: You need to run the simulation for a time period corresponding to at least 1000 bits to get the accuracy needed for the error probability estimate.

  IV. Other forms of binary signaling
  

  Remember to use the check_s0s1 function to see the actual signal shapes you are using.

  1. Maintain the same average signal energy as in the antipodal signal case, and implement an On-Off keying scheme. You need to set the signals s0 and s1 appropriately. Does the threshold for optimal detection change? Evaluate the error probability.
  2. Repeat for orthogonal signaling. Let s0 have constant amplitude and let s1 be positive for half the bit period and negative for the other half. Maintain the same signal energy as in the antipodal case.
  3. Repeat for passband signalling. Multiply the signals for antipodal signalling by a cosine wave with frequency F_CARR and amplitude sqrt(2). This gives a PSK signal with carrier frequency F_CARR.
     To generate the signals s0 and s1, use the commands,

     s1 = sqrt(2)*A.*cos(taxis*F_CARR);
     s0 = -s1;