Questions and Answers of Principles Communications Systems

(a) Given the random binary data sequence 0 1 1 0 0 0 1 0 1 1. Provide waveform sketches for:(i) NRZ change;(ii) Split phase.(b) Demonstrate satisfactorily that the split-phase waveform can
Explain what happens to a line-coded data sequence when passed through a severely band limited channel.
Tell which binary data format(s) shown in Figure 5.2 satisfy the following properties, assuming random (fair coin toss) data: Figure 5.2 (a)?Zero DC level;(b)?A zero crossing for each data bit;(c)
For the ? 1- amplitude wave forms of Figure 5.2, show that the average powers are: (a) NRZ change--- Pave = 1 W;(b) NRZ mark--- Pave = 1 W; (c) Unipolar RZ--- Pave = 1/4 W; (d) Polar RZ--- Pave = 1/2
Which data formats, for a random (coin toss) data stream, have (a) zero dc level; (b) built in redundancy that could be used for error checking; (c) discrete spectral lines present in their power
Evaluate the time-average Poynting vector, = (12) Re {EsÃ— Hˆ—s} for the Hertzian dipole, assuming the general case that involves the field components as given by Eqs. (10),
Evaluate the time-average Poynting vector, = (1/2)Re EsÃ— Hˆ—sfor the magnetic dipole antenna in the far zone, in which all terms of order 1/r2and 1/r4are neglected in Eqs.
A 50-Ω load is attached to a 50-m section of the transmission line of Problem 10.1, and a 100-W signal is fed to the input end of the line.(a) Evaluate the distributed line loss in dB/m.(b) Evaluate
A coaxial cable has conductor radii a and b, where a < b. Material of permeability μr ≠ 1 exists in the region a < ρ < c, whereas the region c < ρ < b is air filled. Find an
Revisit Problem 14.21, but with the current phase allowed to vary with frequency (this will automatically occur if the phase difference is established by a simple time delay between the feed
A two-element dipole array is configured to provide zero radiation in the broadside (ϕ = ± 90◦) and end-fire (ϕ = 0, 180◦) directions, but with maxima occurring at angles in between. Consider
Repeat Problem 14.17, but with a full-wave antenna (2ℓ = λ). Numerical integrals may be necessary.Consider a lossless half-wave dipole in free space, with radiation resistance, Rrad = 73 ohms, and
Suppose that Ï• in Figure 12.17 is Brewster€™s angle, and that Î¸1is the critical angle. Find n0in terms of n1and n2. пz По пy П2
A uniform plane wave is normally incident onto a slab of glass (n = 1.45) whose back surface is in contact with a perfect conductor. Determine the reflective phase shift at the front surface of the
Sulfur hexafluoride (SF6) is a high-density gas that has refractive index, ns = 1.8 at a specified pressure, temperature, and wavelength. Consider the retro-reflecting prism shown in Fig. 12.16, that
Suppose that the length of the medium of Problem 11.31 is made to be twice that determined in the problem. Describe the polarization of the output wave in this case.In Problem 11.31A linearly
(a) Most microwave ovens operate at 2.45 GHz. Assume that σ = 1.2 × 106 S/m and μr = 500 for the stainless steel interior, and find the depth of penetration.(b) Let Es = 50 0◦ V/m at the
Perfectly conducting cylinders with radii of 8 mm and 20 mm are coaxial. The region between the cylinders is filled with a perfect dielectric for which ∈ = 10−9/4π F/m and μr = 1. If E in this
Describe how the attenuation coefficient of a liquid medium, assumed to be a good conductor, could be determined through measurement of wavelength in the liquid at a known frequency. What
A lossless line having an air dielectric has a characteristic impedance of 400Ω. The line is operating at 200 MHz and Zin = 200 − j200 Ω. Use analytic methods or the Smith chart (or both) to
The incident voltage wave on a certain lossless transmission line for which Z0 = 50Ω and νp = 2 × 108 m/s is V+(z, t) = 200 cos(ωt − πz) V.(a) Find ω.(b) Find I+(z, t). The section of line
In Section 9.1, Faraday’s law was used to show that the field E = −1/2 kB0ektρaϕ results from the changing magnetic field B = B0ektaz.(a) Show that these fields do not satisfy Maxwell’s other
Repeat the previous computer exercise with 20 values of θ uniformly distributed in the range - π/4 ≤ θ < π/4.Data From Problem 7.1In this computer exercise we reexamine Example 7.1. A random
Show that the variance of?âML?(Z) given by (11.178) is the result given by (11.179). (11.178) (11.179) K âM, (Z) K k=1
Consider the reception of a BPSK signal in noise with unknown phase, Î¸, to be estimated. The two hypotheses may be expressed asH1 : y(t) = A cos(Ï‰ct + Î¸) + n(t),
Write a computer program to evaluate various digital modulation techniques:(a) For a specified data rate and error probability, find the required bandwidth and Eb / N0 in decibels. Corresponding to
Consider the random process of Problem 7.3.(a) Find the time-average mean and the auto correlation function.(b) Find the ensemble-average mean and the auto correlation function.(c) Is this
A random variable X has the probability-density functionwhere Î± is an arbitrary positive constant.(a) Determine the characteristic function Mx(jv).(b) Use the characteristic function to
An algorithm for generating a Gaussian random variable from two independent uniform random variables is easily derived.(a) Let U and V be two statistically independent random numbers uniformly
In this exercise we examine a useful technique for generating a set of samples having a given pdf.(a) First, prove the following theorem: If X is a con tinuous random variable with cdf FX(x), the
(a) Write the signals of Figure 2.37 as the linear combination of two delayed triangular functions. That is, write xa(t) = a1 Î› ((t - t1) / T1) + a2Î›((t - t2) / T2) by
Write a computer program to find the time duration of a low pass energy signal that contains a certain specified percentage of its total energy, for example, 95%. In other words, write a program to
How would you use the same approach as in Computer Exercise 2.3 to evaluate the Fourier transform of a pulse-type signal. How do the two outputs differ? Compute an approximation to the Fourier
A toroidal core has a square cross section, 2.5 cm < ρ < 3.5 cm, −0.5 cm < z < 0.5 cm. The upper half of the toroid, 0 < z < 0.5 cm, is constructed of a linear material for which
A sinusoidal voltage source drives the series combination of an impedance, Zg = 50 − j50Ω, and a lossless transmission line of length L, shorted at the load end. The line characteristic
In Figure 10.17, let ZL= 250, Z0= 50, find the shortest attachment distance d and the shortest length d1of a short-circuited stub line that will provide a perfect match on the main line to the left
In Figure 12.5, let regions 2 and 3 both be of quarter-wave thickness. Region 4 is glass, having refractive index, n4= 1.45; region 1 is air.
A filamentary conductor is formed into an equilateral triangle with sides of length ℓ carrying current I. Find the magnetic field intensity at the center of the triangle.
Let V(x, y) = 4e2x + f (x) − 3y2 in a region of free space where ρν = 0. It is known that both Ex and V are zero at the origin. Find f (x) and V(x, y).
Given the spherically symmetric potential field in free space, V = V0e−r/a, find.(a) ρν at r = a;(b) The electric field at r = a;(c) The total charge.
Let V = 2xy2z3 and ∈ = ∈0. Given point P(1, 2,−1), find.(a) V at P;(b) E at P;(c) ρν at P;(d) The equation of the equipotential surface passing through P;(e) The equation of the streamline
A two-wire transmission line consists of two parallel perfectly conducting cylinders, each having a radius of 0.2 mm, separated by a center-to-center distance of 2 mm. The medium surrounding the
A potential field in free space is given in spherical coordinates aswhere Ï0 and a are constants.(a) Use Poisson€™s equation to find the volume charge density everywhere.(b) Find
In this computer exercise we reexamine Example 7.1. A random process is defined byX(t) = A cos (2πf0t + θ)Using a random number generator program generate 20 values of θ uniformly distributed in
Check the correlation between the random variables X and Y generated by the random number generator of Computer Exercise 6.2 by computing the sample correlation coefficient of 1000 pairs according to
Write a MATLAB program to plot the Ricean pdf. Use the form (7.150) and plot for K = 1, 10, 100 on the same axes. Use r / Ïƒ as the independent variable and plot Ïƒ2f (r).
Let the sample functions of a random process be given byX(t) = A cos 2Ï€f0twhere Ï‰0 is fixed and A has the pdf This random process is passed through an ideal integrator to
In discussing thermal noise at the beginning of this chapter, we stated that at standard temperature (290 K) the white-noise assumption is valid to bandwidths exceeding 1000 GHz. If the temperature
The received signal in a digital base band system is either +A or -A, equally likely, for T-second contiguous intervals. However, the timing is off at the receiver so that the integration starts
(a) Consider the transmission of digital data at a rate of R = 50 kbps and at an error probability of PE = 10-6. Using the bandwidth of the main lobe as a bandwidth measure, give an estimate of the
Use MATLAB to plot curves of Pbversus Eb/ N0, M = 2, 4, 8, 16, and 32, for(a) M-ary coherent FSK (use the upper-bound expression as an approximation to the actual error probability)(b) M-ary
Show that the noise components N1and N1for QPSK, given by Equations (10.6) and (10.8), are uncorrelated; that is, show that E[N1N2] = 0. (Explain why N1and N12are zero mean.) (10.6) n(t) cos(27f t)
Show that (10.26) and (10.27) are Fourier transform pairs. In 2 (f (10.26) н (f)— еxp 2л? в 2л -B exp In 2 h(t) = (10.27) In 2
(a) Sketch the signal space with decision regions for 16-ary PSK [see (10.47)].(b) Use the bound (10.50) to write down and plot the symbol error probability versus Eb / N0.(c) On the same axes,
(a) Using (10.93) and appropriate bounds for PE,symbol, obtain Eb / N0 required for achieving PE,bit = 10-4 for M-ary PSK with M = 8, 16, 32.(b) Repeat for QAM for the same M values using (10.63).
Repeat Example 10.6 with everything the same except for a propagation delay uncertainty of ± 1.5 ms and a false-alarm penalty of Tfa = 100Ti.
(a) Consider a multi path channel with a delay spread of 5 microseconds through which it is desired to transmit data at 500 kbps. Design an MCM system that has a symbol period at least a factor of
Rework Examples 10.11 and 10.12 for an attenuation exponent of α = 4.
(a) Using (10.95), (10.96), and (10.67), obtain Eb / N0 required for achieving PE,bit = 10-3 for M-ary coherent FSK for M = 2,4,8, 16,32. Program your calculator to do an iterative solution or use
Given the following parameter values from the IEEE802.16 standard:Modulation Coding
Consider the system shown in Figure 8.21, in which an RC high pass filter is followed by an ideal low pass filter having bandwidth W. Assume that the input to the system is A cos(2Ï€fct),
The waveform at the input of a base band system has signal power PT and white noise with single-sided power spectral density N0. The signal bandwidth is W. In order to pass the signal without
Execute the computer program used to generate the FM discriminator performance characteristics illustrated in Figure 8.14. Add to the performance curves for Î² = 1, 5, 10, and 20 the curve
A signal is given byx(t) = 5 cos [2Ï€(5)t]and the noise PSD is given byDetermine the largest permissible value of N0 that ensures that the SNR is ‰¥ 30 dB. If|< 8 S„(f) = No.
The value of the input SNR at threshold is often defined as the value of PT / N0W at which the denominator of (8.172) is equal to 2. Note that this value yields a post detection SNR, (SNR)D, that is
Derive the equation for yD(t) for an SSB system assuming that the noise is expanded about the frequency fx = fc ±1/2W. Derive the detection gain and (SNR)D. Determine and plot Snc (f) and Sns (f).
In analyzing the performance of an FM discriminator, operating in the presence of noise, the post detection SNR, (SNR)D, is often determined using the approximation that the effect of modulation on
In Section 8.1.3 we expanded the noise component about fc. We observed, however, that the noise components for SSB could be expanded about fc ± 1/2 W, depending on the choice of side bands. Plot the
The preceding computer exercise problem examined the behavior of a PLL in the acquisition mode. We now consider the performance in the tracking mode. Develop a computer simulation in which the PLL is
Develop a computer program to verify the performance curves shown in Figure 8.17. Compare the performance of the non-coherent FSK system to the performance of both coherent FSK and coherent PSK with
Assume that an AM system operates with an index of 0.5 and that the message signal is 10 cos(8πt). Compute the efficiency, the detection gain in dB, and the output SNR in decibels relative to the
In Section 8.2 we described a technique for estimating the gain, delay, and the SNR at a point in a system given a reference signal. What is the main source of error in applying this technique? How
An AM system has a message signal that has a zero mean Gaussian amplitude distribution. The peak value of m(t) is taken as that value that |m(t)| exceeds 1.0% of the time. If the index is 0.8, what
Assume a three-bit ADC (eight quantizing levels). We desire to design a compounding system consisting of both a compressor and ex-pander. Assuming that the input signal is a sinusoid, design the
The threshold level for an envelope detector is sometimes defined as that value of (SNR)T for which Ac > rn with probability 0.99. Assuming that a2m̅2n ≅ 1, derive the SNR at
A compressor is often modeled asxout (t) = A tanh[axin(t)]We assume that that the input to the compressor is an audio signal having frequency content in the range 20 ≤ f ≤ 15,000 where frequency
Verify the correctness of (8.59). = E {Ir?t) + n?t»F} – E²in?u) + n?t»)l = 4c; (8.59) ?+n?
An envelope detector operates above threshold. The modulating signal is a sinusoid. Plot (SNR)D in decibels as a function of PT/N0W for the modulation index equal to 0.3, 0.5, 0.6, and 0.8.
A square-law demodulate for AM is illustrated in Figure 8.20. Assuming that xc(t) = Ac[1 + amn (t)] cos(2Ï€fct) and m(t) = cos(2Ï€fmt) + cos(4Ï€fmt), sketch the
Assume that a zero-mean message signal m(t) has a Gaussian pdf and that in normalizing the message signal to form mn(t), the maximum value of m(t) is assumed to be kσm, where k is a parameter and
Compute (SNR)D as a function of PT / N0W for a linear envelope detector assuming a high predetection SNR and a modulation index of unity. Compare this result to that for a square-law detector, and
The input to a communications receiver isr(t) = 5 sin(20πt + 7 /4 π) + ¡(t) + n(t)wherei(t) = 0.2 cos (60πt)and n(t) is noise having standard deviation σn = 0.1. The transmitted signal is 10
An SSB system is to be operated with a normalized mean-square error of 0.06 or less. By making a plot of output SNR versus demodulation phase-error variance for the case in which normalized
Repeat the preceding problem for a normalized mean-square error of 0.1 or less.Data From Problem 8.16An SSB system is to be operated with a normalized mean-square error of 0.06 or less. By making a
Draw a phasor diagram for an angle-modulated signal for (SNR)T >> 1 illustrating the relationship between R(t), Ac, and rn(t). Show on this phasor diagram the relationship between ψ(t), ϕ(t)
Develop a set of performance curves, similar to those shown in Figure 8.8, that illustrate the performance of a coherent demodulator as a function of the phase-error variance. Let the SNR be a
The process of stereophonic broadcasting was illustrated in Chapter 4. By comparing the noise power in the I(t) - r(t) channel to the noise power in the I(t) + r(t) channel, explain why stereophonic
An FDM communication system uses DSB modulation to form the base band and FM modulation for transmission of the base band. Assume that there are eight channels and that all eight message signals have
Using (8.146), derive an expression for the ratio of the noise power in yD(t) with de-emphasis to the noise power in yD(t) without de-emphasis. Plot this ratio as a function of W/f3. Evaluate the
Assume that the input to a perfect second-order PLL is an unmodulated sinusoid plus band limited AWGN. In other words, the PLL input is represented byXc(t) = Ac cos(2πfct + θ) + nc(t)
A base band digital transmission system that sends ± A-valued rectangular pulses through a channel at a rate of 20,000 bps is to achieve an error probability of 10-6. If the noise power spectral
Write a computer program to evaluate the degradation imposed by bit timing error at a desired error probability as discussed in Problem 9.7.Data From Problem 9.7.The received signal in a digital base
Consider an antipodal base band digital transmission system with a noise level of N0 = 10-3 W/Hz. The signal bandwidth is defined to be that required to pass the main lobe of the signal
Suppose N0 = 10-6 W/Hz and the base band data bandwidth is given by B = R = 1 / T Hz.For the Required Signal Power A2 and BandwidthR, bps PE = 10-3 PE = 10-4 PE = 10-4 PE = 10-5 PE =
Write a computer program to evaluate the degradation imposed by Gaussian phase jitter at a desired error probability as discussed in connection with the data presented in Table 9.2. This will require
A receiver for base band digital data has a threshold set at ε instead of zero. Rederive (9.8), (9.9), and (9.11) taking this into account. If P(+A) = P(-A) = 1/2, find Eb / N0 in decibels as a
Design a Monte Carlo simulation of a delay-and multiply DPSK receiver operating in additive white Gaussian noise to show the degradation of its operation relative to the optimum receiver for DPSK.
With N0 = 10-5 W/Hz and A = 40 mV in a base band data transmission system, what is the maximum data rate (use a bandwidth of 0 to first null of the pulse spec trum) that will allow a PE of 10-4 or
Write a computer program to verify Figures 9.28 and 9.29.Figure 9.28Figure 9.29 T'm = T 10-1 10-2 8 =-0.6 8= -0.9 T', = 1 T'm = 0 , =0 10-3 T'm = 1 8 =-0.3 T'm = 0 T'm = 1 8 = 0.6 T'm = 1 8 = 0.3 Tm
Consider antipodal signaling with amplitude imbalance. That is, a logic 1 is transmitted as a rectangular pulse of amplitude A1 and duration T, and a logic 0 is transmitted as a rectangular

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