An Upper Bound on the Probability of Instability of a DVB-T/H Repeater with a Digital Echo Canceller Flavio Zabini WiLAB Univ. of Bologna, Italy flavio.zabini@unibo.it Matteo Mazzotti WiLAB Univ. of Bologna, Italy mazzotti.matteo@unibo.it Davide Dardari WiLAB Univ. of Bologna, Italy davide.dardari@unibo.it Oreste Andrisano WiLAB Univ. of Bologna, Italy o.andrisano@ieee.org Abstract—The architecture of a digital On-Channel Repeater (OCR) for DVB-T/H signals is described in this paper. The presence of a coupling channel between the transmitting and the receiving antennas gives origin to one or more echoes, having detrimental effects on the quality of the repeated signal and critically affecting the overall system stability. A low-complexity echo canceller unit is then proposed, performing a coupling channel estimation based on the local transmission of low- power training signals. In particular, in this paper we focus on the stability issues which arise due to the non perfect echo cancellation. An upper bound on the probability of instability of the system is analytically found, providing useful guidelines for conservative OCR design, and some performance figures concerning different propagation scenarios are provided. I. I NTRODUCTION An advantage of recent Digital Video Broadcasting- Terrestrial/Handheld (DVB-T/H) standards [1] is the possibil- ity to realize a Single Frequency Network (SFN) to broadcast the video signal. As a consequence, the delicate task of planning the service coverage for a given geographical area is greatly simplified with respect to more traditional Multi Frequency Networks (MFNs), both because the frequency distribution on the territory stops being a critical issue and also because proper On-Channel Repeaters (OCRs) can be easily introduced as gap-fillers to extend or enhance the coverage. An important phenomenon to consider when designing and installing an OCR is the coupling between the transmitting and the receiving antennas, which inevitably causes detrimental echoes in the received signal. In practice these echoes degrade the signal and limit the amplifier gain of the repeater, since dangerous oscillations with potential system instability have to be avoided. To address this critical problem, several archi- tectures for digital echo cancellers have been proposed, which mainly differ on the basis of the technique adopted to estimate the coupling channel [2]-[5]. In this work we focus on the low- complexity tecnique proposed in [6], based on the transmission of a low power training signal by the OCR, to estimate the echoes and correspondently set the cancelling unit. The main problem caused by the presence of the coupling channel between the transmitting and the receiving antennas is the possibility that the repeater becomes unstable due to non perfect channel estimation and noise. The rate of occurrence of this condition has to be minimized through a careful design of the OCR, since, at best, an instability situation forces A/D D/A Rx Filter Rx Antenna Tx Antenna FIR Channel Estimator Echo Canceller Training Signal Echoes Tx Filter HPA S + + - Fig. 1. Block architecture of the considered OCR. the OCR in an out-of-service state for several seconds. Even worse, if the mechanisms to detect possible system instabilities are not rapid enough, the signal amplifier may completely burn out. To the best of our knowledge, no mathematical analysis has been developed to quantify the probability that a repeater becomes unstable due to echoes and related cancelling techniques. Here we exploit the results of the pioneeristic work in [8], about the zeroes distribution of a random polynomial, to develop an analytical framework to express an upper bound on the probability of instability as a function of the coupling channel. The goal is to evaluate how the insertion of an echo canceler improves the performance of a repeater in terms of overall system stability. A low probability of instability, in fact, permits to increase the gain of the HPA and, as a consequence, to cover a wider area (reaching more users). II. SYSTEM DESCRIPTION Let us consider the general OCR architecture depicted in Fig. 1, where we have adopted the low-pass equivalent rep- resentation of the different processing blocks. The received DVB-T/H signal is sampled by an ideal A/D converter, with sampling frequency f s =1/T s , chosen high enough to avoid aliasing. Then, it is passed through a digital filter aimed at reducing the amount of noise and possible interference from adjacent channels. Dually, at the output, the D/A conversion is preceded by a digital transmission filter whose main goal is to make the transmitted signal compliant with the elec- tromagnetic compatibility mask. It is worth noticing that, if 978-1-4244-5637-6/10/$26.00 ©2010 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.