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Digital Communication Systems using MATLAB® and Simulink® utilizes a communication systems simulator by The MathWorksTM (echecs16.info) with. Digital Communication Systems Using MATLAB® and Simulink®. 2 Pages · · KB Experiments with MATLAB - MathWorks - MATLAB and Simulink for. use MATLAB® and. Simulink® to design and test digital modems and communication systems. systems course with lab sessions conducted using MATLAB.

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Note that x t represents the irst three terms of the Fourier series of the square wave. Use a 10 s simulation time and Goto and From routing blocks from Signal Routing to simplify the model. Display x t and cos t on a scope with labeled axes. From the Simulink library, add an AM modulation block to the simu- lation and form the difference between x t and the output of the AM library block.

Display x t , cos t , the AM block output and the difference on a scope with four traces. Insert x axis title on bottom trace only; do not label y-axis but add a title to each plot. Assume a 2 s simulation and sine wave block parameters as follows: Show the model with an included information block.

Provide titles for each trace and label only the x-axis. Speciic topics include: The Simulink model parameters for this example are speciied as follows: Sine Wave are provided in Figure 2. Figure 2. As a result, the plot from the scope is produced as shown in Figure 2.

Selecting Edit Figure Properties from the Edit menu in the plot allows the user to change the igure scales, color, line width, etc. To Workspace. The variable tout is the sample values of time displayed every 0. Table 2. Next a change is made to include a phase shift in the sine wave block as displayed in Figure 2.

A Simulink model for determining the spectrum and power spectrum of a sinusoidal signal is shown in Figure 2. In this igure, it can be observed that the 1 Schonhoff, T.

Data windowing controls the width of the main spectral lobe and sidelobe leakage. The rectangular window used to produce Figure 2.

This window provided a closer estimate of the spectrum peak in comparison with the theoretical value. The spectrum calculations using an FFT have demonstrated the need to utilize a window function to control the main lobe width and sidelobe leakage. The length of the FFT, the buffer over- lap, the number of averages and the window selection directly determine the accuracy of the spectrum. Show the Simulink Model using the running Variance block and include an information block. Assume a s simulation time.

Display the output in the scope and label all axes. Show the results in a Display block and compare with the theoretical value.

Use a 0. Display the results in the scope. Show the Simulink model with the simulated average powers and compare the result with the theoretical powers. Develop a model that allows each sinusoid to be displayed separately and label all axes in the scope output.

Selecting the sine block from the Simulink section of the Simulink library 2. Selecting the sine block from the DSP sources in the Simulink library Assume the phase is zero, the sample time is 0. Compute the power for both signals b.

Plot the scope output and compare the results 2. Assume the follow- ing parameters: Show the Simulink Model with an information block. For a 10 s sim- ulation time compute the power of the squared sine wave using the running Variance and running RMS blocks and show the results in Display blocks b. Display the output in the scope and label all axes c. Repeat Part a. Compare the results in Parts a. Mod- ify the scope to display the sine output and the output of the AWGN block a.

Display the revised Simulink model. Change the run time to s and report the results of the signal power from the output of the AWGN block and explain the difference from Part a.

Explain the result- ing change in the power from the output of the AWGN block 2. Insert a buffer overlap while retaining the FFT length. Com- pute the spectrum magnitude. With no buffer overlap reduce the FFT length to Compute the spectrum magnitude and the power spectrum magnitude using the spectrum analyzer. Use the DSP sine wave block as a source and compute the spectrum using 10 spectral averages.

Speciically these topics include: The menu selection for the Random Integer source block is shown in Figure 3. The outputs of this block are random double precision numbers that are either 0 or 1. A corresponding phase offset occurs in the BPSK demodulator. If the phase offsets angles between the modulator and demodulator do not agree, then errors will be made.

Implementation considerations may force such a disagreement and the degradation experienced can then be determined. Pressing the data tab reveals that the output is also double precision as shown in Figure 3. Figure 3. The data type button shown in Figure 3. Table 3. The routing symbols labeled S are connectors for the data, used to avoid cluttering the model, with an extra line.

The simulation time is extended to s allowing the input and output sequences to be observed in the scope display as seen in Figure 3. In Figure 3. Figures 3. Using scope 3, Figure 3. The next step in this simulation, shown in Figure 3. The parameter selections in the error rate calculation block are shown in Figure 3.

The receive delay and computation delay are both set to zero for this example. The computation delay allows transient behavior in the received data to be excluded from the BER estimate. The inal step in the construction of this model is to display the signal and port data types as shown in Figure 3. This selection is available in the Simulink model window menu under Display. In general, the sample time may be changed to explore the vagaries of the channel, which may change at much smaller time intervals.

Often an increase in the number of samples per symbol is desired as the case occurs when synchronization techniques are being investigated. Appendix 3. The time instants at which the signal is deined are the signal sample times, and the associated signal values are the signal samples. For a periodically sampled signal, the equal interval between any pair of consecutive sample times is the signal sample period, Ts.

The sample rate, Fs , is the reciprocal of the sample period. It represents the number of samples in the signal per second. Note that the accuracy of the simu- lated result improves with an increasing number of demodulated symbols.

In the simulated case, a better estimate of the BER at low BER is obtained by using a larger number of transmitted symbols. TABLE 3. There are situations where it is not possible to simply introduce the AWGN block in the simulation and the noise must be added directly. However, it is important to understand that under the proper simula- tion conditions both the AWGN block and the Gaussian noise block used with an adder produce the same results. Note that the seed num- bers are different for the real and imaginary parts of the complex Gaussian noise generator to ensure statistical independence between the quadrature noise components.

Running variance blocks are used to compute the signal power for several signals, which are then displayed in the model. From the displays, it can be observed that the noise power from display 2 is 0.

The simulated BER is 0. The model shown in Figure 3. It is not apparent from the model and the signal powers displayed that these models should produce the same result. The imaginary part is discarded in the demodulator so that including the imaginary Gaussian noise block is unnecessary. It should be noted that complex Gaussian noise is not needed since the BPSK demodulator takes the real part of the input signal to form its decision.

A frame consists of a sequential sequence of samples from a single channel or multiple channels; the user must specify the frame size as an integer number of samples. Frame-based simulations execute faster and are often needed for matrix computations, where it is inconvenient to use sample-based computation. Running 0. In this model, addi- tional blocks, identiied as scatter blocks, display the constellation of the QPSK demodulator and the received input to the QPSK demodulator.

On the right side of Figure 3. In this model, each variance of the real and imaginary parts of the complex Gaussian noise is 0. In these cases, the power of Simulink is not apparent. Fixed point numbers are represented in binary by means of their word length denoted by ws, a binary point and a fraction of length, n. The ixed point structure, shown in the Figure 3. The MSB is assumed to be a sign bit, s, that is assigned 1 for signed representation and 0 for unsigned.

The discussion provided here follows the MATLAB desig- nation where the ixed point number is expressed as ixdt s,ws,n. The selection of the word size and fraction length is based on the eventual implementation in an ASIC or FPGA device where the word size controls the range of the values to be represented and the fraction length controls the precision.

More detail on ixed point representations is available in the MathWorks documentation under the category ixed point numbers. In the model shown in Figure 3. The input parameters for the convert block are shown in Figure 3. Since the BPSK modulator would normally be part of the ixed point implementation, the same ixed point representation ixdt 1,8,4 is used.

The results shown in Figure 3. The choice- of word length and fraction length is usually a compromise involving the numerical range of the numbers to be represented, the precision of these numbers and the quantization errors introduced to deliver the best representation of the digitized signals for the planned hardware implementa- tion.

Saturation may occur if the upper and lower limits of the numbers are exceeded with the consequence that inaccurate estimation or unpredictable errors occur.

An example of ixed point issues identiied thus far is obtained by comput- ing BER results for selected ixed point combinations using the model shown in Figure 3.

Use of a fraction length greater than 4 causes saturation in this model. Simulation results using AWGN blocks and Gaussian noise generator blocks yield identical performance with properly chosen parameters.

Use of a large sample size produces excellent agreement between theoretical and simulated BER performance. The AWGN block or a Gaussian noise block may be selected for either sample-based or frame-based simulation.

A ixed point example is included where theoretical performance is dificult or impossible to obtain. Does the BER remain the same as the case with 1 s symbol duration?

Why does it take longer to execute with 0. Is the BER the same as the case with sample-based simulation? Does the simulation take the same time to complete? The results show the degradation from a ixed channel phase offset compared to the case where no offset exists.

Does this produce the same results? Filter specs: FIR, minimum, single rate; freq specs: Execute the simulation using s and observe the spectrum ana- lyzer output. What are the frequency limits for the lowpass ilter? Add a running variance block at the output of the Gaussian noise block, the output of the sine wave block, the output ofthe low pass ilter, and the output of the adder. What power levels are obtained? Make the following changes in the low pass ilter: Explain what the differences are due to compared with part a.

Topics presented here are listed as follows: As a speciic example, Figure 4. Gray coding is stipulated as well. As an example, the constellation for 8-PSK is shown in Figure 4. Figure 4. The BER results shown in Figure 4. An important choice in simulating the QAM BER perfor- mance is whether the performance is obtained for peak or average power.

Peak power is often an important consideration when the power must be constrained to stay within the power ampliier PA limits to avoid satura- tion. In the next example, BER is computed using average power; subsequent examples will demonstrate the need for peak power computations.

The normalization can be set to average power, peak power, or minimum dis- tance between symbols. It is now seen that the simulated and theoretical results are in good agreement. Good agreement is observed between the theoretical and simulation results. The degradation is most easily observed by examining Figure 4. As a result, a penalty in BER is incurred relative to average power operation when the results are compared with those in the previous section.

In general, power ampliiers exhibit memoryless, nonlinear behavior. One of the power ampliier models, attributable to Saleh1 , will be studied here to estimate the impact on BER performance.

This example highlights the utility of Simulink for a practical case where no theoretical results are available. COM, pp. Saleh notes that an rms error of 0.

These equations and values of the parameters have been found to it measured TWT data. The BER without the nonlinear device is 0. The signal constellation at the output shows scattering and warp- ing of the rectangular QAM constellation resulting in a poor BER. When a QAM modulator output is the input to a nonlinear device, the input voltage is backed off to force the modulated waveform to remain within the linear portion of the device.

Since the Saleh model is an ideal monotonic function up to the saturation point, an ideal predistortion device can be implemented that exactly compensates for the distortion by computing an inverse function of the nonlinear characteristic. Speciically, the S function presented here accomplishes the exact compensation and is a perfect linearizer. The S function, labeled nlinvd.

The m-ile listing is given as follows: The BER without the nonlinear device and with the included predistortion block is 0. It is now evident that the predistortion device compensates exactly for the Saleh nonlinearity. The scatter plots, shown in Figure 4.

Note that the actual implementation of the predistortion device will degrade BER performance. Goto [Tx] scatter scatter scatter [Tx] 0. The use of the bertool was applied extensively in the BER com- putations. QAM signaling required a study of both peak and average power to address issues with saturation in nonlinear PAs. The power of Simulink was revealed in the example where a nonlinear device was introduced in the simulation to address the case where no theoretical results are available.

The incorporation of a user-deined S function, developed in MATLAB, was also illustrated to allow the user to modify the simulation when no library block is available. What is the theoretical peak power degradation? What is the approximate degradation obtained in the simulation? What is the simulated BER in this case? Show the scatter plot at the nonlinearity output.

Change the third order intercept point to 35 dBm and determine the simulated BER and the scatter plot at the nonlinearity output. In the simulation, the spectrum scope computes the FFT with a rectangular window, spectral averages with no overlap, a FFT size and a These settings are obtained by selecting spectrum settings under the View tab in the spectrum scope.

Figure 5. Using a utility block not shown in Figure 5.

As shown in Figure 5. Good agreement can be observed between the theoretical and simulated results. Speciic input parameters are as follows: Wireless Communications Prentice Hall, p. Using the Simulink model in Figure 5. The spectrum analyzer uses averages with a Hann window and no overlap. The constants in the simulation are selected to force the gain at zero frequency to be approximately 0 dB.

The spectrum analyzer was used extensively and shown to offer a wide selection of spectral estimation techniques and parameters. A sine wave has a power of 0. Explain why the modulator output power is 1 W. How does this result com- pare with the MSK power spectrum? Speciically these topics include the following: Here it is useful to review the theoretical BER performance for Rayleigh fading channels in order to establish a framework for Simulink model construction.

Appendix 6. The time-varying nature of the channel is also characterized by its power spectral density S f. A summary of the model parameters is speciied as follows: The estimated BER is 0. Figure 6. Salehi, Digital Communications, 5th ed, pp. Running 1 [tx] [tx] VAR 0.

This function is required to track the channel time-variability where the receiver implementation ordinarily incorporates an automatic gain control AGC. In this model, the box for selection of Rician fading channel parameters is checked to open the channel visualization at the start of the simulation.

In this simu- lation, speciic parameters include the Rician K factor that speciies the ratio of the specular component to the diffuse multipath components, the Doppler shift associated with the specular line-of-sight component, and the max- imum Doppler shift associated with the diffuse multipath components. Figures 6. The Simulink model for this case is provided in Figure 6.

Multipath parameters are not speciied in this simulation since lat fading is assumed.

Note that increasing the value of the Rice factor suggests a stronger dominant received signal component, thus resulting in an improved Figure 6.

Good agreement is observed between theoretical and simulated BER for all cases. Introducing added parameters allows the insertion of multi- path as a vector of path delays and a vector of average path gains. Here two paths are introduced with a main path and a second delayed path that has an average path gain deined as X. The average overall path gain is normalized to 0 dB. Using the Simulink model in Figure 6.

It is observed that a null in the frequency response, resulting from the presence of multipath, occurs at 0.

Comparing Figure 6. To conirm this result, Figure 6. The error probability is then seen to be 0. The model shown in Figure 6. The interference introduced by the multipath is seen to cause a severe increase in BER even when the second multipath component is 3 dB lower than the main path. Using the bertool, Figure 6. The model parameters are speciied as follows: As the multipath gain X gets larger, signiicant loss in BER occurs.

When the channel exhibits fading, BER performance for speciic modulations depends on the selected fading model and is severely degraded from performance in AWGN. Examples provided here included Rayleigh and Rican fading models. Simulink models allow the BER performance in the presence of multipath to be readily estimated.

This capability provided by Simulink is important since estimation of BER in the presence of multipath is not easily obtained analytically. E In Appendix 3. Salehi, Digital Communications, 5th ed pp. What is the resulting BER? Using a modiied simulation based on the same Rician and AWGN parameter selections, show that over the 10, s simulation time, the main component magnitude is on average greater than the sec- ond component magnitude.

What is the magnitude of these components after 10, s in your simulation? What is the resulting BER and how do you explain the change? Find the frequency null and explain its location. Determine and explain the magnitude of the normalized spectrum from Prob 6.

Increase the delay to 4 s and determine the location of the null. The time-varying nature of the channel is again characterized by its power spectral density S f according to the Jakes fading model presented in Chapter 6.

This plot was obtained from the spectrum analyzer with scope settings: Figure 7. Good agreement is observed between the theo- retical and simulated BER performance. The the- oretical result for the probability of error Pb is summarized in Appendix 7. A summary of the model parameters is provided as follows: In Figure 7.

The model shown in Figure 7. This implementation allows the effects associated with variations in the second average path gain, X to be investigated. The model parameters are as follows: Using the bertool, Figure 7. It is clear that even with relatively weak multipath, BER performance is severely degraded. However, when the channel exhibits fading, BER performance for speciic modula- tions depends on the selected fading model and is severely degraded from performance in AWGN. This capability, provided by Simulink, is important since estimation of BER in the presence of multipath is not easily obtained analytically.

From Appendix 6. List the model parameters. How does this result compare with theoretical performance? Explain the result. And discuss how it compares with the simulated BER. Figures 8. The parameters for this model are speciied as follows: Using the BER formula in Appendix 8.

A, theoretical results for diversity 1 and 2 are displayed for com- parison with the simulated data. B with two transmit antennas and L receive antennas.

A Simulink model for two transmit antennas and two receive antennas is provided in Figure 8. The Rayleigh fading channel model is displayed in Figure 8. However, when the channel exhibits fading, BER performance for speciic modulations depends on the selected fading model and is severely degraded from perfor- mance in AWGN.

The scheme is summarized here for two transmitting antennas and one receiving antenna employing maximal ratio combining. The space—time view is illustrated in Figure 8. In this igure, symbol u0 is transmitted over antenna 0 and symbol u1 is simultaneously transmitted over transmitting antenna 1. The estimates are then used to form the decision based on the minimum Euclidian distance. For the two transmit antennas each carrying one symbol and two symbols sent over successive intervals i.

Ramesh, and A. Find the theoretical BER for the parameters shown in Figure 8. Display the Simulink model and the channel model. Model param- eters are speciied as follows: In Figure 9. Data from the random integer source is buffered into length 16 symbols for use by the BCH encoder.

The parameters for the Hamming encoder are shown in Figure 9. The default condition is selected to use a primitive polynomial over Galois ield 2m. Note that m is capitalized in the Hamming encoder block parameters. Simulink model parameters are speciied as follows: Levesque, op. In the RS encoder and decoder, the default generator is selected and noncoherent detection with hard deci- sions is performed in the FSK demodulator. Figure 9.

The channel path coeficients are 1. The Simulink multipath channel is shown below the main Simulink model in Figure 9. The BER results are shown in Figure 9. The results indicate that coding improves the BER when multipath is present but does not completely eliminate the degradation due to multipath.

An example was provided to demonstrate the degradation due to multipath with and without coding. A summary of the simulated and theoretical BER results for each case is provided in Table 9. TABLE 9. What is the minimum distance of the code? What is the theoretical upper bound on the BER? Use the same model parameters as those in the Figure 9.

For this code what is the minimum distance and number of cor- rectable errors? Speciic topics include the following: The Rayleigh fading channel model is displayed in Figure Figure The scope is used to identify the misalignment between the transmitted and decoded sequences and thus obtain the delay. The input data sequence is delayed as seen in Figure The model parameters for the frame-based simulation are speciied as follows: BER [S] Running 0.

Doppler spectrum Frame count: The BER results for both interleavers are shown in Figure With a FSK modulation, an appropriate match is an RS 31,15 code, which has a minimum distance of The Rayleigh channel model is the same as that in Figure Sub- stantial coding gain is evident from this igure. The Rayleigh channel model is again the one used in Figure Once again, substantial coding gain is observed in the igure. Display9 Running 1.

A second channel model is now considered, where the Rayleigh fading channel is changed to introduce a Jakes Doppler spectrum with a 0. The BER results are shown in Figure Two separate paths are implemented where the only difference is the choice of a Rician or Rayleigh channel. The Rician channel is modeled with a Jakes fading spec- trum having the maximum diffuse Doppler shift and the line-of-sight Doppler shift both selected to be 0.

In this igure, it is observed that Rayleigh fading produces the poorest BER results. Multiple antennas for the transmitter, the receiver, or both offer this improvement without expanding the bandwidth and allow for an increase in data rate. In a two-antenna transmit diversity scheme with a single receive antenna, two symbols are sent simultaneously over the two transmit antennas and are then resent after space—time encoding in the next symbol interval; the receiver then combines the symbols over two symbol intervals and makes a decision using a maximum likelihood detector.

The Simulink model shown in Figure The four Rayleigh channel paths all assume a Jakes Doppler spectrum with a maximum Doppler shift of 0. The four-path Rayleigh channel model is the same as the one used in Figure The performance beneit of using STBC is easily seen.

The four-path Rayleigh channel model is the same as the one shown in Figure The performance beneit of using STBC is again observed. The four path Rayleigh channel model is the same as the one shown in Figure The performance beneit of using STBC is observed again. By incorporating interleaving, the block error control codes can utilize their individual distance properties to correct bit errors and provide signiicant coding gain over uncoded schemes that use the same modulation.

Most of the results were developed for Rayleigh fading but an example with Rician fading was included, to demonstrate that Rayleigh fading causes the worst case BER.

The last sections of this chapter repeated the block error control coding and modulation cases with interleaving and Alamouti STBC. The STBC results indicate signiicant gain over uncoded modulations with large diversity order.

Identify the model parameters and display the Simulink model b. Compare the results with theoretical uncoded BPSK Identify the model parameters in a. Identify the model parameters in c. The BPSK demodulator is followed by a maximum likelihood decoder using the Viterbi algorithm VA where hard-decision decoding is selected. Simulink implements the convolutional encoder and decoder by means of a trellis structure for the generator polynomial with a speciied constraint length and feedback taps given in octal.

As an example, the poly2trellis 7, [ ] notation represents a trellis structure for a binary convolutional code with constraint length 7 and feedback taps located at the octal numbers binary and binary The free distance dfree of the convolutional code is the minimum distance in the set of all arbitrarily long paths that diverge from the all zero state and reenter the all zeros state.

The Hamming distance corresponds to the number of positions in which the symbols differ. The free distance for the convolutional code poly2trellis 7, [ ] is The Simulink model, depicted in Figure The simulation is stopped once errors are obtained. The Simulink model parameters for the convolutional code poly2trellis 3, [5 7] are speciied as follows: Theoretical upper bounds obtained with the bertool are also depicted. The principal difference between Simulink models shown in Figures An expanded view of the quantizer block, displayed by looking under the mask, is shown in Figure McGraw-Hill , pp.

Three-bit soft decisions are selected in the Viterbi soft-decision decoder. The Simulink model parameters for the convolutional code poly2trellis 7, [ ] with soft decisions are speciied as follows: Assuming that the all-zeros code word is sent, a variable ad is deined to be the number of paths of distance d from the all zero path that merges with the all zero path for the irst time.

It is observed that there is about a 2 dB gain for soft over hard decisions. From Figure Due to the fad- ing behavior, the models must include an interleaver to disperse error bursts allowing the code to be effective in correcting the errors. The Simulink models presented for hard decisions in Figure The input to the matrix interleaver is entered row-by-row and its output is produced column-by-column; the number of rows and columns are each 14 for the mod- els as shown in Figures The scopes shown in Figure The Simulink model parameters for the model shown in Figure You can change your ad preferences anytime.

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