1 / 14

Evaluating the Bit Error Rate for M-PSK

Evaluating the Bit Error Rate for M-PSK. Presented by: Idris Ajia Assessor: Dr. Tareq Al- Naffouri Date: Saturday, 12 December 2009. Introduction: Importance of Digital Communications. Increasing dependence on Digital Communication. Need for accurate data TX Calculating BER.

luisa
Download Presentation

Evaluating the Bit Error Rate for M-PSK

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Evaluating the Bit Error Rate for M-PSK Presented by: IdrisAjia Assessor: Dr. Tareq Al-Naffouri Date: Saturday, 12 December 2009

  2. Introduction:Importance of Digital Communications. • Increasing dependence on Digital Communication. • Need for accurate data TX • Calculating BER. • Improving the System • Aim of Paper:

  3. Method Use of grey coding to map the symbols on the Constellation plot Then use the geometric property of the constellation plot.

  4. The generic equation for an M-PSK message is: Where Pre-Analysis ETP is the symbol energy, T is the symbol period.

  5. Computing BER • Use Mathematical induction. • Start with 4-PSK • Each bit = a0a1 • Pi is the probability of an error occurring based on the decision made with respect to the i-axis Constellation of 4-PSK

  6. 4-PSK • Given symbols are equiprobable. • Then: • And • Hence, probability of error for 4-psk is:

  7. Then 8-psk • For an 8-PSK, there are 3 bits per symbol as shown below: • It follows that: • Which approximates to: • Let the bits in each symbol be a0a1a2. • Notice two new Axes C1 and C2

  8. 8-PSK cont. • Then: • It can now be seen that by means of induction,

  9. BER for M-psk • Now the BER of M-PSK can be determined by calculating Pa. To do this, we know that: • For any MPSK signal space representation, there are four quadrants and each quadrant contains the same number of constellation point. • This means there are M/4 possible values for the vertical distance of each constellation to the a-axis. • The value for these distances, by observing the constellation plot is given by: • Since all symbols are equiprobable, the probability for any given symbol over an AWGN channel is given by: • So the probability of error due to the decision made with respect to the a-axis, given any symbol is given by:

  10. BER for m-psk • Then Where di = distance between each symbol and the a-axis. Now, • By means of substituting (7) into (6), we get the BER of MPSK as: • But

  11. Finally... • The Ber for M-PSK is:

  12. Comparison My Approximation Real Value

  13. Confused yet??? • Don’t blame me, • Blame the likes of Fourier, Mr Gauss and Dr. Tareq. • I will now entertain your questions...

  14. Applauds

More Related