Coursework EE401: Advanced Comm. Theory
Part-A
“Multipath Spatiotemporal SIMO Wireless Comms”
1 Aims
• The main objective of this assignment-study is to simulate a SIMO QPSK-DS- CDMA communication system and design space-time array receivers to handle mul- tipaths, suppress MAI (multiple access interference) and improve the overall capacity of the system.
2 Equipment and Software
• PC (operating system Windows 10+ or Mac OS)
• MATLAB, Visual C++, Labview, or any other suitable language.
• Three digital photos (size: smaller than, or equal to, 160 × 112).
• The MATLAB functions given with AM1 experiment (to be downloaded).
• There are four task in this assignment and, for the 4th task, there is your personal data file that should be downloaded from the course-website.
3 Definitions
• X ,alphabetical order of the 1st letter of your surname
• Y ,alphabetical order of the 1st letter of your formal firstname.
4 Tasks
Task-1 [10%]
• With reference to Figure 1, consider three users with each user transmitting a digital photo, at the same time, on the same frequency band.
Figure 1: System Architecture for Tasks 1 and 2.
• Modulation: All three users use the same constellation diagram given in Figure 2,
where the angle φ is given in degrees according to the following expression
φ , X +2Y (1)
Figure 2: QPSK constellation diagram.
• PN-codes: The three PN-code sequences {α1 [k]}, {α2 [k]} and {α3 [k]} are gold- sequences produced using the following two primitive polynomials:
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1st polynomial (m-sequence)
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2nd polynomial (m-sequence)
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D4 + D +1
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D4 + D3 +1
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The desired user’s gold-sequence {α1 [k]} is produced by adding (modulo-2) a delayed version (d-bits) of the 2nd m-sequence to the 1st m-sequence where d is the smallest integer that:
– gives a ”balanced” gold-sequence and
– satisfies the inequality:
d ≥ 1+ (X + Y)mod12 (2)
The gold-sequences of the remaining two users {↵2 [k]} and {↵3 [k]} are produced with delays d + 1 and d +2 respectively.
• Channel: the three transmitted signals s1 (t), s2(t) and s3 (t) arrive at the input of
the receiver (point T1) according to the parameters given in Table-1. The point T1 is taken as the origin (0,0,0) of the 3-dim real space.
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Table-1: Channel Parameters (there are no multipath efects)
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signal-paths arriving at the receiver
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relative delay
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fading coef.
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(azimuth, elevation)
(θ , φ)
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one path of s1 (t)
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(⌧1 mod15) = 5
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β 1 = 0.4
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(30。, 0。)
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one path of s2 (t)
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(⌧2 mod15) = 7
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β 2 = 0.7
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(90。, 0。)
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one path of s3 (t)
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(⌧3 mod15) = 12
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β 3 = 0.2
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(150。, 0。)
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• Noise: The noise at point T1 is assumed to be additive white Gaussian noise of zero mean and power
i. 0dB, and ii. 40dB
below the power level of the desired signal at point T1 .
Task-1a: Using the above description, simulate the system up to the receiver’s input
(point T1). No MATLAB buildin functions should be used for generating noise and modulation/demodulation.
Task-1b: Considering all the channel parameters unknown, design a receiver to receive ”photo-1” (i.e. { a1 [n]}) and remove the other 2 signals as unwanted multiple- access interference (MAI). Make a comparison at diferent levels of noise (0dB and 40dB) [10%]
Task-2
• As in Task-1 but replacing the channel described by Table-1 with the multipath
channel of Table 2 where the desired user’s signal is received at point T1 via three paths (multipaths).
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Table-2: Channel Parameters (with multipath efects)
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signals arriving at the Receiver
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relative delay in Tc
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fading coef.
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(azimuth, elevation)
(θ , φ)
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1st path of s1 (t)
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(X + Y)mod4
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β 11 = 0.8
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(30。, 0。)
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2nd path of s1 (t)
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4 + (X + Y)mod5
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β 12 = 0.4exp(−j40。)
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(45。, 0。)
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3rd path of s1 (t)
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9 + (X + Y)mod6
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β 13 = 0.8exp(+j80。)
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(20。, 0。)
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s2 (t)
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8
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β 2 = 0.5
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(80。, 0。)
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s3 (t)
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13
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β 3 = 0.2
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(150。, 0。)
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Design the best receiver for this environment. Note: the fading coefficients may be assumed known. [40%]
Task-3
• As in Task-1 but by employing at point T1 (see Figure 3) a uniform circular array of 5 isotropic elements (antennas) with half-wavelength inter-antenna spacing (1st element: 30。 anticlockwise with respect to the x-axis). Design the best possible receiver for this environment.
Figure 3: System Architecture for Task-3 [40%]
Task-4
• Personal data file: For this task please download your personal data file from http://skynet.ee.imperial.ac.uk/notes/notes.html
• PN-codes: With reference to Figure 4, each of the three users is transmitting a text message of sixty 8-bit characters. The desired-user uses a gold-sequence {α1 [k]} that is generated based on the following two primitive polynomials:
1st polynomial (m-sequence) 2nd polynomial (m-sequence) 1st user: D5 + D2 +1 D5 + D3 + D2 + D +1
by adding (modulo-2) a delayed version (d-bits) of the 2nd m-sequence to the 1st m-sequence where
d , the parameter ”phase shift” in your personal file (3)
No information is provided about the PN-codes of the other two users.
Modulation: The desired user uses the constellation diagram shown in Figure 2,
where the angle φ is given in degrees by the parameter “phi mod” . That is
φ , ”phi mod” in your personal file (4)
Figure 4: System Architecture for Task-4
• Channel: The channel parameters are unknown to the receiver - except the fading coefficients of the multipaths of the desired user β 1,1 , β 1,2 and β 1,3 which have been already estimated using another approach. These are given by the elements of the
(3×1) complex vector ”Beta 1” in your personal file, i.e.
⇥β1,1 , β 1,2 , β 1,3 ⇤ T = ”Beta 1” in your personal file (5)
• Channel output: The complex received array signal-vector x(t) at output of the antenna array is given in your personal data file by the parameter “Xmatrix” . That is, it is given in the form of L snapshots (i.e. the vectors x(t`) for ` = 1,2,3, .., L)
forming the matrix X ∈ CN×L, where N is the number of array elements, i.e.
X = ”Xmatrix” in your personal file (6)
Note that the system is asynchronous with unknown time delays with respect to the receiver’s clock.
Task-4a: Estimate the various channel parameters associated with the desired user’s paths.
Task-4b: Design a receiver (preferably a spatiotemporal beamformer) to receive the 60- character desired text-message.
5 Deliverable
• MATLAB/C file(s) - with brief comments. That is four MATLAB script. files (one per task) where the system parameters are defined and a number of MATLAB functions (with comments) are called.
• A pdf file with the results of the above four tasks (photos/messages) supported by 2-5 lines of some brief comments per task.
• Comments, if any, of how to run the programs to observe the results of the four tasks.
• A user interface may be useful - but not essential.
• Please upload a zip file (including all the files) named by your login name (eg. kl209.zip)
6 Some Notes
1. The messages are first modulated using QPSK, then spread by the gold sequences.
2. The PN-codes are generated by seeting the initial state of the shift register be all ones (i.e. [1 1 1 1 1]);
3. The Xmatrix in your ”mat” file contains the received signals which has the form.
[x(1), x(2), . . . , x(L)] (N × Lmatrix)
in which x(i),i = 1,..,L is a N × 1 vector. Note that x(1) is the first snapshot of the signal-vector received and x(L) is the last snapshot of the signal-vector received.
4. Please download and use the ”Matlab Wrappers” from
http://skynet.ee.imperial.ac.uk/notes/notes.html
7 References
[1] Lecture Notes on Advanced Communication Theory
[2] your own references.