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Designing a Bandlimited M-ary Modulation System over an AWGN Channel using Simulink

1. You are requested to design a bandlimited M-ary modulation system over an AWGN channel as shown in the following block diagram using Simulink.The center (or carrier) frequency is set to fc=0Hz for simplicity. The other system parameters such as bit rate (fb), transmission bandwidth.

Calculate the required values for your system parameters such as modulation level M, filter roll-off factor ? (of the Tx and Rx filters used in the “M-ary MODULATOR” and “M-ary DEMODULATOR” blocks, to meet the zero-ISI and above requirements, and derive the filter parameters and responses, and the bit error rate (or bit error probability, Pb) versus Eb/No performance expression. Develop the Simulink model to evaluate the Tx spectrum and performance in terms of bit error rate (or bit error probability, Pb) versus Eb/No for a Pb range from 10-8 to 10-1. Show your Simulink design diagrams with details.

Hint: The “Bernoulli Binary” block can be used to generate the random input Tx bit stream to the “M?ary MODULATOR”. For Bit Error Rate computation, the output Rx bit stream will be compared with the input Tx bit stream for bit error rate calculation using the “Error Rate Calculation” block. Note that due to the processing delay in both the Transmitter and Receiver, correct alignment of the Tx and Rx bit streams by using the “Align Signals” block before feeding them to the “Error Rate Calculation” block is necessary for correct bit error rate calculation. The “computation delay” parameter of the “Error Rate Calculation” block may need be adjusted/set to ignore some samples at the beginning of the simulation. You need to provide and explain the values of delay/ alignment parameters with explanations.

Compare the performance results obtained by analysis (derivation) and Simulink measurement. Provide (i) the Tx eye diagrams, and Tx spectrum at point B, and (ii) Rx eye diagrams, signal constellations (measured after the Rx filter) at Pb~10-4, 10-8, 0.

To improve the performance of the system designed in 1, you are requested to use a rate-½ convolutional code Select theappropriate code, and derive the bit error rate (or bit error probability, Pb) versus Eb/No performance expression for the coded system. Simulink encoder and decoder are inserted at points A and D, respectively. Develop the Simulink model to

evaluate the performance in terms of bit error rate (or bit error probability, Pb) versus Eb/No. Show your Simulink

design diagrams with details.

Compare the performance results obtained by analysis (derivation) and Simulink measurement. Replace the single-carrier un-coded (i.e., without convolutional codes) system in 1 by a 64-subcarrier un-coded OFDM. Due to some system design requirements, you only can use 54 inner subcarriers for data transmission while the 10 edge carriers are kept unused. Derive the required values for your system parameters to meet the same requirements (i.e., bit rate (fb), transmission bandwidth (B), modulation scheme given in Table 1), and derive the bit error rate (or bit error probability, Pb) versus Eb/No performance expression.

Develop the Simulink model to evaluate the Tx spectrum and performance in terms of bit error rate (or bit error probability, Pb) versus Eb/No for a Pb range from 10-8 to 10-1. Show your Simulink design diagrams with details. Compare the performance results obtained by analysis (derivation) and Simulink measurement. Show your Simulink design diagrams with details. Provide (i) the Tx spectrum at point B, and (ii) Rx eye diagrams, signal constellations at Pb~10-4, 10-8, 0. For each problem, provide the developed Simulink models with detailed descriptions, including (i) definitions of all supported variables/parameters, (ii) initialization conditions, and all the required steps for successfully running themodels.

NOTES: The assignment requires the developed Simulink models for each question as part of the solutions. In addition, the Simulink models must have detailed descriptions, including (i) definitions of all supported variables/parameters, (ii) initialization conditions, and all the required steps for successfully running the models. Moreover, please find the following notes/hints for the 3 problems:

Problem 1:

- The “M-ary MODULATOR” and “M-ary DEMODULATOR” blocks should include the pulse shape filters (e.g., Root Raised Cosine) to meet the limited bandwidth and zero-ISI requirements. Details of filter parameters and responses must be provided.

- To be able to calculate the Bit Error Rate computations can be realized by one of the following two approaches

o Approach 1: At the input to the Scrambler of the Transmitter, the “Bernoulli Binary” block can be used to generate the random Tx bit stream. At the receiver (output of the Descrambler), the detected Rx bit stream will be compared with the Tx bit stream for bit error rate calculation using the “Error Rate Calculation” block.

Note that due to the processing delay in both the Transmitter and Receiver, correct alignment of the Tx and Rx bit streams by using the “Align Signals” block before feeding them to the “Error Rate Calculation” block is necessary for correct bit error rate calculation. The “computation delay” parameter of the “Error Rate Calculation” block may need be adjusted/set to ignore some samples at the beginning of the simulation. You need to provide and explain the values of delay/ alignment parameters with explanations.

o Approach 2: Since Scrambler is used in the Transmitter to randomize the Tx bit stream, the input to the Scrambler can be set as the all-0 bit stream by using the “Signal From Workspace” block (and defining the appropriate signal in its “Signal” parameter, e.g., using zeros function). Correspondingly, the output of the Descrambler must be 0 for correct detection. Therefore, the bit error rate can be calculated from the number of 1’s in the Rx bit stream (output of the Descrambler). In practice, to measure the BER, the

transmitter transmits a known bit streams, usually all 0s, and at the receiver, counting the number of 1s gives the number of errors. To simulate this case, the students can use the “Signal From Workspace” block to define a specific signal at the transmitter (by defining appropriate signal in its “Signal” parameter, ex: using zeros function) in the Simulink model. Then, a copy of this “Signal From Workspace” block can be used at the receiver along with the output bit stream to feed into the “Error Rate Calculation” for

calculating the Bit error rate.

However, in this case the scrambler and descrambler polynomial and initial states should be chosen carefully to avoid the repetition of short bit streams which may lead to not good spectral and eye diagram. Below is an example of the Tx spectrum with a short scramble polynomial (order 8 only). In part (ii), the Rx eye diagram and signal constellations should be measured after the received Root Raised Cosine filter.

Problem 3:

- The Simulink model should not include the convolutional code (from Problem 2)

- In part (ii), the Rx eye diagram and signal constellation should be measured after the OFDM demodulation

process.