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Characterization of Radio Frequency Echo Using Frequency Sweeping and Power Analysis Amar Zeher, Stéphane Binczak, Jerome Joli

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Characterization of Radio Frequency Echo Using Frequency Sweeping and Power Analysis Amar Zeher, Stéphane Binczak, Jerome Joli Characterization of Radio Frequency Echo using frequency sweeping and power analysis Amar Zeher, Stéphane Binczak, Jerome Joli To cite this version: Amar Zeher, Stéphane Binczak, Jerome Joli. Characterization of Radio Frequency Echo using fre- quency sweeping and power analysis. 2014 IEEE REGION 10 TECHNICAL SYMPOSIUM, Apr 2014, Kuala Lumpur, Malaysia. pp.356-360, 10.1109/TENCONSpring.2014.6863057. hal-01463734 HAL Id: hal-01463734 https://hal.archives-ouvertes.fr/hal-01463734 Submitted on 17 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Characterization of Radio Frequency Echo Using Frequency Sweeping and Power Analysis Amar Zeher Stephane´ Binczak Jerome´ Joli LE2I CNRS UMR 6306, Laboratory LE2I CNRS UMR 6306, SELECOM, Universite´ de Bourgogne, Universite´ de Bourgogne, ZA Alred Sauvy, 9 avenue Alain Savary, BP47870 9 avenue Alain Savary, BP47870 66500 Prades, France. 21078 Dijon cedex, France 21078 Dijon cedex, France Email: [email protected] Email: [email protected] Email: [email protected] Abstract—Coupling between repeater’s antennas, called Radio as Wiener Filter, Linear Prediction [4] or Non-linear Acoustic Frequency Echo (RFE) deteriorates signal quality and compro- Echo Cancellation Based on Volterra Filters [5]. Some of these mises system stability. If the channel insulation is insufficient, techniques are applied to radiocommunication. Depending on the power in the closed-loop raises with time according to the gain margin value. Multiple methods of echo cancellation exists. the nature of concerning signal, the efficiency of these methods Generally, these techniques are based on correlation calculation could be called into question. Indeed, modulation constraints and adaptive filtering. However, their efficiency and algorithm’s as guard interval, Error Vector Magnitude (EVM), Modulation convergence speed are calling into question under signal’s mod- Error Ratio (MER) have to be satisfied when filtering. ulation and real-time constraints, specially with narrow band signals having frequency hopping as GSM or TETRA. This paper Narrow band signal (NBS) with frequency hopping, as in describes a real time method of RFE detection and estimation GSM or TETRA standards, is one major difficulty when using independently of the nature of the incoming signal. It is based on linear filtering because of the convergence rate of adaptive frequency sweeping and analysis of power ripples, and it can be algorithms which are generally too slow when compared with implemented on FPGA for real-time purpose. It gives an accurate the hopping frequency rate and randomness [6]. Under these estimation of corresponding gain margin and loop delay. constraints, linear filtering increases transmission errors and Index Terms—Radio frequency echo, gain margin, narrow band, frequency hopping. creates an Adjacent-Channel Interference (ACI). Radiofrequency signal can also be Wide Band Signal I. INTRODUCTION (WBS), which occupies a range of frequencies such as DVB- T/H (8 MHz in France) and CDMA. NBS has a narrower In regions where reception quality is poor, it is usual to band width, generally less than 1 MHz as GSM (200 KHz) locate repeaters which are deployed to expand and enhance and TETRA standards (25 KHz). Part (a) of Fig. 1 shows an coverage region of Base Station Transceiver (BTS) cost- example of WBS and NBS displayed in the frequency domain effectively, without the need for modulation and demodulation without RFE. setups. A repeater receives signals from the main transmitter Ripples indicates the presence of a RFE and, as illustrated in which is generally BTS on the selected carriers ; then, it re- part (b) of the Fig. 1, they are only distinguishable in WBS and transmits them to receivers which are generally Mobile Station the noise floor parts. With noise floor or wide band, it is easily (MS) such as cell phones, Personal Digital Assistant (PDA) detectable and voidable by using linear adaptive algorithms. and communication terminals. The receiving signal is filtered, amplified and re-transmitted; if the repeater retransmits signals Nevertheless, the narrower the band is, the more difficult in the same frequencies, it is called Iso-Frequency Repeater these solutions can be used effectively. For example, adap- (IFR), otherwise, it is called Transposing Frequency Repeater tive filtering using Wiener solution based on the correlation (TFR). Deploying TFR to extend coverage area is robust, but it calculation is a good solution when used with DVB-T or is expensive. Contrariwise, IFR are cost-effectively and simple CDMA standard, but it cannot be used when GSM signal to set up. Nevertheless, with IFR, if the channel insulation is with frequency hopping is used, because of the ACI and the insufficient, a part of the transmitted signal could be picked unwanted spurious which are created. up by the receiving antenna of the repeater, leading to RFE The transmitted signal can reach the receiving antenna by creation.This phenomenon is well known as the issue was one or more paths (it is then called multipath), depending on first posed in acoustics field [1]. When using repeaters, Echo the topology of the location. In this paper, RFE phenomenon Cancellation is one method of compensating for external Ra- is modeled using only the direct path. It is also supposed in dio Frequency (RF) coupling between antennas [2]. The echo the simulation part that the repeater includes three functions signals must be reduced to an allowable level in order to avoid which are a controllable amplification, delay and Additive problems with distortion and oscillation [3]. Many techniques Gaussian White Noise (AWGN). The channel parameters are exist for cancelling echoes, notably in the area of acoustics chosen to be a constant delay and variable attenuation (other System (1) can be expressed such as y(t) = g · i(t − τ0) + ga · y(t − τ0 − τ1): (2) Eq. (2) is a recursive equation, which can be expressed by y(t); y(t − (τ0 + τ1)); s(t − 2(τ0 + τ1)); : : : ; s(t − l(τ0 − τ1)); s(t − (l + 1)(τ0 − τ1)); s(t − (l + 2)(τ0 − τ1)), while l is the number of secondary echoes. Introducing g · a = δ; τ0 + τ1 = τ; eq. (2) can be expressed by the following sum y(t) = gi(t − τ0)+ l+1 h X n i g δ i(t − nτ − τ0 + (3) n=1 Fig. 1. a) Spectrum of wide band signal (10 MHz centered on 35 MHz) δl+2y(t − (l + 2)τ) ; and narrow band (200 KHz centered on 45 MHz). b) Echo is given for gain margin ∆ = 5 dB and loop delay τ = 0:5 µs. which can be reduced to its simplest expression, so that l+1 h X i y(t) = g δnit − (nτ + τ ) + δl+2yt − (l + 2)τ: (4) parameters as fading are therefore not taken into account) and 0 n=0 the propagation delay in wires is supposed negligible. The article is organized as follows: In section II, mathe- Using Fourier Transformation, eq. (4) leads to matical equations modeling the system are presented and l+1 l+2 −j!(l+2)τ X n −j!(nτ+τ ) the relationships between the power in the repeater and the Y(!) = δ e Y(!) + gI(!) δ e 0 ; system parameters as the repeater gain, repeater delay, channel n=0 (5) attention are stated. These theoretical results are consistent where Y(!) and I(!) are the Fourier Transformation of y(t) with findings from the simulation presented in section III. and i(t), respectively. The transfert function is defined as Simulink tool is used to realize the closed-loop system and Y(!) results are analyzed using Matlab. Finally, as a conclusion, H(!) = : (6) the main results are summarized and discussed. I(!) From eq. (5), H(!) can be written such as II. THEORY l+1 X Taking into account the set of assumptions previously g δne−j!(nτ+τ0) mentioned, a system composed of a repeater, two antennas H(!) = n=0 : (7) and a channel is simplified, as shown in Fig. 2. The closed 1 − δl+2e−j!τ(l+2) When the repeater steady state is reached, l tends towards infinity. Let H1 be this limit. Then, from equation (7), the system transfer function leads to ej! (τ+τ0) H (!) = g : (8) 1 −δ + ej! τ Thus, the power p of the system can be written so that Fig. 2. Radiofrequency coupling, considering only the direct echo path. g2 p(!) = jH (!)j2 = : (9) 1 δ2 − 2 δ cos (! τ) + 1 loop of the system is expressed by the following equations : Let us define in dB the following parameters : s(t) = i(t) + e(t) ; Power : P = 10 log(p) e(t) = ay(t − τ1) ; (1) Gain : G = 20 log(g) (10) y(t) = gs(t − τ0) ; Attenuation : A = 20 log(a) where i(t) is the incident signal, y(t), the transmitted signal Gain margin : ∆ = 20 log(δ) = G + A: and e(t), the feedback signal (echo). g and τ0 are respectively Using these notations with eq. (9), the power in dB is given the repeater gain and the repeater delay, while a and τ1 are by respectively the channel attenuation and the channel delay. P (!) = G − 10 log δ2 − 2δ cos (! τ) + 1 : (11) In practice, most of the variables are expressed in dB, thus Nevertheless, a positive gain margin without AGC or RFE can- cellation system cannot exist in practice, because electronics P (!) = G − 10 log 10∆=10 − 2 · 10∆=20 cos (! τ) + 1: (12) circuits may be damaged before reaching zero gain margin.
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