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# Final Project on TELE9754 Coding and Information Theory: PERFORMANCE OF SPACE-TIME BLOCK CODES, CAPACITY OF ALAMOUTI CODES

UNSWTELE9754Coding and Information TheoryMIMO-OFDM SYSTEMCAPACITY OF MIMO FADING CHANNELSCODED OFDM SYSTEMSPACE-TIME BLOCK CODES FOR 4 TRANSMIT ANTENNAS

TELE9754 FINAL PROJECT (SUBMISSION DEADLINE: 23:59, 24 NOV. 2023) 0

Final Project on TELE9754 Coding and Information Theory

I. PERFORMANCE OF SPACE-TIME BLOCK CODES

Project ID: P1
Project Description:
For i.i.d. Rayleigh fading and QPSK transmission with orthogonal STBC.
1) Plot the symbol error rate (SER) as a function of SNR (from 0 to 20 dB) for

a MIMO channel with M transmit antennas and N receive antennas: M=1,N=4(nocoding)

M = N = 2 (Alamouti Coding)
M = 4, N = 1 (Orthogonal STBC for 4 transmit antennas, see the code

example in Lecture note)
2) Derive pair-wise error probability (PEP) of the Alamouti code for
M = 2

and N = 2 and determine the diversity order.

II. CAPACITY OF ALAMOUTI CODES

Project ID: P2
Project Description:
For i.i.d. Rayleigh fading and Gaussian signaling with Alamouti coding scheme.

1. 1)  Plot the ergodic capacity as a function of SNR (from 0 to 30 dB) for a MIMO

channel with M transmit antennas and N receive antennas: M=2,N=1

M=N=2

M=2,N=4

2. 2)  In the same graph, plot the ergodic capacity of uncoded MIMO channels

with the same antenna configurations. Compare with preceding results and comment with reasoning.

III. SPACE-TIME BLOCK CODES FOR 4 TRANSMIT ANTENNAS

Project ID: P3
Project Description:
Consider a transmission of QPSK symbols over a
4 × 2 channel with i.i.d.

1) Plot the symbol error rate (SER) as a function of SNR (from 0 to 30 dB) for

an orthogonal STBC which is given by [1]

2) In the same graph, plot the SER of a quasi-orthogonal STBC for four transmit

antennas, which is given by [2]

Compare with preceding results on the diversity gain and symbol rate. Com- ment with reasoning.

[1] O. Tirkkonen and A. Hottinen, “Square-matrix embeddable space-time block codes for complex signal cosntellations,” IEEE Trans. Inform. Theory, vol 48, pp. 1122–1126, Feb. 2002.

[2] H. Jafarkhani, “A quasi-orthogonal space-time block code,” IEEE Trans. Commun., vol. 49, pp. 1–4, Jan. 2001.

IV. CODED OFDM SYSTEM

Project ID: P4
Project Description:
Consider a transmission of BPSK signals in an OFDM system with
64-point

IFFT at transmitter and FFT at receiver. The sampling frequency of the OFDM system is 20 MHz. The ISI Rayleigh fading channel is given by the 2-tap channel model with path delay [0, 0.5]μs.

1. 1)  Plot the symbol error rate (SER) as a function of SNR (from 0 to 30 dB) of the OFDM system by choosing an appropriate length of cyclic prefix for the OFDM.

2. 2)  Consider that a rate-1/2 convolutional code and a viterbi-decoding are applied to the OFDM system. Plot the SER of the coded OFDM system. Compare with preceding results and comment with reasoning.

V. MIMO-OFDM SYSTEM

Project ID: P5
Project Description:
Consider an MIMO-OFDM system with
2 transmit antennas, 2 receive antennas

and 64-point IFFT/FFT for OFDM. The sampling frequency of the OFDM is 20 MHz. The channel from transmit antenna j(j = 1, 2) to receive antenna i(i = 1, 2) is a 2-path Rayleigh fading channel model with path delays of [0, 0.5]μs. Alamouti- coding of QPSK symbols is applied at the transmitter on each OFDM subcarrier.

1. 1)  Plot the symbol error rate (SER) as a function of SNR (from 0 to 30 dB) for the MIMO-OFDM system.

2. 2)  In the same graph, plot the SER of the uncoded QPSK for the MIMO-OFDM system.

3. 3)  Determine the diversity gain achieved by the Alamouti-coded MIMO-OFDM system. Is that the maximum diversity gain? Comment with reasoning.

TELE9754 FINAL PROJECT (SUBMISSION DEADLINE: 23:59, 24 NOV. 2023) 6

VI. CAPACITY OF MIMO FADING CHANNELS

Project ID: P6
Project Description:
Consider a MIMO channel with
M transmit antennas and N receive antennas.

Assume that the channel experiences Rayleigh fading.

1. 1)  Plot the ergodic capacities and 99% outage capacities (for SNR ranging from

0 dB to 40 dB) of the following antenna configurations:

M=N=1
M=1;N=2 M=2;N=1 M=N=2

2. 2)  Comment with specific reasoning on the relative values of the above capaci- ties.

calculate the capacity of channel at SNR of 10 dB through waterfilling.

21
calculate the capacity of channel at SNR of 10 dB through waterfilling.

2 1
calculate the capacity of channel at SNR of 10 dB through waterfilling.

Compare with your preceding results and comment with reasoning.
4) Plot the capacity of the above three channels for SNR ranging from 0 dB to

20 dB (with a step size of 2 dB).

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