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

## Problem 1: 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.

## Problem 2: Improving the Performance of the Bandlimited M-ary Modulation System using Rate-½ Convolutional Code

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.