EEEM061: Advanced 5G Wireless Technologies
Semester 2 2023/4
Q1.
(a) In relation to single-user, 5G Multiple-Input Multiple-Output (MIMO) systems:
(i) Explain, in less than 100 words, what a MIMO channel is and how this can be represented in matrix form in the case of flat fading (i.e., single tap) channels. [10 %]
(ii) Give the mathematical relationship that links the transmit and received vectors over a MIMO channel. Define the parameters that you use and explain the dimensions of the vectors and matrices. [10 %]
(b) In relation to detection/decoding of wireless communication systems:
(i) Give the definition of Log-Likelihood-Ratio (LLR) and explain in less than 100 words, what information can be obtained from its amplitude and its sign. [10 %]
(ii) Based on the definition of part (ii), if a bit b hasan LLR value of 0.5 calculate the probability of this bit to be equal to one (b = 1) and the probability of this bit to be equal to (b = 0). [10 %]
(c) Assume a 1 × 2 Single-Input, Multiple-Output (SIMO) system, where the
corresponding flat-fading channels are h1 = 1 and h2 = j and the additive white Gaussian noise variance at each receive antennas is one. Also assume that transmitted symbols belong to a 4-QAM constellation (i.e., 1 + j, 1 − j, −1 + j, −1 − j).
(i) Explain what kind of processing should be performed at the receiver in
order to maximize the corresponding signal-to-noise (SNR) ratio and derive the equation describing the post-processed received signal. Then, calculate the corresponding SNR. [20 %]
(ii) If the signals at each receive antenna are y1 = 2 − j andy2 = −1.5,
perform. symbol detection based on the method you described in part (i). [10 %]
(iii) If the signals at each receive antenna are y1 = 2 − j andy2 = 1.5, and if you know that repetition coding of ½ rate has been applied, first explain how one would perform. optimal detection/decoding. Then, optimally decode the transmitted bit, when you know that Gray coding has been applied for bit-to-symbol mapping, and that the bits 00 are mapped onto the symbol 1 + j. Justify your answer.
[30 %] [SEE NEXT PAGE]
Q2.
(a) In relation to wireless transmissions:
(i) Fig. 1 shows channel frequency responses of two different channels. In less than 100 words explain 1) what are characteristics of the time domain impulse responses for these channels; 2) how to counter the effect of these channels. [10%]
Figure 1
(ii) In less than 100 words explain the advantages of OFDM. [10%]
(iii) Given the original rate ½ code shown in Fig. 2, suggest a technique to change the code rate to 5/6 and explain your solution mathematically and schematically.
Figure 2
[15%]
(iv) In less than 100 words explain the three main benefits of non-orthogonal multiple access (NOMA) in comparison to orthogonal multiple access (OMA). [10%]
(b) In relation to Reconfigurable Intelligent Surfaces (RISs), the far-field path loss model of the end-to-end channel through RIS is expressed as
where Rc is the reflection coefficient, N is the number of elements on the surface,A is the area of each element,dg is the distance between the transmitter and the surface,dh is the distance between the surface and the user.
(i) Consider the size of each element is 2/λ, the area of each element is A= 2/λ × 2/λ, where λ is the wavelength and c is the speed of light. Assume that N = 2000, f = 3.5 GHz, dg = 6 m,and dℎ = 3 m. Calculate the end-to- end channel gain through this RIS. For simplicity, assume Rc = 1. [20%]
(ii) Suppose that there is a blockage between the transmitter and the user. In this case, the direct channel between the transmitter and the user is modelled as follows:
patℎlossdirect (dB) = peL − 28 log10 (ddirect ),
in the decibel scale, where the penetration loss peL = −35dB.
Calculate the gain of direct link between the transmitter and the user when ddirect = 6 m. [10%]
(iii) In less than 100 words, explain what can be inferred by comparing the obtained results in part (i) and part (ii). [10%]
(iv) Suppose that the channel gain has to be greater than -25 dB for reliable transmission. Determine the minimum number of RIS elements Nmin that is required to achieve reliable communications. Justify your answer. [15%]
Q3.
(a) In relation to 5G wireless systems:
(i) In less than 100 words explain the purpose of network densification and discuss the two contradictory effects when the cell density becomes higher. [10%]
(ii) Explain the main requirements for the massive machine type
communications (mMTC) and ultra-reliable and low latency communications (URLLC) services, respectively, and discuss how you can use different numerologies to support them. Describe the problems encountered if these two services are provided by 4G-LTE networks. [20%]
(iii) Consider an OFDM system with N subcarriers, where its peak to average power ratio (PAPR) is given by PAPRdB = 10log10 N . Calculate the PAPR when N=1,16, 64, 256, respectively, and explain whether it is preferrable to have a very small number of subcarriers in OFDM systems in order to minimize PAPR. [15%]
(b) In relation to the sparse code multiple access (SCMA) system with 10 users sharing 5 subcarriers as shown in Fig. 3:
Figure 3
(i) Derive the signature matrix of such an SCMA system. [20%]
(ii) Calculate the value of the overloading factor, and the effective spreading dv and the multiplexing factor dc. Explain the practical significance of each parameter. [15%]
(iii) Illustrate how to construct the four codewords required to form the codebook for the 7th user using the following permutation pattern. Explain the main benefit of constellation permutation.
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Codeword 1
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Codeword 2
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Codeword 3
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Codeword 4
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1
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2
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4
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3
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2
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1
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3
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4
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Table: Permutation Pattern
[20%]