代写EEEM061: Advanced 5G Wireless Technologies Semester 2 2022/3调试R程序

EEEM061:  Advanced 5G Wireless Technologies

Semester 2 2022/3

A1.

(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 that consists of flat fading (i.e., single tap) single antenna sub-channels. Define the parameters that you use and explain the dimensions of the vectors and matrices.  [10 %]

(iii)        Explain, in less than 100 words, how we can identify the number of

concurrently transmitted information streams the MIMO channel of part (ii) can support, and how this number relates to the dimensions of its matrix representation.  [10 %]

(b)        In  relation to an uplink, 2x2 spatially  multiplexed, multi-user 5G MIMO system with single antenna users that transmit independent 4-QAM symbols (i.e., 1+j, 1-j, -1+j, -1-

j) and H is the corresponding MIMO matrix andy is the corresponding received vector, with

 

and

 

(i)         Apply Zero-Forcing (ZF) detection to find the transmitted vector. Justify your answer.  [20 %]

(ii)        Calculate what the maximum achievable throughput is, when applying ZF detection and when assuming that the noise is additive white Gaussian with a variance of one.   [20 %]

(iii)       Assume that the first  receive antenna is destroyed, and that the  received vector becomes y = 1.5. Explain how many users we can now decode and how.  [10 %]

(iv)        For the scenario of part (iii), propose a method to decode the corresponding user or users, and decode them appropriately. Justify your answer.  [20 %]

A2.

(a)        In relation to detection/decoding of wireless communication systems:

(i)          In less than 100 words explain the difference between “hard” and “soft”

detection/demapping. Then, give an example of a “hard” and an example of a “soft” detection/demapping outcome.   [10 %]

(ii)        Give the definition of Log-Likelihood-Ratio (LLR) and explain in less than 100 words, what information you can obtain from its amplitude and its sign.   [10 %]

(iii)        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 zero (b = 0).   [10 %]

(b)        Assume an 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 that are Grey encoded. In particular, the bits 00 are mapped onto the symbol 1 + j, the bits 01 are mapped onto the symbol 1 − j, the bits 10 are mapped onto the symbol −1 + j, and the bits 11 are mapped onto the symbol −1 − j.

(i)          In less that 100 words, explain what kind of processing should take place at the receiver in order to maximize the corresponding signal-to-noise (SNR) ratio and derive the equation describing the post-processed received signal.   [10 %]

(ii)         For the processing method of part (i) and based on the corresponding

equation, calculate the signal-to-noise (SNR) ratio of this post-processed received signal.  [10 %]

(iii)       Calculate the SNR in the case that, instead of the processing of part (i), you just decode the signal received at one antenna and calculate the corresponding throughput loss that would incur with such processing, when decoding the signal at the antenna that minimises this capacity loss. Justify   your answer.  [20 %]

(iv)        If the signals at each receive antenna are y1   = 2 − j andy2   = −1,  and if you know that repetition coding of ½ rate has been applied, first explain  how one would perform. optimal detection/decoding. Then, optimally detect and decode the transmitted information bit by performing a simple comparison. Justify you answer.  [30 %]

A3.

(a)         In relation to OFDM systems:

(i)          In less than 100 words describe the orthogonality condition in OFDM

systems in the frequency-domain and in the time-domain, respectively.   [10 %]

(ii)         In less than 100 words explain how inter-symbol interference (ISI) and

inter-carrier interference (ICI) can be avoided in OFDM systems.   [10 %]

(iii)       Calculate the Peak-to-Average Power Ratio (PAPR) of the following

complex exponential signal of frequency f and duration T: s(t) = exp(j2πft), where 0 ≤ t ≤ T.   [10 %]

(b)        In relation to the sparse code multiple access (SCMA) system for which the factor graph is shown in the figure below.

(i)         Convert the graph into a signature matrix and identify the values of the multiplexing factor, spreading factor and overloading factor from this graph or signature matrix.   [15 %]

(ii)         Illustrate how to construct the four codewords to form. the codebook for the 3rd user, using a simple diagram. Justify your answer.   [10 %]

(c)        In relation to Reconfigurable intelligent surfaces (RISs):

(i)         The reflection coefficient of a practically designed reflective surface is defined   as follows:

Rc  = 0.9 × [1 + 0.3 × sin(θi  − θr )] × cos3 (θi ),

where  θi  is the angle of the incident wave,  θr  is the angle of the

reflected wave. The reflected signal is deemed useful when RC   ≥ 0.4.

Calculate the working range of  θr  when θi   =   0°  , i.e., the angle of the incident wave is perpendicular to the reflective surface.   [15 %]

(ii)        Calculate the working range of  θr    when θi  =   60° .   [15 %]

(iii)       Suppose the incident angle and reflection angle differ by 30°  .

Calculate the reflection coefficient when 1) θi  =  0°, θr  =  30° ; 2) θi  =  30° , θr  =  60° ; 3) θi  =  50° , θr  =  80° .    [15 %]