CS547 Wireless Networking And Security Exam 1 Question 1 Sim

Cs547 Wireless Networking And Security Exam 1question 1 Simplify Th

CS547 Wireless Networking and Security Exam 1 Question 1: Simplify the following expression (10 pts): cos (2Ï€ft + Ï€/2) + sin(2Ï€ft – Ï€)

Question 2: Support the fact that, in a transmission system using radio frequencies, increasing the transmission frequency by a factor of 3 incurs a penalty (loss) of approximately 9.5 dB (10 pts).

Question 3: How much bandwidth does a communication channel need to achieve a capacity of 40 Mbps with a Signal-to-Noise ratio of 255? (Note: 1 Mbps is 1,000,000 bps) (10 pts)

Question 4: Given the following parameters: N = number of hops between two end systems; L = message length in bits (e.g., length of the original message, before being divided in several packets); B = data rate in bps, on all links; P = fixed packet size in bits; H = overhead (header) in bits per packet; D = propagation delay per hop in seconds. The number of packets (Np) required to send the original message of length L (in bits) can be computed as: Np = L / (P - H). The total end-to-end time delay for packet switching is calculated using the formula: T = Np (P / B) + (N - 1) (P / B) + N * D. Assume that L / (P - H) is an integer. What value of P, as a function of N, L, and H, would minimize the end-to-end time delay? (10 pts)

Question 5: A Virtual Channel Identifier (VCI), in the header of an ATM cell, is used for routing to and from the end user. Explain why a VCI is needed together with the Virtual Path Identifier (VPI). (10 pts)

Question 6: Is there a need for a network layer in a broadcast network? Justify your answer. (10 pts)

Question 7: Describe the significance of the following IPv4 header fields (10 pts): (a) Time to live (b) Protocol

Question 8: The transmit power of a station is 57.67 dBm (10 pts). (a) How much power in KW is this equivalent to? (b) Using an antenna with 1 GHz carrier frequency, what will be the received power in dB at a free space distance of 0.5 km?

Question 9: Research Problem: Describe in detail the various diversity techniques in wireless communication systems (10 pts).

Question 10: Research Problem: What is carrier-to-noise ratio (CNR)? Describe why, in general, raising radio frequency (RF) levels improves the carrier-to-noise ratio (10 pts).

Paper For Above instruction

The provided questions relate to core concepts in wireless networking, radio frequency transmission, digital communication systems, and network protocols. In this paper, each question is methodically addressed to demonstrate a comprehensive understanding of the theoretical and practical aspects involved.

Simplification of the Trigonometric Expression

The first question asks to simplify the expression: cos(2πft + π/2) + sin(2πft – π). Recognizing that cosine and sine functions are phase-shifted versions of each other is fundamental. From the standard identities, cos(θ + π/2) = –sin(θ). Therefore, we interpret cos(2πft + π/2) as –sin(2πft). The second term, sin(2πft – π), can be simplified using the identity that sin(θ – π) = –sin(θ). Consequently, the entire expression simplifies to: –sin(2πft) – sin(2πft) = –2 sin(2πft). Thus, the original complex expression reduces to –2 sin(2πft). This simplification not only clarifies the form but also highlights the phase relationship between the trigonometric functions involved (Reddy & Narayana, 2018).

Radio Frequency Transmission Penalty

Increasing the transmission frequency by a factor of three incurs a significant penalty of approximately 9.5 dB. This estimate stems from the Friis transmission equation, where free-space path loss (FSPL) increases quadratically with frequency. Path loss (L) in dB is expressed as: L = 20 log10(d) + 20 log10(f) + constant, where d is distance and f is frequency. The term 20 log10(f) directly indicates that tripling the frequency increases the loss by 20 log10(3) ≈ 9.54 dB, supporting the claim (Rappaport, 2002). This relationship illustrates an important trade-off: higher frequencies enable higher data rates but at the cost of increased propagation losses, necessitating more power or advanced materials for reliable communication (Tse & Viswanath, 2005).

Bandwidth Calculation for Achieving a Specific Capacity

According to Shannon's capacity theorem, the maximum data rate C for a channel with bandwidth B and Signal-to-Noise Ratio SNR is: C = B log2(1 + SNR). To find B when C is 40 Mbps and SNR is 255, we rearrange the formula: B = C / log2(1 + SNR). Substituting the known values yields B = 40,000,000 / log2(1 + 255) ≈ 40,000,000 / 8 ≈ 5,000,000 Hz or 5 MHz. Therefore, a bandwidth of approximately 5 MHz is needed to achieve 40 Mbps capacity under the given SNR conditions (Proakis, 2001). This emphasizes the importance of bandwidth in high-speed data transmission systems.

Optimizing Packet Size for Minimal Delay

The third question involves calculating the packet size P that minimizes end-to-end delay. Since delay T involves terms proportional to P / B and with the number of packets Np = L / (P - H), the goal is to optimize P. By differentiating T with respect to P and setting the derivative to zero, the optimal packet size is found to be P = (L + H N) / N, balancing transmission time and overheads. This expression indicates that P depends directly on message length L, header overhead H, and the number of hops N, providing a practical guideline for network packet sizing to minimize latency (Tanenbaum & Wetherall, 2011).

VCI and VPI in ATM Networks

In ATM (Asynchronous Transfer Mode) networks, the Virtual Channel Identifier (VCI) and Virtual Path Identifier (VPI) serve distinct yet complementary roles. The VPI identifies a collection of virtual channels grouped into a virtual path, simplifying management and signaling. The VCI, on the other hand, uniquely identifies a specific connection within that virtual path, enabling precise routing to end users. The necessity of both stems from the hierarchical structure of ATM networks, which streamlines switching and reduces signaling complexity (Leinmüller, 1998). The separation of VPI and VCI allows scalable, efficient routing and resource allocation, essential for multimedia and high-speed data services.

Importance of Network Layer in Broadcast Networks

In broadcast networks, the presence of a network layer is often debated, as the fundamental operation involves transmitting data from one source to multiple recipients (one-to-many). Technically, the physical and data link layers can perform broadcasting without a network layer. However, a network layer provides essential functionalities such as addressing, routing, and managing data flow across heterogeneous systems. For instance, in Ethernet networks, the Ethernet MAC handles delivery within a network segment, but IP addresses and routing protocols are necessary to connect multiple segments or networks. Hence, the network layer is crucial for scalable, manageable broadcast systems that span diverse locations and infrastructures (Kurose & Ross, 2017).

IPv4 Header Fields: TTL and Protocol

The IPv4 header contains important fields for packet management: the Time to Live (TTL) and Protocol. TTL limits the lifespan of a packet in the network, preventing it from circulating indefinitely. Each router decrements TTL by one; when TTL reaches zero, the packet is discarded, which averts routing loops. The Protocol field specifies the upper-layer protocol (e.g., TCP, UDP) encapsulated within the IP packet. It informs the receiving host how to interpret and process the payload, facilitating proper delivery of services across diverse network applications (Stevens, 1994). Both fields contribute critically to reliable and efficient network operations.

Power Conversion and Signal Attenuation

The fourth question involves converting transmit power and estimating received power over free space. A power of 57.67 dBm corresponds to: P (dBm) = 10 log10(P (mW)). Hence, P (mW) = 10^{(57.67/10)} ≈ 4.68 million milliwatts, or approximately 4.68 kW. Regarding received power at 0.5 km with a carrier frequency of 1 GHz, the Friis transmission equation estimates free space path loss (FSPL): FSPL (dB) = 20 log10(d) + 20 log10(f) + 20 log10(4π/c). Substituting d = 0.5 km, f = 1 GHz, and c ≈ 3×10^8 m/s, yields an FSPL of approximately 116.4 dB (Rappaport, 2002). The received power is then P_r = P_t – FSPL ≈ 57.67 dBm – 116.4 dB = –58.73 dBm.

Diversity Techniques in Wireless Systems

Wireless communication systems employ various diversity techniques to combat fading, multipath interference, and improve signal reliability. Spatial diversity involves multiple antennas placed at different locations, such as MIMO systems, which utilize multiple input and output channels to increase capacity and robustness (Goldsmith, 2005). Frequency diversity spreads the signal over different frequencies, reducing the impact of frequency-selective fading. Time diversity employs coding schemes that transmit the same information at different times. Space-time coding combines multiple antennas over space and time to exploit spatial and temporal variations. Selection combining, where the strongest among multiple received signals is chosen, is a simple yet effective method. These techniques significantly enhance link reliability and throughput, especially in environments with severe multipath effects (Proakis, 2001).

Carrier-to-Noise Ratio (CNR) and RF Level Enhancement

The carrier-to-noise ratio (CNR) measures the power ratio between the received signal's carrier and the background noise, reflecting the quality of the communication link. A higher CNR indicates a clearer, more reliable signal. Increasing RF levels—either through higher transmission power or better antenna gains—directly improves the CNR by boosting the carrier power relative to noise. This enhancement reduces error rates and improves data accuracy. Nonetheless, increasing RF power must be balanced against regulatory limits and potential interference, emphasizing the importance of efficient antenna design and signal processing techniques to optimize CNR in practical systems (Sklar, 2001). The fundamental principle is that better RF signal strength relative to noise fosters improved communication performance.

References

• Goldsmith, A. (2005). Wireless Communications. Cambridge University Press.
• Kurose, J. F., & Ross, K. W. (2017). Computer Networking: A Top-Down Approach. Pearson.
• Leinmüller, T. (1998). ATM Networks: Concepts, ATM switching, signaling, protocols and test methods. Wiley.
• Proakis, J. G. (2001). Digital Communications. McGraw-Hill.
• Rappaport, T. S. (2002). Wireless Communications: Principles and Practice. Prentice Hall.
• Reddy, M., & Narayana, M. (2018). Trigonometric identities and their applications in signal processing. Journal of Signal Processing, 12(3), 45-52.
• Sklar, B. (2001). Digital Communications: Fundamentals and Applications. Prentice Hall.
• Stevens, W. R. (1994). TCP/IP Illustrated, Volume 1: The Protocols. Addison-Wesley.
• Tanenbaum, A. S., & Wetherall, D. J. (2011). Computer Networks. Pearson.
• Tse, D., & Viswanath, P. (2005). Fundamentals of Wireless Communication. Cambridge University Press.