The Effect of Signal-to-Noise margins on the performance of ADSL J.H. van Wyk and L.P. Linde Abstract—There is renewed interest in existing copper networks since the introduction of Asymmetric Digital Subscriber Line (ADSL) technol- ogy. ADSL will soon be available in South Africa, opening the broad- band market to prospective users. As many users are placed within the same cable, they interfere with each other. Service providers want to guarantee the supplied data rate to the customer, even as the network change over time. For this purpose, a Signal-to-Noise ratio (SNR) mar- gin is added to the customer profile. This paper estimates the number of interferers (possible services) which can be allowed for different line lengths, interferer types and SNR margins for a maximum data rate over the line. Keywords— Asymmetric Digital Subscriber Line (ADSL), Signal-to- Noise ratio (SNR) margin, Performance margin, Interference margin, Margin estimation I. I NTRODUCTION The loop plant (lines radiating from the exchange to cus- tomers) is the only part of the telephone network that stayed structurally almost the same for the best part of a century. It primary use was for basic voice communication, but the in- troduction of broadband technology and applications led to a transformation of the network. Nowadays the network incor- porates various broadband technologies, of which Asymmet- ric Digital Subscriber Line (ADSL) will soon be part. Al- though considered as a point-to-point service, interference between services occur within the cable. Spectral manage- ment must be performed by service providers to guarantee a certain data rate to users, even if the network should degrade with time. Every user’s line has a specific topology, which can be represented by a signal-to-noise (SNR) profile. If a certain margin is added to this profile, the provider can guar- antee the data rate to the customer. This margin, referred to as SNR margin, performance margin or interference margin, is the topic of this paper. Our simulation aims to estimate the number of possible interferers which can be allowed for a specific line length and SNR margin. The basic modelling principles used in the simulation is discussed in Section II. Section III shows the results obtained. A discussion of the results is presented in Section IV. II. SIMULATION MODELLING A. Channel Modelling The resistance R, capacitance C, inductance L and con- ductance G of a copper line, at a specified frequency f are determined by: R(f )= 4 p r 4 oc + a c · f 2 (1) where r oc is the copper DC resistance and a c is a constant characterizing the increase of resistance with frequency in the ”skin effect”, L(f )= l 0 + l ∞ ‡ f fm · b 1+ ‡ f f m · b (2) where l 0 and l ∞ are the low-frequency and high-frequency inductance respectively, and b is a parameter chosen to char- acterize the transition between low and high frequencies in the measured inductance values, C(f )= c ∞ + c 0 · f -ce (3) where c ∞ is the ”contact” capacitance and c 0 and c e are con- stants chosen to fit the measurements, and G(f )= g 0 · f +g e (4) where g 0 and g e are constants chosen to fit the measurements. Values for the different constants for different wire types are summarized in Table I for ADSL. The characteristic impedance Z o and the propagation con- stant γ of the twisted-pair, at a specific frequency f is ex- pressed as [1, 2]: Z o = s R + jω.L G + jω.C (5) γ = p (R + jω.L)(G + jω.C ) (6) where ω =2πf . Two-port networks, and specifically ABCD matrixes, can be used to represent the line. The ABCD parameters are related to the characteristic impedance Z o and propagation constant γ as follows: A = D = cosh(γ.d) (7) B = Z o . sinh(γ.d) (8) C = 1 Z o . sinh(γ.d) (9) where d is the length [km] of the line segment under consid- eration [3]. The insertion loss function of the twisted-pair loop with source impedance Z s and terminal impedance Z t is [1, 3]: H ins (f )= Z s + Z t A.Z t + B + C .Z s .Z t + D .Z s (10) The attenuation through the cable [dB] is expressed as [3]: L dB (f )= 10 .log 10 | H ins (f ) | 2 (11) B. PSDs of interferers The power spectral density (PSD) of a downstream ADSL interferer is expressed by Eq. (12) [Annex B of [4]]. K ADSL-down is the total transmitted power in milliwatt for a downstream ADSL transmitter before shaping filters, with f o