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Digital Communication Systems using MATLAB® and Simulink® utilizes a communication systems simulator by The MathWorksTM (ronaldweinland.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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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 Note that only the Jakes model and a single value of 0.

The simulated results illustrate the degradation in performance due to Rayleigh fading versus AWGN transmission. The Simulink model parameters for Figures In Rayleigh fading channels, the use of interleaving allows the convolutional error control codes to utilize their free distance properties to correct bit errors and provide signiicant coding gain over uncoded schemes that use the same modulation. The last section of this chapter repeated the convolutional error control coding and modulation cases with interleaving and Alamouti STBC.

Incorporation of STBC indicates that much of the per- formance loss due to Rayleigh fading is recovered.

List the Simulink model parameters and determine the upper bound on post-decoding BER from the bertool. List the Simulink model parameters. Display the Simulink models for hard- and soft-decisions. Rician parameters shown in Figure P. The channel is modeled as a discrete-time channel ilter with delay values corresponding to the symbol interval T and channel coeficients that represent the channel distortion.

The channel model seen in Figure Adaptive equalizers compensate for these channel dis- tortions and provide signiicant improvement in BER. This section presents linear LMS equalizers implemented using a inite duration impulse response FIR ilter with delay elements corresponding to the symbol duration and coeficients that are adaptively determined by an LMS algorithm.

In some equalizer designs, known symbols are multiplexed with unknown symbols. Giordano, op. For clarity, it is helpful to present a simple analytical example prior to pro- ceeding with the Simulink model. The results indicate that no errors occur using the three coeficients computed above. The ixed channel coeficients assumed earlier ordinarily apply for a lim- ited interval. In general, the equalizer must track the time-varying channel characteristics. In this case, the equalizer coeficients must adapt to the time- variation.

An algorithm that accomplishes this task for channels with slow time variations is referred to as a stochastic gradient algorithm and is more commonly referred to as an LMS algorithm. A Simulink model that implements a three tap LMS adaptive equalizer using a training signal is shown in Figure The received signal is synchronized to the center tap of the equalizer.

The magnitude of the ilter response is shown in Figure Two-path multipath 1, 0. This igure indicates that in this noiseless case a detector would make the correct decisions, that is, no errors with equal- ization, even though the equalized signal is a distorted version of the transmitted signal.

The real parts of the coeficients are obtained from scope1, scope2, and scope3 shown in Figure In this simulation, the training sequence utilized was the data from the BPSK modulator.

In an actual implementation, two common schemes include: The equalizer parameters, shown in Figure As a result, Figure Substantial improvement in BER is then attained by use of the adaptive equalizer. The top trace shown in Figure In this case, the ISI does not affect the symbol error probability. Scatter plot Scatter plot 1. Table With equalization the resulting errors are reduced with symbol error probabilities that are close to the system without the digital ilter.

The data in Table An implemen- tation of a symbol-spaced DFE is shown in Figure An example is now presented to compare the performance of a linear LMS equalizer with a decision feedback equalizer assuming BPSK modulation. The channel is a two-tap multipath channel spaced at the symbol rate with real gains 1, 1.

The top trace is the BPSK demodulator output using the linear LMS equalizer; the middle trace is the source output delayed by three symbols; the bottom trace is the BPSK demodulator output using the decision feedback equalizer. A 50 s computation delay is used in both equalizers to allow them to converge before computing the BER. Agreement among the three traces is then observed after the 50 s computation delay.

As a consequence, RLS algorithms offer improved performance in time varying channels where fading is preva- lent. A brief summary of the RLS algorithm is presented prior to proceeding with Simulink modeling. RLS algorithm deinitions are provided in Table The RLS equations are presented as follows: RLS estimated output7: Since there is no computation delay, the irst pulse in Figure For the selected model parameters, it is seen in Figure Delayed Source Output; Middle Trace: The Simulink model parameters for this example are listed as follows: The equalizer choice is a tradeoff between the rate of convergence and the implementation complexity.

Decision feedback equalizers were shown to offer better performance than linear LMS equalizers. For fading channels with rapid time variation, an RLS equalizer offers the best perfor- mance. In all cases, inal performance is dictated by the selection of relevant parameters such as the scale factor in LMS equalizers and the forgetting factor in RLS equalizers. Plot the error magnitude and the real part of the center tap coeficient as a function of time and compare the results to the case with the 0.

Display the Simulink model as in Figure Identify the normal equations in matrix form for this case 3. Compute the ideal equalizer coeficients 4.

Display the magnitude of the error and the real part of the two equal- izer coeficients versus time for a simulation of 10, s 5. Using bertool plot the BER with and without the equalizer along with the theoretical result with no multipath Using the bertool obtain the BER for the linear LMS and decision feedback equalizers and compare the results to the channel with no multipath.

Assume that the RLS decision feedback equalizer has 8 feed forward and 8 feedback taps with a 0. Assume that the lin- ear RLS equalizer has 8 taps with 0.

This chapter presents a number of illustrative examples; the topics covered here include the following: The reader is encouraged to execute the models and experiment with the parameters of the model and selections made for running the model.

Unvoiced sounds, known as plosive, due to mouth closure, and fricative, due to narrow passage of air through the mouth, occur in the case where the vocal cords do not vibrate.

The pitch period, P, for human speech typically ranges from 2. The gain G, representing the volume of air passing through the vocal tract, determines the loudness of the voice. These coeficients are then sent to the receiver where an all-pole synthesis ilter is used to reconstruct the speech. Thus instead of sending the speech signal itself at a high transmission rate, a lower transmission rate is used to transmit the prediction coeficients instead.

This Simulink model uses a variable-step with a discrete solver. The sam- ples are generated at intervals of 0. The voiced signal consists of a train of impulses with a pitch period of 10 ms. The unvoiced signal is bandlimited white noise. The gain is arbitrarily set to be 0. The multiplier output is passed through an all-pole ilter with its six denominator coeficients selected to be [1 0. The output of this ilter then represents a model of a speech signal. The correlations are computed using the autocor- relation function ACF block with input from the buffer.

The 10 coeficients are displayed along with the prediction error power. The analysis ilter accepts the speech input and produces the error signal. The synthesis ilter accepts the error signal and reconstructs the speech signal. From top to bottom, the traces are: Note that the speech signal exhibits bursts with silent periods.

Time series plit: Since this simulation is idealized, the error signal is zero. BPSK modulation is selected, where two demodulators are used in order to compare the BER bit error rate perfor- mance with and without the canceller.

The RLS ilter has length 8 with outputs that include the error signal and ilter weights in addition to the iltered output. The eight complex ilter weights are seen in Figure The power spectrum for the two ampliied sinusoids is displayed in Figure In the RLS ilter, the desired signal is the signal plus interference and the input is the interference alone. The RLS ilter output is then an estimate of the interference, which is then subtracted from the signal-plus-interference to form an estimate of the transmitted signal labeled as EQ in Figure The signal-plus-interference labeled SPI in Figure It is evident from Figure This igure illustrates that the two errors occur early as the RLS ilter con- verges and no errors occur thereafter.

Note that in Figures From Table The s simulation shown in Figure This igure illustrates that errors occur early as the RLS ilter converges and no errors occur thereafter. Once again Table TABLE Additive noise is included but no interference is added, in order to illustrate the spread spectrum system characteristics.

The traces from top to bottom are: In Figure For simplicity, an inter- fering sinusoidal signal is introduced as seen in the Simulink model shown in Figure The peak for the 1 kHz complex sinusoid is visible along with the data observed at 0 kHz.

As shown in Figure The output from the error rate calculation demonstrates that errors are now observed. Figures As a result, this simulation demonstrates that the interference is effectively elimi- nated and no errors occur at the demodulator output. The RLS error magnitude shown in Figure A simple Simulink antenna nulling example will now be presented after a brief discussion of the theory.

The array uses weights w0 and w1 to multiply the received signals y1i and y2i , respectively, on the individual branches. The output of the array is the estimate of the interferer. A Simulink model for a noise-free example of interference nulling using an LMS algorithm is presented in Figure The real and imaginary parts of coeficients w0 and w1 are displayed in Figures For this special case, it is observed that the simulated values of w0 and w1 are converging to the theoretical values computed earlier.

The error rate calculation shown in Figure Another Simulink simulation is presented in Figure The Kalman ilter can be viewed as a generalization of the recursive lease squares algorithm for stochastic signals and applies when the signals and noise are nonstationary. Start on. Show related SlideShares at end. WordPress Shortcode. Published in: Full Name Comment goes here. Are you sure you want to Yes No. Be the first to like this.

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