8PSK Demapper



In the context of a DVB-S2 receiver, we propose an 8-PSK demapper using the polar coordinates to represent the received symbols. The demapper directly computes the Log-Likelihood Ratio (LLR) of the 3 bits associated to the received symbol directly as a function of the polar coordinate. With a simple interpolation, we significantly reduce the complexity of the demapper while having almost optimal performances. Simulation shows a 0.02 dB degradation of the Signal to Noise Ratio at the output of the DVB-S2 error control code (Low-density parity-check code) between the optimal LLR generation and the proposed one.

This project is a joint collaboration with INICTEL-UNI


This figure represents the 8-PSK modulation with the binary mapping of bit b2b1b0


This figure represents the classical quantization grid (I and Q are quantized on 5 bits).


This figure represents the proposed polar quantization grid (rau and theta are also quantized on 5 bits).


(The matlab file to generate the two previous figures is available here)

This figure represents the evolution of the LLRs of the 3 bits for a fix variance of the noise, rau constant and theta varying.


This figure represents the evolution of the LLR of b0 for a fix variance of the noise, different values of rau, and theta varying.


Based on the two last figures, one can see that the LLR can be approximated by a linear function of rau and theta.

The following figures show the approximation between the simplied method based on linear approximation and the optimal method. The parameters are R=6 and alpha = 0.046 (see the give matlab function and the related papers).


This figure shows, in a 3D view, the error (always bounded by 1) between the exact value of the LLR and the one obtained thanks to a simple linear interpolation. The x and y axis give the position of the quantized point and the z-axis show the quantization errror.

The matlab file to generate the four last previous figures is available here

To generate the same figures, type [llr0 llr1 llr2 llr0q llr1q llr2q] = Linear_interpolation_LLR(6,0.046) on matlab)

More information

Poster presented by Anthony Barré at the 2013 SoC-SiP meeting (june 2013): slides.

Related papers

  1. Anthony Barré, Neysser Blas, Daniel Diaz, Emmanuel Boutillon, Démappeur 8-PSK en coordonnées polaires, GRETSI 2013, Brest, Sept. 2013 (in French).


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