CSCE 464 Wireless and Mobile Systems

Homework 5

(175 points; Submit through canvas.tamu.edu) Name: Your Name

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Signal Encoding (40 pts)

Covert the following values for power from [W] to [dBm]: 1.25 × 10−4W, 2.5 × 10−4W, 5 × 10−4W, 1 × 10−3W, 2 × 10−3W, 4 × 10−3W, 8 × 10−3W. In one sentence explain what pattern you observe. [3pts]

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Decompose a signal (1 + 0.1 cos(5t)) cos(100t) into a linear combination of sinusoid functions and find the amplitude, frequency and phase of each component. Hint: use the identity for cos(a)cos(b). [5pts]

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How are binary values represented in amplitude shift keying and what is the limitation of this approach? [2pts]

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Given a bit rate of 10Mbps and carrier frequency of 20MHz, draw an ASK signal for the bit sequence 10110. [10pts]

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Given a bit rate of 10Mbps and carrier frequency of 20MHz, draw an FSK signal for the bit sequence 10110. [10pts]

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Channel Capacity, Models (45 pts)

Show that the pathloss for the log-distance propagation model is PL(d) = PL(d0)+10αd/d0. [5pts]

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(6 points) Consider a transmitter-receiver pair at distance d. Assume the log-distance path loss model, with path loss exponent α = 2.4. The path loss is 40dB when distance is d0. Determine the path loss in [dB] for distance d = 2d0 and 4d0. At what distance is the path loss 64dB? [5pts]

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(c)

Enter your answer here.

ConsiderthreenodesA,BandCplacedalongastraightline,intheorderA,B,C.Assumethat d(A,B) = 30m and d(B,C) = 20m. All nodes use transmit power 1mW when transmitting. Assume a log-distance propagation model, with pathloss exponent α = 3, and pathloss at distance d0 = 1m as 20dB, noise spectral density N0/2 = 4 × 10−21 W/Hz and bandwidth W = 10MHz. Also assume that the rate of reliable information delivery on a link is given by Wlog2(1 + SINR). Each node may either transmit or receive at any given time, but not both simultaneously. Determine the maximum throughput achievable for a flow from node A to node C, when using the route: A−⟩B−⟩C. Assume that there is no other traffic in the network. Hint: the maximum throughput is achieved when the two links (AB and BC) are enabled different percentages of time, e.g., link AB might be active 40% of time and link BC might be active 60% of time - these numbers are just examples). Think about when each link should be active. [30pts]

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Given a channel of intended capacity of 20Mbps, the bandwidth of the channel of 3MHz. What signal-to-noise ratio is required to achieve this capacity? [5pts]

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Coding and Error Control (10 pts)

(d)

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Consider two wireless nodes A and B. They choose the (7,4) single error correcting code as their channel encoding mechanism. Map the following 7-bit messages received to the corresponding 4-bit data. Refer to Hamming(7,4) code discussed in class.

(a)

(b)

(c)

(d)

(e)

0110111 [2pts]

Enter your answer here.

1010101 [2pts]

Enter your answer here.

1110011 [2pts]

Enter your answer here.

1110110 [2pts]

Enter your answer here.

1111100 [2pts]

Enter your answer here.

Signals (20 pts)

(a) Show that doubling the transmission frequency or doubling the distance between transmitting antenna and receiving antenna, attenuates the power received by 6dB. (5 pts)

Enter your answer here.

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(b)

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Suppose a transmitter produces 50W of power. i) Express the transmit power in units of dBW and dBm; ii) If the transmit power is applied to a unity gain antenna with a 900MHz carrier frequency, what is the received power in dBm at a free space of 100m? iii) Repeat for a distance of 10km; iv) Repeat previous, but assume a receiver antenna gain of 2. (10 pts)

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What is the range of path loss exponent that will satisfy the following requirements: Transmit power = 2W, Received power = -105dBm, Unity gain antenna for transmit and receive, Carrier frequency = 1.8GHz, Distance = 5.2km. (5 pts)

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Wireless Networks (20 pts)

A cellular operator plans to cover the area of a circular city, having an area = 50km2, with a wireless system. A young engineer is hired to design a system that minimizes the network deployment cost and maximizes its capacity.

The engineer proposes to deploy a unique omnidirectional antenna located in the center of the city. The propagation model follows a power law, i.e., Prx(r) = cPtxr−α where Ptx is the transmitted power, Prx is the received power, r is the distance between sender and receiver, α is the propagation loss exponent, and c is a constant.

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In order to estimate the propagation loss exponent, two sets of measurements are done: at 0.1 km from the base station the average Prx is 31W; while at a distance of 1 km the Prx drops to 10mW. Determine the value of α. (10 pts)

Enter your answer here.

Find the minimum Ptx to cover the surface of the city such that at the edge of the city the

received power is Prx = 8mW. Assume c = 1 (the units of c are rα in kilometers). (10 pts) Enter your answer here.

Physical/Virtual Carrier Sensing in Wireless Networks (40 pts)

The figure below shows a network of 5 nodes named A, B, C, D and E. The number shown on links connecting various nodes are the path gains between the corresponding pair of nodes. Suppose that nodes use IEEE 802.11 DCF with both virtual and physical carrier sensing.

Assuming the following:

• For virtual carrier sensing, no physical carrier sensing is performed, i.e. treat the two carrier sensing techniques independently.

• Physical carrier sense threshold at each node = 2 × 10−9mW.

• Transmit power for each transmission = 2mW.

• A packet is received reliably if and only if the SINR exceeds 15dB.

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• The noise N at each node is 10−10mW, and there are no transmitters aside from A.

In this network, suppose that node A sends data to node B. For each of the nodes C, D and E, determine whether they will detect the communication between A and B using virtual carrier sensing or/and physical carrier sensing. Enter your answer in the table shown (each entry entered in the table should be Y (yes) or N (No)). Please show your work.

CDE Physical CS Enter your answer here. Enter your answer here. Enter your answer here. Virtual CS Enter your answer here. Enter your answer here. Enter your answer here.

7 Submission Instructions

Please submit: 1) the PDF as obtained from the provided latex template. Name your submission as ⟨your lastname⟩.hw5.pdf and submit it on canvas.tamu.edu; 2) any source code as a single zip or tar file.

References

[1] Nitin Vaidya, “ECE/CS 439 Wireless Networks” Lecture Notes, 2010

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