Optimization of Adaptive Communication Systems with Feedback Channels Anatoliy A. Platonov Institute of Electronic Systems, Warsaw University of Technology Warsaw, Poland plat@ise.pw.edu.pl Abstract—The work presents a new approach to the concurrent optimization and design of transmitting and receiving parts of the adaptive communication systems (ACS). There is shown that optimal ACS used in the threshold mode provide, under given BER, a bit rate equal to the capacity of the forward channel. Keywords - adaptive transmission systems, optimization, ideal systems, information limits. I. INTRODUCTION The main tendency in development of wireless communi- cation and data-transmission systems (CS) is increasing the rate and the range of reliable transmission under simultaneous minimization of the sizes, energy consumption and production costs of peripheral transmitting units (PTU). This task is inter- nally contradictive: diminution of the energy consumption re- quires application of low-power transmitters that worsens the quality, range and the rate of transmission. Known results of information and communication theory [1,2] determine the upper boundaries of achievable performance of transmission but do not give strict analytical recommendations for practical realization of corresponding systems. In the paper, some non-conventional approach to optimiza- tion of adaptive CS (ACS) with the noiseless feedback channel is discussed. This task belongs to classical tasks of communi- cation theory (see e.g. [3,4]). Common feature of investiga- tions in this field is inclusion of the coding/decoding units as necessary elements of CS architecture. The latter makes im- possible full optimization of the systems (concurrent optimiza- tion of their transmitting and receiving parts) due to invincible mathematical difficulties. For this reason, known solutions of this task are approximate and differ from the optimal ones. Below, we show a possibility of accurate solution of full op- timization task for the special but practically useful class of ACS transmitting the signals using only adaptive analogue (amplitude - AM) modulators. Surprisingly, but being properly organized, this “simplest” method of modulation enables ideal transmitting the information with a bit-rate equal to the capaci- ty of the forward channel. The considered ACS (see Fig. 1) consist of the peripheral transmitting unit (PTU) and base station (BS). Apart of receiv- ing and processing the signals, BS computes the controls transmitted to PTU through the noiseless feedback channel M2-Ch2-DM2 (for not too large distances, practically noise- less feedback channel can be always realized due to the lack of special limitations on the power of BS transmitter M2). The transmitting part of PTU consists of the sample and hold (S&H) unit and adaptive modulator, which includes the subtracting unit Σ and modulator-transmitter M1. Receiver of BS consists of the analogue receiver (DM1) and digital signal processing unit (DSPU). Each sample of the input signal is held at the input of subtractor Σ during the time T and is transmitted in n cycles (iterations) independently from pre- vious samples. In each k-th cycle ( 1,..., k n = ), BS processes the signal received from PTU and computes and stores, until the next cycle, the intermediate estimate of the sample. Simul- taneously, it computes the control signal transmitted to PTU through the feedback channel. We assume the duration 0 t Δ of the cycles and the distance between PTU and BS are sufficient for this signal could be delivered to PTU and used for setting its units before the beginning of next cycle of transmission. The discussed approach is based on approach [5,6] devel- oped for optimization of adaptive estimation systems with ad- justed analogue parts. II. FORMAL DESCRIPTION OF ACS WORK We assume the signals t x at the PTU input are band- limited Gaussian processes with known mean value 0 x and va- riance 2 0 σ . The samples ( ) m x = ( ) x mT are held at the input of adaptive modulator during the time 1/2 T F = , ( 1,2... m = ; F is a baseband of the signal t x ). Each sample ( ) m x is transmit- ted independently in 0 / n T t = Δ cycles ( 0 0 1/2 t F Δ = is duration of the single cycle, 0 F determines a bandwidth of the chan- nels). In this case, analysis of ACS can be reduced to analysis of the single sample transmission that allows us to omit indic- es in notations of the samples ( ( ) m x x = ) and related variables. M1 Ch1 DM1 M2 DSPU Peripheral Transmitting Unit Base Station S&H DM2 Ch2 Σ DM k B k B ˆ n x t x x − k e t,k s t,k s  t ζ k y  k M k ν Figure 1. Block-diagram of adaptive communication system. 978-1-4244-2948-6/09/$25.00 ©2009 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.