代做ENG4052 Digital Communication 4 2023调试R语言程序

ENG4052

Digital Communication 4

Tuesday, 09 May 2023

Q1. 5 fair coins are tossed and the outcome is recorded as the number of “heads” visible.

(a) [3] Determine the probability for each possible outcome .

(b) [4] If each outcome represents a symbol in a code, what is t he entropy of the code?

(c) [8] Devise a Huffman prefix source code for this symbol set.

(d) [3] What is the average bits per symbol for your Huffman code?

(e) [2] How does the value obtained in part (d) compare to the e ntropy calculated in part (b)? Is this what you expect?

Q2. This question refers to the modulation format of the common implementation of 16-QAM.

(a) [2] What is the number of bits per symbol?

(b) [5] Sketch a constellation diagram for this modulation s cheme with the Gray code labels.

(c) [3] What is the advantage of using Gray coding in QAM?

(d) [4] What is the average symbol power in terms of the units you used to label the constel-lation diagram in part (b)?

(e) [6] The symbol period is three times the clock period. Make a sketch (as a function of time) of the carrier, the in-phase and in-quadrature components of the modulated waveform. for the bitstream 011010000001.

Q3. (a) [6] Multiple access methods are introduced to avoid interferences or collisions of two channels. Specify which multiple access methods are implemented in GSM and UMTS mobile networks. Describe how channels are allocated in the networks.

(b) [7] Which collision becomes a dominant problem in the code division multiple access (CDMA) technique? How the problem affects user connections to the networks? Suggest a possible solution to overcome the problem.

(c) [7] Specify, with an aid of diagrams, the differences of a radio network (or access) subsystem used for UMTS and LTE mobile networks. Describe handover procedures in relation to the differences.

Q4. A convolutional encoder is shown in Fig. Q4, where the three outputs shown are bit interleaved into a single output stream.

Figure Q4: A convolutional encoder

(a) [2] What is the rate of this convolutional code?

(b) [1] Is this code recursive or non-recursive?

(c) [1] Is this code systematic or non-systematic?

(d) [1] What is the constraint length of this convolutional co de?

(e) [4] Draw a state transition diagram for this convolutional encoder.

(f) [3] Using a Trellis diagram, or otherwise, find the convolutional code corresponding to the digital input 10110. You can assume the shift register is initially in the default all-zero state.

(g) [8] A received code, which may contain bit errors, is 011110101000100. Using the Viterbi algorithm and a Trellis diagram, determine the most likely binary data sequence that generated this code.

Q5. A survey of a proposed RF telecommunications link finds that multipath interference is an issue with a delayed signal of no more than 20 μs, so this quantity is chosen to be the guard interval in a proposed OFDM implementation.

(a) [3] Explain how the use of a cyclic prefix in the guard interval facilitates the detection of the start of an OFDM symbol.

(b) [2] Specify a typical ratio for the guard interval to OFDM symbol duration. Hence, what is your OFDM symbol duration (excluding guard interval)?

(c) [2] Why is the total number of subcarriers (including pilot tones and empty subcarriers) in OFDM implementations always a power of 2?

(d) [3] Taking 4096 total subcarriers, what is their frequency spacing?

(e) [5] 256 subcarriers are used for pilot tones, 1024 subcarriers have zero input, and the remainder carry data. What is the Occupied BandWidth (OBW)?

(f) [5] What data rate is obtained for the OFDM transmission, where 16-QAM is used for the subcarrier modulation?