A New Approach to Drift Compensation in Adaptive Feedback Communication Systems Konrad Jędrzejewski Institute of Electronic Systems, Faculty of Electronics and Information Technology, Warsaw University of Technology, 15/19 Nowowiejska Street, 00-665 Warsaw, Poland, e-mail: Konrad.Jedrzejewski@ise.pw.edu.pl Abstract—A new approach to drift compensation in adaptive feedback communication systems is presented in the paper. The proposed approach is based on application of the extended multidimensional algorithm that estimates simultaneously the value of a transmitted sample and the value of an unknown drift rate. The knowledge of a drift rate enables compensation of drifts and improves transmission efficiency of systems suf- fering problems with drifts. I. INTRODUCTION The paper presents results of investigations on drift com- pensation in optimal adaptive feedback communication systems (AFCS). The optimal AFCS have been recently considered in works by A.A. Platonov [1-3] and refer back to earlier investigations on optimization of transmission in analog AFCS from the 1960s, e.g. [4-7]. The main particu- larity distinguishing optimal AFCS is a lack of digitizing and coding units in transmission unit (TU) (see Fig. 1) which are replaced by the adaptive pulse-amplitude (PAM) modulator Σ+M1. This enables formulation and solution of optimization task for AFCS and determines the optimal values of parameters of both the transmission unit (TU) and base station (BS) in AFCS and its operation ensuring the maximal quality and rate of data transmission. Base station (BS) Transmission Unit (TU) Σ M1 R2 S&H Ch1 Ch2 DM1 T2 DSPU () xt x k ν t ξ k e k B k M , k k B M , tk s , tk s ɶ k y ɶ ˆ n x Fig. 1. Block diagram of optimal AFCS This paper extends the investigations on the optimal AFCS whose results are presented in [1-3] and shows a new method of optimal drift estimation and compensation. The method robustifies AFCS on possible drifts occurring in the transmission system, which can cause abnormal errors and degrade dramatically transmission in AFCS. Drift-like er- rors appear in many electronic circuits and their compo- nents. As it is shown below, even small level of drift-errors in some components of AFCS may be of crucial importance for transmission efficiency. An especially sensitive compo- nent of AFCS is a sample-and-hold unit (S&H). Its output voltage may drift (droop) during a time needed to transmis- sion of a single sample. The output voltage of S&H is not stable because of a leakage current flowing into or out of the hold capacitor which is connected with imperfections in the hold capacitor, switch or S&H output amplifier [8,9]. The level of drift errors can be reduced by increasing the value of the hold capacitor, but this increases also acquisition time and reduces the bandwidth of S&H [8,9] and, in conse- quence, AFCS. In this paper, another method of drift com- pensation based on application of the digital signal pro- cessing algorithm that estimates simultaneously the value of a transmitted sample and the value of an unknown drift rate is proposed. The method is based on the original approach to optimal estimation of signal parameters proposed in [10]. A similar method of drift-like errors compensation was used earlier in analog-to-digital converters [11]. II. OPTIMAL AFCS PRINCIPLES A. AFCS operation A simplified block diagram of optimal AFCS [1-3], which illustrates the principles of its functioning, is present- ed in Fig. 1. The system consists of two parts: the peripheral transmission unit (TU) and the base station (BS). The input signal () xt is sampled in the sample-and-hold unit (S&H) of TU. Each sample ( ) ( ) m x x mT = formed by the S&H unit ( 1, 2,... m = is a sample number and 1/2 T F = is a sam- pling interval) is transmitted to BS independently on the previous samples in 0 0 / / n T t F F = ∆ = cycles ( 0 0 1/2 t F ∆ = is a duration of a single cycle of transmission). Further the superscript (m) is omitted, because samples ( ) m x are transmitted independently and analysis of AFCS can be reduced to the consideration of a single sample transmis- sion. The adaptive modulator Σ+M1 forms an analog signal emitted to BS in particular cycles. In our consideration, the following model of the double-sideband suppressed-carrier (DSB-SC) adaptive modulator, which takes into account possible overmodulation (saturation of the transmitter) dur- ing the transmission, is assumed: , 0 0 ( ) ( ) if | | 1 cos(2 ) sign if | | >1 k k k k k k tk k k k k k k M x B B x B B M x s A ft M x π ϕ − − − ≤   = +   −   , (1)