A New Approach to Time-Domain Equalization

A theoretical study is made of the time-domain equalization procedures for the correction of delay distortion in high-speed data transmission lines. In the first part of the paper the conditions that insure valid and effective use of a class of conventional time-domain equalizers are reviewed. In the second part of the paper, a new type of nonlinear time-domain equalizer is proposed, in which iterative methods are not required. The theoretical basis is given for the new equalization method. where So = e So In this paper we shall refer to systems in which the signal-element response for a ONE is Sex) and the signalelement response for a ZERO is -Sex). • Figure of merit for signal reception When a series of bits is sent, the m bits preceding a given bit and the n bits following it may interfere with this bit. For the worst-case pattern, the value V of the signal at the sampling instant for the given bit is (4) (3) (2) o for {i > n i < -m The origin, i 0, corresponds to the sampling of the given single bit. The value So satisfies: Isol ?: Is,l for any i, The quantity So is the value at the sampling instant of the given bit. We shall refer to So as the information sample. The s, where i -:;e 0, are the values of the signal-element response at the sampling instants of the bits following and preceding the given bit. When the s, for t -:;e 0 are not all zero, the phenomenon commonly referred to as "inter-symbol interference" occurs. The first nonzero received value is L m and the last one is s'" s, Introduction In the time-domain method of correcting for the delay distortion of data pulses on telephone networks, the received pulse is operated upon with a series of delay lines. Automatic methods'I" for utilizing delay lines to correct the received waveform permit rapid adjustment of highspeed pulses on switched networks. The analyses in the present paper pertain to the efficiency of the equalization procedures. The signal response of a transmission system to a given bit pattern is usually sampled at specified instants determined by the system clock. The information used for retrieviug each bit pattern is completely contained in the received signal at these sampling instants. In this paper we will assume that the sampling instants are equidistant, which is almost always the case. In the first part of the paper we discuss the conditions for efficient use of conventional linear devices for timedomain equalization and then we analyze the iterative processes. In the second part we describe a nonlinear equalizer that uses a decision threshold device. The proposed equalizer would have the decided advantage of operating without iteration processes. As an outgrowth of the analyses we show a hypothetical application of the nonlinear equalizer. • Signal-element response The signal-element response of the transmission system is the response of the system to a single bit, as indicated in Fig. L We shall represent this response by the polynomial Sex): presented at and pnblished in the Record of the Communications Convention, Boulder, Colo., June 228 i-+n S(x) = L S,X' i--m *" Based on a First Annual 7-9, 1965. n > 0 m > 0, (1) ±L In order to compare this value to the one corresponding to another signal, it is useful to define the figure of merit, f[S(x)], denoted simply by f(8): IBM JOURNAL • JULY 1965 This figure of merit is such that: If f(S) ~ 0, it is always possible to find a pattern such that at least one bit of this pattern will systematically be recovered in error. If f(S) > 0, every bit of any pattern will theoretically be recognized without error in the absence of noise. If f(S) = 1, the received signal is theoretically perfect for sampling. Maximum security in data transmission is expected (Nyquist's first criterion is satisfied). Let us denote by 8(x) an equalized signal-element response. The equalization capability of the equalizer will be measured by the quantity: Figure 2 Conventional linear device for time-domain equalization. Units designated by D are analog delay elements. (9) 8(x) = S(x)· P(x). If Sex) is the signal entering this equalizer and 8(x) is the signal coming out, we may write:" • Purpose of equalization Perfect utilization of this conventional equalizer implies that the choice of the coefficients of the polynomial P(x) yields a maximum value for f(8). An equalization procedure consists in defining a method for choosing the q + r coefficients Pi, that is, a method for adjusting the q + r weights, Pi, in the equalizer. (6) (5) (7) f(S) = 1 L: I~I i;o'O So f(S)