Experiment 4 Detection of Antipodal Baseand Signals INRODUCION In previous experiments we have studied the transmission of data its as a 1 or a 0. hat is, a 1 volt signal represented the it value of 1 and a zero volt signal represented a it of value 0. We will now expand that to a general concept of a symol. We will create pairs of symols with two goals in mind. First, the symols are such that they cannot e confused for one another. Second, each symol represents either a 1 or a 0 it of data. In the future we will see how a set of symols can e used to represent groups of its, with each symol representing or eing mapped to two or more its. In a previous experiment we explored the idea of finding an optimum or matched filter. Now we can define and further investigate this concept with correlators. By using a comination of symols and their correlators, we will construct and test data links that use various symols. We will investigate the relationship etween the ratio of the energy contained in each it (E ) to the power spectral density of the noise (N o ) and the it error rate (BER). We will discover what effect the shape of the symols used has on this relationship. PRE-LAB Consider two symols, s 1 (t) and s 2 (t) a shown elow: 1 1-1 S 1 (t) S 2 (t) -1 Show the following relationships s ( t) s ( t) 1) 1 2 2) 1 1 s ( t) s ( t) 3) 2 2 s ( t) s ( t) Assume the transition occurs at /2.
What is the average power for these two symols? If each symol represents one it, what is the energy per it? Design a transmitter and correlation receiver in Simulink to estimate which of these two symols has een sent. (Hint: look at the procedure in this experiment for inspiration.) Design two other symols lasting for, with peak amplitudes of +1 and -1, that are antipodal. What is the average power for your symols? If each symol represents one it, what is the energy per it? Design a correlation receiver for your symols. Calculate the theoretical it error rate (BER) for an antipodal signaling system with one it per symol, using a correlation receiver, and with E /N o of 0, 1, 2, 3, 4, 5, 6, 7, and 8 db. PROCEDURE 1. Set up a complete data link simulation that uses two simple antipodal symols, +1 and -1 to represent a 1 it and 0 it, respectively. You will e constructing a transmitter and a correlation receiver with an AWGN Channel etween them. Be sure to make your simulation sample rate more than your symol rate y 10 times. hat is the Pulse Length parameter in the Ideal Rectangular Pulse Filter should e 10. Rememer to adjust the Linear Amplitude Gain accordingly. Your simulation may look similar to that shown elow. he section of locks efore the AWGN Channel will e referred to as the transmitter. he section after the AWGN Channel will e referred to as the receiver. Set the Sample time for the Random Integer Generator to 1/1000 and make the M-ary Numer equal to 2. Be sure to set the M-ary Numer in the Unipolar to Bipolar Converter also to 2. Set
the AWGN SNR to 100 db for now. Calculate the power ased on a 1 ohm load in the signal coming out of the Unipolar to Bipolar Convertor and set the Input Signal Power in the AWGN lock accordingly. Set the Symol Period in the AWGN lock to the time period of one it. A numer of new locks are introduced here. he Integrate and Dump lock is self-explanatory. here are two critical parameters in the lock. he Integration Period should e set to the symol period in simulation samples. he Offset should e set to 0 for now. Notice that the Output Intermediate Values is not checked. his means the integrator will only output a single sample of the final value for each symol, if the Integration Period is the same as one symol. his allows the Error Rate Calculation lock downstream to compare the transmitted symol with the receiver s estimation of the symol. he Sign Block is used here as a decision threshold to decide which symol was sent. If the output of the Integrate and Dump is greater than zero, then the receiver will estimate a +1 symol was sent. Conversely, if the output of the Integrate and Dump is less than zero, the receiver will estimate a -1 symol was sent. Following the Sign lock, a Lookup ale is included. his deals with the extremely rare possiility that the Sign lock will output a 0 instead of -1 or +1. Set the input vector to [-1 0 1] and the ale Data to [-1-1 1]. his means that any zero will e counted as a negative numer. he last lock in the receiver chain is the Error Rate Calculation. he lock is self-explanatory. However, you will have to adjust the Receive delay to account for the delays introduced in the receiver. Calculate the delay or use the scope to measure the delay etween the transmitted and received signals. Run this system for 2 seconds and verify that there are no errors. he Display lock shows the percent error in the first window, the numer of simulation samples in error in the second and the total numer of simulation samples in the ottom window. Note the frequency of the first null on the spectrum scope and record the spectrum. Given the it rate and what you have learned, what is the smallest symol error rate you can measure y running this system for 2 seconds? 2. Set the E /N o ratio in the AWGN lock to 0, 1, 2, 3, 5, 6, 7, and 8dB and run the lock for enough its to ensure you will get an accurate error rate. A good place to start is the theoretical data from the pre-la. Note and graph the symol error rate vs. E /N o. Compare this in the same graph with the theoretical curve. 3. Use the Offset parameter in the Integrate and Dump lock to simulate a synchronization error, i.e. the transmitter and receiver are not running on the same clock. Set the E /N o to 3dB and run the system with various offsets. Note and graph how the offset affects the BER?
4. Otain the message file for this experiment from your instructor. It will e a workspace file with a variale called exp4signal. he variale will e used as a source in your system as shown elow. It uses +1 and -1 as symols for 1 and 0 respectively. Encoded in the file is a short, five yte message (8 its to the yte) using the standard ASCII code. he ytes are sent in a serial stream with the most significant it (ms) first. here are ten simulation samples per it. Noise is also present on the signal. Plot the signal variale using plot. he signal was sent over a channel with a 5dB E /N o. Looking at the plot, do you elieve you will e ale to recover the message? 5. Modify your system to receive the signal from the workspace as shown elow. Be sure to set the Offset parameter on the Integrate and Dump lock ack to 0. Use the Signal From Workspace and Signal o Workspace locks from the Signal Processing Blockset. Output the result to the workspace as a variale called exp4its. Note: you will have to adjust the simulation time to process all the samples in the file depending on the Sample time parameter you use in the Signal from Workspace lock. he size of the variale is in simulation samples. Decode the message y hand or use the Matla exp4decode.m script file to do so. You may otain this file from your instructor. Save this script file. You will need it in future las. Include the resulting message in your la report. 6. Open a new model and use Simulink locks to generate a random sequence of its represented y the symols S 1 and S 2 presented in the pre-la. Use the Pulse Generator Block to generate one of the pulses with Pulse ype of Sample ased, an amplitude of 2, Period of 10 samples, Pulse wih of 5 samples and a Phase delay of 0. Use an Add lock to sutract 1 from the pulse generator output and multiply it y the output of the Random Integer Generator through the Ideal Rectangular Filter to produce the sequence of symols. Use the Scope with two axes to compare the output of the multiplier and the output of the Ideal Rectangular Filter. Run the model for 0.01s and verify the symols correlate to the its to e sent. 7. Add a correlation receiver to detect the pulse stream generated in step 6. Use a second Pulse generator set with the same parameters as those in the transmitter. Again add 1 to the output of the Pulse generator and multiply this signal y the output of the AWGN channel. he output
of this multiplier feeds the Integrate and Dump Block. Verify that your system has no errors with an E /N o of 100 db. Note and record the spectrum. What is different aout it? 8. Run the system for enough time to get an accurate BER E /N o equal to 0, 1, 2, 3, 5, 6, 7, and 8dB and note the BER. How do these results compare with those from Step 2? 9. Simulate a synchronization error y adjusting the Phase Delay of the second Pulse Generator. Note and graph how this system responds to synchronization error. 10. Modify the system to transmit and receive the antipodal symols you designed in the Pre-La. Be sure to adjust the Input Signal Power parameter in the AWGN Channel lock, if necessary. Run the system for 2 seconds with 100 db E /N o. Verify that you have no errors and note the first null in the spectrum scope. Run the system with for enough time for accurate BER measurement with E /N o equal to 0, 1, 2, 3, 5, 6, 7, and 8dB and note the Error Rate. How do these results compare with those from Step 2? 11. Simulate a synchronization error as you did in Step 9. Is your system more or less tolerant of synchronization error? HOUGHS FOR CONCLUSION How does the BER performance of each of the correlation receivers used in this experiment compare with that of an ideal matched filter receiver? Does the shape of the symol waveform affect the receiver performance, provided the symols have the same energy per it? By using symols other than +1 and -1, what, if anything, was gained? Was there a cost in energy, andwih or something else? How important is synchronization in this type of data system? Again, do not limit your conclusions to these questions.