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The possibility of rendering a gradient-type adaptive equaliser able to acquire automatically the optimal adjusting step has been proved in the paper by proposing a new type of equaliser. The mentioned possibility enables the equaliser to be independent of the channel characteristic and very slightly dependent on the noise.

The recent published literature contains a description of a data-transmission system in which the data signal at the transmitter is fed through a channel equaliser that includes a device for holding the transmitted signal within a given range of values. The paper presents a theoretical analysis of the system, together with the results of computer simulation tests, and proposes a simple modification to the equaliser that maximises the tolerance of the data-transmission system to additive white Gaussian noise. It is shown that the original and modified equalisers are equivalent, both in their basic methods of operation and in their tolerances to noise, to the corresponding conventional nonlinear equalisers, used at the receiver. Finally, a simple error detector is described which operates on the received signal, with no need for any redundant data, and which gives extremely powerful protection against errors when used with the original nonlinear equaliser at the transmitter.

The effect of 2-level quantisation of the signals within the equaliser on its performance is studied in two cases:(a)when the tap coefficients are updated after every sample of the message, and (b) when the updating is performed after an averaging period equal to the length of a pseudorandom binary signal. In particular, the effect on the stability and the mean square error in the steady state is analysed. A relationship between the mean square error in the steady state and the ‘random walk’of the tap coefficients is derived. Numerous computer-simulation results confirm the analysis.

The paper describes the synthesis of arithmetically symmetrical, broadband LC filters having prescribed amplitude response and nearly constant group delay, with particular reference to i.f. filters for radio-relay systems. These filters must suppress unwanted signals, particularly the adjacent carrier frequencies, without significantly distorting the required signal. For low distortion, the filters must have both flat amplitude and constant group-delay responses over the passband centre. Filters synthetised for 1800- and 960-channel systems have satisfied these requirements, the transfer-function design and measured characteristics of the filter for the 960-channel system being given as an example. The filters have the advantages that they can be inserted in the i.f. chain without the need for further phase equalisation, and that they give improved amplitude responses compared with conventional filter and equaliser combinations.

The structure of a conventional nonrecursive equaliser is modified so as to provide the equaliser with an automatic means of maintaining a frame of reference at all times. The output of the new equaliser is effectively the same as that of the conventional equaliser; the two equalisers merely differ in the procedure adopted for computing the forward tap weights. Another principal result is the formulation of a linear recursive adaptive equaliser which may be operated with or without a stability constraint. The paper concludes by presenting computer simulation studies of the performance of both nonrecursive and recursive adaptive equalisers.

The conventional method of transfer-function synthesis, which employs the passive symmetrical lattice network satisfying the constant-resistance driving-point condition, is applied to a nonreciprocal active network. This network has lattice-like properties, including the non-minimum-phase feature, even though it is unbalanced, thereby avoiding the problem of lattice-to-ladder conversion. A greater variety of single-ended constant-resistance sections is made available for synthesis purposes, including a constant-resistance amplifier and nonreciprocal versions of the well known passive (e.g. attenuation equaliser) sections, as well as non-minimum-phase types (such as phase equalisers). Although active and nonreciprocal (i.e. having internal feedback), the sections are shown to be stable under the constant-resistance condition. The synthesis technique may be extended to derived networks, e.g. purely unilateral ones.

A theoretical analysis, using the properties of linear vector spaces, is applied to the design of a nonlinear equaliser. The design minimises the probability of error in the detection of a serial digital signal, subject to the accurate equalisation of the time-invariant channel, when the signal is received in the presence of additive white Gaussian noise with a high signal/noise ratio. The equaliser contains a conventional combination of linear feedforward and nonlinear feedback transversal filters. Certain commonly used assumptions are made concerning the transmitted signal and the channel, but it is not assumed that the channel can necessarily be equalised by a linear feedforward transversal filter of limited length. A simple example shows the advantage in tolerance to additive Gaussian noise, which is achieved by the nonlinear equaliser over the corresponding linear equaliser, in a particular case where accurate equalisation of the channel is achieved by the linear equaliser.

Residual attenuation equalisation of broadband coaxial-cable systems has been achieved elsewhere by a set of harmonic cosine characteristics based on an almost linear frequency scale. This method is, however, not efficient for systems which exhibit high distortion near the bandedges. A simple analysis of measured characteristics yields the requirements for suitably transforming, or `warping?, the frequency scale. Generalisations of the transversal-equaliser principle offer the realisation of cosine characteristics with frequency scales which match particular problems. The investigation on which the paper is based was concerned with the coaxial-cable network of the British Post Office, and led to novel designs, of which the `twin cosine equaliser? has been accepted for service use. This device enables residual distortion of up to 6dB to be reduced to rather less than 1dB, with a minimum of auxiliary instrumentation.

A method of synthetising RC equaliser networks for general loads is given. The configuration specially considered is that of a low-pass RC ladder. The necessary and sufficient conditions for realisability are derived, taking the source resistance into consideration.

Group-delay equalisers operating at microwave frequencies may find application in multicharinel-telephony radio-relay systems, e.g. in systems without translation to an intermediate frequency in repeaters. Studies to ascertain the feasibility of such equalisers operating in the 4 Gc/s band are described. Several equalisers have been designed and constructed in standard waveguide WG11, using a pair of identical bandpass ladder networks terminating a waveguide hybrid or a 3dB directional coupler. In all cases except one, the equalising networks had delay characteristics that were arbitrarily assumed; the exception was a network designed to equalise the group-delay performance, over a bandwidth of 20 Mc/s, of a pair of bandpass filters in tandem. Basic equaliser insertion losses of 0.5–2dB have been observed, the figure depending on the complexity of the network. The effect of temperature changes on the equaliser and filters in tandem resulted in the midband frequency of the equaliser shifting in step with the frequency of the filters, so that the group-delay performance remained equalised over a temperature range of 20degC. It is concluded that, although the performance of the equalisers is satisfactory, they are less flexible in operation and are mechanically bulky compared with intermediate-frequency equalisers.

Using time-series algebra, the operation of adaptive equalisers for both minimum-mean-signal-error and minimum-mean-square-error criteria are considered, and the convergence properties of the iterative procedures generally used are discussed. It is pointed out that, in any practical situation, the control criterion and the iterative algorithm to be used, must be selected to provide the desired performance over the range of situations likely to be encountered. The effect of the equaliser on the regenerator-input signal/noise ratio is also considered, and this, together with the economic need to minimise the equaliser length, is shown to lead to a requirement to select the reference sampling point accordingly. One selection algorithm is described, and its operation is demonstrated in an example.

A network is described enabling the variation of a linear phase characteristic by a single terminating resistor. The network is based on one form of Bode's variable equaliser, the theory of which is briefly presented. Design equations are developed for evaluating the elements of the network. It is shown that variation of the basic loss of the network provides another means of controlling the slope of the resulting phase characteristic. The starting point in the design procedure is the formulation of a realisable linear phase characteristic. This characteristic is realised by two constant-resistance bridged-T networks and an all-pass structure connected in cascade with a variable terminating resistor. Experimental results are given and close agreement with theory is demonstrated.