Questions and Answers of Principles Of Embedded Networked Systems Design

Power spectral density of PAM The low-pass equivalent representation of a PAM signal isuðtÞ ¼X n Ingðt nTÞ:Suppose g(t) is a rectangular pulse and In ¼ an an3;where {an} is a sequence of
Impulse response of raised-cosine filter Determine the inverse Fourier transform of the frequency response P(f) of the raised-cosine filter.
QAM transmission with raised-cosine filtering The bandwidth BT of the raised-cosine filter is defined by 2W f1 ¼ W(1þ). A computer outputs binary data at the rate of 56 kb/s. The computer output
Gray code The property of the Gray code is that the code words of adjacent symbols only differ in one bit. For example, the code words of 8-PAM symbols are as illustrated in Figure 6.21. This results
Error probability for FSK Using the approximation of symbol error probability PðeÞ NdminQ dffimffiffiffiiffinffiffiffiffi 2N0 p ;prove the symbol error probability of M-FSK is PðeÞ ðM 1ÞQ
Hard-decisions vs. soft-decisions In Example 6.5, if hard-decisions are used instead of soft-decisions:(a) How many errors can the code detect and correct, respectively?(b) Compute the error
Minimum HD decoding A given code consists of the codewords: 0000000, 0011110, 0101101, 0111000, 1001100, 1011001, 1101010, 1110100. If 1001110 is received, what is the decoded codeword based on the
A rate-1/3 convolutional encoder Consider a convolutional encoder for a K¼4 shift register with v¼3 modulo-2 adders. At each clock time the outputs of the v adders are sampled by a commutator.Thus
Linearized PLL The linear model of the analog PLL is depicted in Figure 6.22.(a) Derive the closed-loop transfer function o (f )/i(f ).(b) If F(s)¼1/(s¼ffiffiffi2 p), using the Laplace transform
PLL transfer function Assume that the loop filter of a PLL is a low-pass filter, as shown in Figure 6.23.Evaluate the closed-loop transfer functionH(f ) for a linearized PLL, and compute the 3 dB
Noise in a PLL Consider the noise characteristic of a PLL. The internal phase noise of the VCO is modeled by the input n(t) as shown in Figure 6.24.(a) Find an expression for the closed-loop
Costas loop The Costas loop uses both in-phase and quadrature phase detectors to keep a VCO centered at the suppressed-carrier frequency, as shown in Figure 6.25. Let the input be b(t)cos (!ctþi),
Differential PSK (DPSK)In DPSK, the information is encoded using the differences between bits in two successive bit intervals. The output digits after the arbitrary starting digit are determined by
Sinc pulse trains The overall pulse shape p(t) of a baseband binary PAM system is defined by pðtÞ ¼ sinc tTb ;where Tb is the bit duration of the input binary data. The amplitude levels at the
Early–late gate In the early–late gate synchronizer, the outputs of two correlators can be viewed as the following two samples although their values are not equal. The correlator can be replaced
Multipath interference In the presence of multipath interference, replicas of the transmitted signal arrive at the receiver with various attenuations and delays. In this problem, assume that there is
ZF LEQ Find the tap coefficients required for a ZF transversal equalizing filter for the case of a three-tap filter. For a single flat-topped pulse into the transmit filter the responses of the
Five-tap ZF LEQ Find the tap coefficients if the three-tap filter in Problem 6.18 is replaced by a fivetap filter. In the desired output sequence, there are two samples before and after the peak
Equalization of a non-return-to-zero (NRZ) signal A2-kb/s unipolarNRZsignal is sent over a band-limited channel. The channel has the impulse response hc(t)¼e2000tu(t). Design a five-tap ZF
DPSK on a fading channel Given the bit error rate of DPSK in the AWGN channel, compute the bit error rate of DPSK with a Rayleigh fading channel and plot the bit error rate for each as a function of
PN sequence properties A PN sequence is generated using a feedback shift register of length m¼5. The chip rate is 106 chips per second. Find the following parameters:(a) the PN sequence length;(b)
PN sequence generation Figure 6.26 shows a four-stage feedback shift register. The initial state of the register is 1000. Find the output sequence of the shift register.
PN sequence statistical properties For the feedback shift register given in Problem 6.23, two properties can be demonstrated.(a) The balance property states the number by which the number of 1s
Processing gain The processing gain of a DS-SS system may be expressed as the ratio of the spread bandwidth of the transmitted signal to the despread bandwidth of the received signal. Justify this
Selection diversity It is assumed that there are M diversity branches and each branch has the same average SNR given by .(a) Derive the cdf of the SNR after selection diversity processing.(b) Derive
MR combining for diversity In MR combining, the optimal weight is Gi¼ri/N0, where ri is the received signal amplitude at the ith branch. Derive the average SNR improvement.
Five-branch diversity Assume five-branch diversity is used, where each branch receives an independent Rayleigh fading signal. If the average SNR is 20 dB, determine the probability that the SNR will
SIR in a cellular network with a reuse factor of 7 A cellular network with a frequency reuse factor of 7 is depicted in Figure 7.12, where cells with the same letter share the same set of
Linear prediction Consider a zero-mean stationary random process x(n) that has the following correlation function:RXðnÞ ¼1 n ¼ 0 0:8 n ¼ 1 0:5 n ¼ 2 0:3 n ¼ 3 0 any other
MIMO equalization A discrete time two by two MIMO system is shown in Figure 7.14, where s1(n), s2(n) are source sequences, and y1 and y2 are measurement sequences. The channel transfer functions
MR combining Consider the system shown in Figure 7.15, where the signal s is coherently sensed by two receivers. The measurements y1 and y2 can be expressed as follows:y1 y2 ¼h1 h2 s þ1 1
Array processing A uniform linear array consists of ten sensors in the pattern depicted in Figure 7.16.The array is steered to 0¼p/3. The sensor separation is d¼l/4, where l is the wavelength of
Source–sensor separation Consider the problem of deploying sensors to monitor a certain area, in this case a square of unit area. Within the square, there is a uniformly distributed point source
Source–sensor separation Consider deploying n sensors in a disk of unit area. A point source appears in the disk according to a uniform distribution. Supposing the sensors are placed in the disk
MAC schemes Consider the following cases in conjunction with MAC schemes. Which MAC scheme appropriately describes each situation?(a) Cars are waiting at a crossing for the traffic lights to turn
Maximal length sequence Consider the feedback shift register of length 4 depicted in Figure 7.18. It consists of four flip-flops and a modulo-2 adder.(a) Assuming the initial state of the shift
DS-SS The information bit duration of a DS-SS communication system is Tb¼8.191 ms. The PN sequence has a chip duration of Tc¼1ms. What is the processing gain of this spread spectrum system?What is
Ground reflection model In a two-ray ground reflection model, the transmitter and receiver are placed ht and hr above the ground, as shown in Figure 7.19. Assume the wave obeys the free-space
Little’s Theorem A packet arrives at the server every K seconds. Each packet requires 2K/3 seconds for transmission and K/2 seconds for processing. What is the average number of packets in the
Aloha In a MAC system, users transmit equal length packets through a shared channel.The transmission time for each packet is T seconds.Acollision occurs when two or more packet transmissions overlap
Connectivity Connectivity is usually used to describe the reliability of the network. In a network, if there is a path connecting nodes i and j after removing (k1) other nodes and their associated
Diameter The distance between a pair of nodes in the network is the length of the shortest path connecting the two nodes. In the case of disconnected nodes, the distance is set to infinity. The
Flooding Flooding is often used in a local network to update path state information. To limit the number of transmissions, two rules are observed during flooding: the node does not relay the packet
Shortest-path routing: Bellman–Ford algorithm In this problem, we use the network topology in Figure 8.29 to illustrate the Bellman–Ford algorithm for finding the shortest route to a node. In the
Shortest-path routing: Dijkstra algorithm We will use Figure 8.29 to illustrate the Dijkstra algorithm for finding the shortest route to a destination node. The length of the direct arc connecting
DSR For the network topology in Figure 8.30, assuming the same transmission delay on all the links, use the DSR algorithm to determine the routes from node 1 to node 12, from node 3 to node 12, and
Spanning tree Find all possible spanning trees for the two graphs in Figure 8.31 subject to the constraint that node 1 must be the root. Determine the number of nodes N and arcs A in each of these
Directed diffusion Consider the situation in Figure 8.32, which is similar to Example 8.6. The solid lines represent transmission links between nodes, and dashed lines indicate boundaries of tiers.
M/M/1 queues Consider the infinite length M/M/1 queue discussed in Example 8.7.(a) Given that the probability that there are n customers in the queue is P(n)¼(1)n, where ¼l / , show that the
ARQ Consider a simple ARQ scheme through a single transmission link of data rate R.The ARQ scheme works as follows. The sender transmits a data packet across the link. Once the receiver receives the
Source localization Consider source localization using clusters of sensors. Shown in Figure 8.33 are the source and two clusters of sensors located at coordinates (0,0) and (1,0). Using the
Channel capacity – Gaussian channel The channel capacity of a continuous Gaussian channel is given as C ¼ B log2 1 þS NB in which S is the signal power, N is the noise power density, and B is
Slepian–Wolf coding Consider two discrete random variables X and Y. Their joint distribution is given in Table 8.5.(a) Compute H(X), H(Y), H(X|Y), H(Y|X), and H(X,Y).(b) Supposing X and Y are
Network capacity Use R1 and R2 as two coordinates. Plot the rate region that is achievable in a twouser Gaussian multiple access channel assuming P/N¼1.
Rate distortion Consider rate distortion coding with a single helper. Suppose 2 X ¼ 1, DX¼0.1.Plot the lower bound of RX as a function of R1 for ¼0, 0.4, 0.7, and 1. Comment on how this bound
Timing offset and GPS GPS uses a constellation of 24 satellites and their ground stations as reference points to calculate positions accurate to a matter of meters. Suppose we find our distance
Linearizing GPS equations In order to find position using the GPS system, we need to know the location of at least three satellites and the distance to each of those satellites. Assume that the three
Averaging to reduce error in TOA TOA is based upon the measurement of the arrival time of a signal transmitted from the to-be-located object to several reference nodes. For radio signals, the
TOA with low-cost clocks In order to make accurate range measurements in a GPS system, the receiver and satellite both need clocks that can be synchronized down to a nanosecond, which potentially
TDOA in a two-dimensional space TOA requires that all the reference nodes and the receiver have precise synchronized clocks and the transmitted signals be labeled with time-stamps. TDOA measurements
TDOA in a three-dimensional space Assume that five reference nodes are known to be at (0,3,0), (6,0,0), (3,4,0),(4,3,0), and (0,0,8) respectively. Also, t12¼0 s, t13¼1 s, t14¼0.7 s, t15¼0.7 s,
Position estimation without the range error covariance matrix Let u denote the node with unknown position, and let the position of reference node j be (xj, yj). Denote by rj,u the range measurement.
An alternative approach for position estimation Assume a¼(1,1), b¼(1,1), c¼(1,1), and d¼(1,1). Locate node d using the noisy range estimates la¼0.7, lb¼1.5, lc¼1.6, ld¼2.2.(a) Calculate
Weighted centroid computation Three beacons are located at a¼(1,1), b¼(1,1), and c¼(1,1). The received powers from nodesa, b, and c are 1.2, 1.5, and 1.7 respectively. Calculate the unknown
Collaborative multilateration Execute the second iteration of Example 9.5 using (9.5)–(9.8). That is, calculate u2 using A, C, and v1, and then calculate v2 using B, D, and u1.
Linearization of AOA location determination The intersection of the angles from two or more sites may be used to provide an unknown position in the plane. For this triangulation problem, denote the
Energy supply In Example 10.1, a node uses a zinc–air battery (at 1 V) instead of a lithium-ion battery. How large must the battery be for reliable operation of the node for 15 days? Further, the
Cost of storing energy and service life(a) An installation requires 60 cells in series to produce 120 V. Depending on the application, this output is converted to different ac voltages. The cost of a
Dynamic power consumption in CMOS.(a) Discuss the different ways of reducing power consumption in CMOS.(b) What is the net effect on the power consumption in CMOS if the transition frequency is
Parallelism, power, and delay How does parallelism affect power consumption and delay in circuits? Consider the power consumption and delay equations as in Example 10.3.
Scheduling based on deadlines Consider an application of a sensor network that demands a distributed processor platform. We have three processors (P1, P2, P3), each having four modes of operation –
Direct transmission vs. multihop.Consider the scenario depicted in Figure 10.5. The Nþ1 nodes are placed in a straight line. All adjacent nodes are spatially separated by distance r. The radios on
Dynamic modulation scaling revisited Redo Example 10.12 taking the energy consumed by the receiving radio, CR, into account. Assume CR¼12 nJ.
Network lifetime The lifetime of any network depends on the power dissipated. Using relaying rather than direct transmission extends the lifetime, as well as giving frequency reuse benefits. Let ES
Best-energy route Find the minimum-energy path in Figure 10.7 from source S to destination D.The diagram shows the connectivity with associated energy cost.
Traveling salesman problem The energy mule example is an instance of the well-known traveling salesman problem. It is not always possible to use brute force to solve the equations. Two algorithms
ACID properties Which ACID properties are illustrated by the following transactions?(a) While a new row is being added to a table by one process, another process reads the entire table but the new
Database layers and programming How do the database layers of physical, conceptual, and user levels correspond to the layering of computer code between assembly code and compiled C programs?
Resolution of uncommitted dependency Transaction B begins with an update request at time t1 and would ordinarily finish by time t3. In the meantime transaction A begins at time t2,t1
Replication for reduced communication Data replication can provide both robustness and faster response time. A further potential benefit is reduction of long-range communication costs. While on the
Sufficient sampling A field has the spatial autocorrelation function sincð2x=dÞ;where d is some constant and x is the distance variable.(a) What is the maximum permitted separation of sensors to be
Data storage times Consider a three-tier sensor network. The first tier generates the raw data and keeps it for a period T1. It passes to the second tier its decisions and associated likelihoods. The
Refinement with age As data age they are progressively refined into more compact (lossy) representations.Suppose, e.g., that data might be stored in three buffers: raw, reduced resolution, histogram.
Interest diffusion Repeat the problem in Example 11.8 but with sink 1 having interest 4, sink 2 having interest 2, and the cost of each link being 1.
Adaptive sampling The sampling density required in time and space depends on the variability of the phenomenon, the noise, and the reconstruction method. Suppose linear interpolation is to be used
Deductive arguments Reduce the following arguments to symbolic form and then determine their logical validity.(a) If pigs can fly, then cats can fly; cats cannot fly; therefore pigs cannot fly.(b) If
Hypotheses about causes Arguments about cause and effect are fraught with peril. The reason is that such arguments are in essence probabilistic rather than deterministic. Discuss the validity of the
Green eggs and ham orientation A burning scientific question is how characters in stories end up being green eggs and ham fans/disdainers. Is like/dislike for green eggs and ham an innate property
Going to the dogs Categories (fox, box, goat, boat) enable a compressed description of diverse things which share some attributes. This enables inductive reasoning about things which have never been
Sensor density and resources(a) Qualitatively, how does increasing sensor density reduce the error in reproducing a source at a fusion center?(b) Instead of increasing sensor density, an
Network throughput with mobile nodes Consider a network with n mobile sensors. The source nodes transmit the message to the corresponding destination pair in two steps. In step 1 the source transmits
Work, force, and power It is required to lift a sensor node from ground to the height of 40m in 12 s. This work requires 950 J.(a) What force and power are required to lift the sensor?(b) Calculate
Nodes in freefall A sensor node is to be dropped from a height of 15 m, sending out readings as it falls. Calculate the total energy of a 2 kg sensor node when it is dropped at the velocity of 2 m/s.
Stepping up A 7.58 stepper motor accelerates from zero to 45.84 steps/s in 1 ms. If the rotor and load inertia, J, is 2103g m2, calculate the required torque.
Effects of environmental obstacles Consider a sensor field deployed at uniform node density,d, which yields an intersensor spacing,a, in a regular grid deployment. Let the area for which one sensor
Gain from mobility The gain from mobility, G, can be characterized as the ratio of Pmiss (static sensor node) to that of Pmiss (mobile sensor node). Using the same set-up as Problem 12.6, let a¼100,
Shadow area In Figure 12.18, cameras with a 1808 field of view are denoted by triangles and occlusions by dark squares. Mark and calculate the area of the shadow region.
Exploiting gaps Repeat Example 12.17 for Figure 12.19. Figure 12.18 Obstacles and cameras. Figure 12.19 Camera path and obstacles.
The data mule track Consider the four node sensor network as shown in Figure 12.20. Note: G is the data sink. Communication is by means of a data mule. Movement of one unit costs 3Wh.(a) Find the
Distributed environmental monitoring design An ENS application is directed at agriculture control including comprehensive monitoring of soil moisture, solar radiation flux, atmospheric humidity,

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