Stable Compensation of Nonlinear Communication Systems

Abstract

Stable compensation of intermodulation effects is crucial for high throughput communication systems 3 such as those typified by C I communication systems. In this paper a versatile technique for compensation of broadband intermodulation effects is presented. Clever parametrization of the block transfer functions guarantees the stability of the complete compensator over the entire parameter space. Examples in the paper demonstrate both the simplicity and the high degree of effectiveness achievable through this new methodology. 1 . INTRODUCTION Modern avionic communication systems are enormously complex, often involving multiple transmitters and receivers. Extreme care is needed not only in the design of the individual transmitter-receiver link, but also in the minimization of electromagnetic cross-couplings between the multiple paths. Failing this, collocated transmitters can cause in-band interference and on the other hand, the channel nonlinearities can cause out-of-band intermodulation interference. In such channels many sources for nonlinear distortion may exist, from nonlinear discrete devices in amplifiers to the distributed metal-tometal oxide junctions in aircraft skins, antenna structures, etc. The susceptibility to interference in these systems can be especially pronounced when transmitter-receiver pairs are located on an electronically dense command platform in a profusion of collocated RF emitters and receptors. For example, when multiple carriers are amplified simultaneously by one transmitter, Intermodulation (IM) products are generated due to the nonlinearities in the power amplifier (TWT or Klystron). Similarly, a strong (locally) transmitted signal leaking into a receptor can, when it is processed simultaneously with a weak but desired received carrier in a nonlinear element, produce degrading intermodulation effects in the receptors. Reduction of the intermodulation effects, when these are otherwise unavoidable, is possible through suitable post compensation as demonstrated in this paper. This work was done under Research Contract No. F30602-82-C-0135 from Rome Air Development Center, Griffiss Air Force Base. D. J. Kenneally Reliability & Compat. Div. Rome Air Development Center Griffiss Air Force Base NY 13441-5700 A new design approach to reduce the effects of nonlinear distortion in communication channels is developed here. Using the known (linear and nonlinear) characteristics of the channel, and an appropriately selected post-compensator structure, optimum parameter values are found for the compensator. The resulting design achieves a significant reduction of nonlinear effects [1]. It features: 0 reduction of intermodulation distortion by 15 to 50 dB 0 guaranteed stability of the compensation network, and 0 a minimum specified damping ratio (of the transfer functions of the linear blocks of the compensator). Thus, not only does the procedure result in a reduction of the intermodulation distortion but it also produces a compensator which is well behaved in the time domain. The amount of reduction of nonlinear distortion achieved thereby is of course not possible by conventional ad hoc methods [6]. Our design of the post compensator is based on Volterra System Theory. We formulate a mean square IM criterion — for the frequency band of interest and use the computer program VC0MP3 [5] to compute and minimize this criterion function relative to the compensator parameters. The program yields the optimum compensator parameters. High reliability in the minimization process is achieved by use of a powerful optimization package NL2SN0 [7]. An innovative parameterization of the block transfer functions guarantees the stability of the complete compensator over the entire parameter space, and thus, in particular, for the optimum values. Furthermore, a broadband compensation is made possible. The design procedure discussed here is computer-based, and although the basic ideas are sufficiently general, details are given for designing a post compensator (of fixed structure) for the third order nonlinearities. We assume that the system nonlinearities are of odd order; hence, only the effects due to the third order nonlinearity are considered of interest with the higher order effects assumed negligible. Examples provided in the paper demonstrate both the simplicity and the high degree of supression effectiveness achievable through this new methodology. 399 CH2116-2/85/0000-399 $1.00 © 1985 IEEE Most communication channels exhibit some degree of performance degradation due to unintentional nonlinearities in the system [4], Analysis and correction of the inevitable nonlinear distortion produced are clearly not feasible with linear methods alone, since they fail to capture all of the phenomena involved. Because of this, the Nonlinear Transfer Function (NLTF) approach, based on the Volterra theory of nonlinear systems [2], which has recently been applied to the pulse testing and * identification of weakly nonlinear systems [3], is used here. 2. COMPENSATOR REQUIREMENTS In this section we introduce some canonic system formulations and the basic concepts associated with the requirements of a nonlinear compensator. 2.1 The pth-Order Inverse O Fig. 1 Volterra model of a nonlinear system Suppose the input-output relationship of Fig. 1, representing a weakly nonlinear system, is [1 ] y(t) = H[x(t)] two conditions must be satisfied [ 2 ] for a secondorder inverse of H to exist: = ^[x(t)]+H2[x(t)]+H3[x(t)]+ where Hn is the nth order Volterra operator: (1) G, H, = I 1 1