Mar 01

Copper Line Attenuation MAR1 Model

One of the homeworks I had to do during my Communication Systems course at the PoliTO was calculating some attenuation values of a copper line in function of distance and frequence, based on the MAR1 model. Oddly enough, Googling MAR1 I couldn’t find a single thing about the model so I decided to post my work here so people can take a look at how it works. I’ve made this in Matlab.

The following function computes the attenuation:

function [att] = mar1(d, f)
% mar1(d, f)    Calculates the attenuation in dB
%               depending on length d (in km) and
%               frequency f (in Hz)
 mu0 = 4*pi*10^-4;
 R0 = 277.623806;
 Lalpha = 421.576013 * 10^-6;
 Linf = Lalpha;
 a = 1.470148;
 b = 2;
 c = 2.765;
 delta = 0.001123;
 C1Mhz = 49.792437 * 10^-9;
 Zl = 100;
 Zs = Zl;
 Cf = C1Mhz * (f / 10^6)^-(2*delta/pi) * cos(delta);
 sf = (mu0 * 1i * f) / ((0.75^2) * R0);
 Zf = 1i * 2 * pi * f * Linf + R0 * ((1/4) + (3/4) * sqrt(1 + (a*sf*(sf+b))/(sf+c)));
 Yf = 2*pi*f*Cf*(1i+tan(delta));
 Z0 = sqrt(Zf/Yf);
 gamma = sqrt(Zf * Yf);
 A = cosh(gamma*d);
 B = Z0*sinh(gamma*d);
 C = (1/Z0) * sinh(gamma*d);
 D = cosh(gamma*d);
 ratio = Zl / (A*Zl + B + C * Zl * Zs + D * Zs);

If you put this in a nested loop that iterates over some distances and frequencies and plot it afterwards, you get a nice result such as this.

MAR1 Copper Line Attenuation

MAR1 Copper Line Attenuation

This shows you why ADSL is slower than for example internet access by cable. A reason why more recent versions of ADSL and VDSL are faster is because the line length is shortened and thus the frequency can be raised, and in turn so is the symbol rate.

Jan 29

Communication Systems Exam ’12-’13

Today I had my first exam at PoliTO. When I first came to Torino in September there were also exams going on and they seemed to be pretty organised. People were called by their name to be able to enter the room, they told us you needed to use the terminals in the hallways to print some kind of “entry ticket” which you had to show as your name was called.

Fast forward to today, we could just enter the room where we had exam, everyone was just talking until the professor arrived. People just had to sit at both ends of a row and one in the middle, didn’t matter if your coat and backpack were next to you. Nothing was said about having your wallet or a cellphone in your pocket but to be sure I turned it off and put it away.

The professor came around during the exam, writing down your name on a paper to ‘register’ your attendance. That’s about all the formalities there were today, no papers or name calling at all!

For those who want to know which questions we got on the first exam day of Communication Systems, feel free to download the list of all possible questions: List of questions 2012 2013

The ones asked on the exam were questions 2, 5, 7, 14, 18 and 21.

Jan 15

The Bingham formula

During my time at the Politecnico di Torino I attended a Communication Systems course which focused on systems such as ADSL/VDSL, DVB-T, LTE and modulation techniques such as PSK, QAM, DMT/OFDM. That being said, the one formula we always used to compute the cardinality of the constellation used was the famous Bingham formula.

When I was looking at the different parameters of this formula I figured I would do a search on Google to see if there was more information to be found. However, a search for “Bingham formula” resulted in not a single useful link. If this is such a famous and used formula, why is there nothing on the searchable web about it? Not even an entry on Wikipedia? This is an honest question, if someone knows please tell me.

What does this formula look like you ask? Here it is:

Bingham Formula

m: the number of bits
1/10: used when solving for a BER of P(e) = 10^-7, 1/14 if you’re using a BER of 10^-10 (e.g. for DVB-T)
Prx: received power
Pn : noise power
Yc/Ys: non-ideality in relation to Shannon + recovery by coding gain
Ym: margin parameters taking other losses into account

When computing the achievable bitrate for a given band, you’d use Rb = Rs * m, where Rs is the symbol rate. Not going in to much detail here as I could spend another three paragraphs on things such as delay spread, guard time and cyclic prefix, just know that once you have solved the equation and have m, you know which QAM you can use. For example, if m = 3, you can use a 2^m = 2^3 = 8-QAM constellation, so that would mean 3 bits per symbol.

The difference with the Shannon formula is that you take into account some non-ideal properties, if you want the ideal bitrate, just take Yc/Ys = 1 and neglect 1/Ym.