Question 1 (100% = 50 Marks)

For this question you cannot use the Matlab-ready code to produce AWGN and equally

probable 16-QAM symbols, to produce the MIMO Channel, or to perform detection. Instead you

can write your own script based on the rand and randn functions. When you use results from

the literature do not forget to add the corresponding references).

All the results and explanations for Question 1 should be on the report (not on additional files).

Whatever is not in the report will not be considered in the marking.

We consider a 5G multiuser-MIMO system with 2 base-station antennas and 2 singleantenna users that concurrently transmit (in the uplink) independent and identically

distributed transmitted 16-QAM symbols, with no channel coding, using spatial

multiplexing.

1) After searching the corresponding literature,

a) Explain in less than 500 words (and provide references to the corresponding

literature) all the steps required in order to perform zero-forcing (ZF), “hard”

detection in order calculate what the transmitted symbol is.

[15%]

b) Provide a Matlab script that simulates the average symbol-error-rate (SER)

performance of ZF detection, in logarithmic scale, as a function of the signalto-noise ratio (SNR), in dB, when assuming an independent and identically

distributed (i.i.d.) Rayleigh fading MIMO transmission channel. All the details of

your code should be explained. Plot the simulation results for a range of SNRs

such that the SER ranges from approximately 10-1 to approximately 10-4 (Hint:

verify your results with the literature).

[20%]

2) After searching the corresponding literature,

a) Explain in less than 500 words (and provide references to the corresponding

literature) the steps required to perform, “hard” Maximum-Likelihood (ML)

MIMO detection by exhaustive search (i.e., not with sphere decoding).

Calculate, and explain, what is the complexity of such an approach in terms of

complex multiplications for the above 2×2 multi-user MIMO system.

[15%]

b) Provide a Matlab script that simulates the average symbol-error-rate (SER)

performance for “hard” ML detection through exhaustive search as a function

of the signal-to-noise ratio (SNR), when assuming an i.i.d. Rayleigh fading

MIMO transmission channel, similarly to part 1.b. All the details of your code

should be explained. Plot the simulation results together with the results of part

1.b and compare the results. (Hint: Verify your results with the literature).

[20%]

3) Assume that the number of base-station antennas increases from 2 to 64 (i.e., as

in the case of Massive MIMO).

a) Explain in detail how this change affects the received SNR, in comparison to

the case of 2 base-station antennas.

[10%]

b) For this case with 64 base-station antennas, simulate and plot the SER as a

function of the SNR for hard ZF (similarly to 1.b) and ML (similarly to 2.b)

detection for the case of 2 users, and again assuming a for Rayleigh MIMO

channel. Discuss the changes you have made to the previous code. In addition,

discuss your conclusions in comparison to the 2 users and 2 base-stations case.

Explain if your results agree with the literature.

[20%]

Question 2 (100% = 50 Marks)

In this part of the coursework assignment, we implement an IEEE 802.11a based

OFDM system and investigate the impact of different design parameters, e.g.,

modulation level, code rate, interleaver, equalizer, etc. on the system performance.

The IEEE 802.11a system model to be implemented is shown in the lecture notes

which can be found on SurreyLearn.

The following m-files can be found on SurreyLearn:

test: Main program for Tasks 1-5

modulator: Perform modulation, i.e., bit-to-symbol mapping

demodulator: Perform demodulation, i.e., symbol-to-bit mapping

getchannel: Generate IEEE 802.11 multipath channel

onetap_equalizer: Implement one-tap equalization

fig: Serve as a template to make matlab plots based on simulation results

The system parameters are specified in Table 1.

Table 1

FFT Size | 64 |

Length of CP | 16 |

SNR | [6 8 10 12 14 16] dB |

The number of taps in the channel | 11 |

RMS delay spread of the channel | 50 ns |

System sampling frequency | 20 MHz |

Equalizer type | MMSE, unless otherwise stated |

Modulation scheme | QPSK, unless otherwise stated |

Convolutional code | Generator polynomial (133,171) constraint length 7 |

AssignmentTutorOnline

The following issues will be investigated in this assignment:

1) Effect of channel effect in OFDM systems

The OFDM signal model is shown by the figure below and can be expressed

as

,

where

Yk is the kth sample of the DFT output;

Xk is the symbol carried by the kth subcarrier;

Hk is the channel frequency response at the kth subcarrier;

Vk is the noise at the kth subcarrier;

Wk is the equalizer coefficient for the kth subcarrier;

Design and simulate the system in the following three scenarios:

1) The receiver doesn’t have any knowledge of the channel, thus no

equalization can be performed;

2) The receiver has the knowledge of the channel Hk, but does not know the

noise variance N0. Design and implement the equalizer Wk to remove the

channel effect by utilizing the channel knowledge;

3) The receiver not only has the knowledge of the channel Hk, but also knows

the noise variance N0. Design and implement the equalizer Wk to remove

the channel effect by utilizing the knowledge of the channel as well as the

noise variance.

Plot a BER vs. SNR curve in each scenario and compare their performance in

one figure. Note that you need to implement ZF equalizer by yourself. In the

report, give the mathematic expressions and matlab implementation of the

equalizers, describe what can be observed by comparing the performance of 3

different scenarios.

[15%]

2) Combatting burst errors in OFDM systems

Due to the fact that OFDM channel coefficients are correlated, OFDM signal

will experience burst errors as depicted by the upper diagram of the figure

below. Propose and implement an algorithm to convert burst errors into random

X0

H0 V0 W0

XN-1 HN-1 |
VN-1 WN-1 Y0 YN-1 ZN-1 |

Z0

Y X H V k N k k k k = + = ; 0,1, 1 ! –

errors and compare its performance to the case when the burst errors are left

untreated.

In the report, show which part of the matlab code you have changed, discuss

what can be observed from the performance comparison and explain why.

[15%]

3) Effect of channel coding for OFDM systems

Remove channel coding/decoding, interleaving/de-interleaving in the main

program and simulate the performance of an uncoded OFDM system. In the

report, show your matlab implementation of the uncoded system, and compare

the performance of coded and uncoded OFDM systems in the same figure,

discuss what can be concluded from the simulation results and explain why.

Hints: For the uncoded systems, you need to make hard decisions on the

transmitted bits based on the equalizer outputs.

[20%]

4) Repeat Task 1 for uncoded OFDM systems and compare the performance of

two equalization algorithms in one figure. Explain the rationale why the

comparison result seems unusual and departs from people’s common belief.

This requires rigorous thinking and analysis.

[20%]

5) OFDM systems with different data rates (1)

Perform the following tasks for 3 OFDM systems with different data rates:

1) Implement a baseline system employing QPSK modulation, channel coding

and interleaving;

2) Design and implement an OFDM system which doubles the data rate

compared to the baseline system;

3) Design and implement an OFDM system which triples the data rate

compared to the baseline system.

In the report, specify which part of the simulation code is changed in

different systems, compare the performance of 3 systems in the same

figure, discuss the price to pay for the increasing the data rate as well as

the engineering trade-off.

[10%]

6) OFDM systems with different data rates (2)

Perform the following tasks for 4 OFDM systems with different data rate:

1) Implement a baseline system employing QPSK modulation, the (133,171)

code with code rate ½ and interleaving;

2) Design and implement an OFDM system that achieves about 33.3% higher

data rate than the baseline system;

3) Design and implement an OFDM system that achieves 50% higher data

rate than the baseline system;

4) Design and implement an OFDM system that achieves 60% higher data

rate than the baseline system;

In the report, specify which part of the simulation code is changed in each

system, compare the performance of 4 different systems in the same figure,

discuss the price to pay for the increasing the data rate as well as the

engineering tradeoff.

Hints: check matlab help manual to see how puncturing can be incorporated in

the functions convenc (for encoding) and vitdec (for decoding). You need to

adjust the number of data blocks in order to have integer number of transmitted

bits.

[20%]

In order to have high precision value for bit error rate, set output format as

>> format short e or >> format long

A report together with matlab simulation codes should be submitted online.

Note that you should not attach the simulation codes that are supplied on

SurreyLearn to your report. The requested matlab codes are specified above.

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