Nonlinear signal filtering

Abstract

In a nonlinear signal filtering system, a signal having a series of signal samples is filtered. The signal samples are affected by interactions with adjacent signal samples and nonlinear distortions. The system contains a series of alternating linear system elements and nonlinear system elements that are used for mitigation of distortion resulting from the nonlinear distortions with memory effects. The linear system elements can scale each signal sample in the series of signal samples by scaling parameters and sums a plurality of consecutive scaled signal samples, and the nonlinear system elements can transform the output of the linear system elements according to instantaneous nonlinear functions.

Description

RELATED APPLICATIONS[0001]The application is a continuation of U.S. patent application Ser. No. 15 / 906,958, filed Feb. 27, 2018 and entitled “Nonlinear Signal Filtering”, which claims benefit of U.S. Provisional Patent Application No. 62 / 466,513 filed on Mar. 3, 2017 and entitled “Look-Up-Table Based Modification of Transmission Signals”, and claims benefit of U.S. Provisional Patent Application No. 62 / 527,860 filed on Jun. 30, 2017 and entitled “Nonlinear Signal Filtering,” which are incorporated herein by reference in their entirety for all purposes.BACKGROUND[0002]Systems affect signals by inducing both linear and nonlinear distortions, including those due to memory effects. Memory in this context means that a system response at a time instant of interest (that was otherwise intended to be uncorrelated with other time instances) depends on, and is influenced by, signal values in surrounding time instants. Some examples of electrical systems containing signals that suffer from lin...

AI Technical Summary

Benefits of technology

The patent text describes a method of filtering a nonlinear signal by using two system elements: a first linear system element and a first nonlinear system element. The first linear system element scales each signal sample by a scaling coefficient and adds multiple consecutive scaled samples. The output of the first linear system element is then filtered using the first nonlinear system element, which transforms the output according to an instantaneous nonlinear function. This helps to correct for signal sample interactions and nonlinear distortions in the value of each signal sample. The technical effect of this method is that it provides a more accurate and reliable representation of the original signal.

Problems solved by technology

However, filters employing the Volterra series are complex to implement in practice.

The exponential nature of nonlinear filters employing the Volterra series can be expensive to implement, and impractical in high-speed systems, due to the large amount of operations that are necessary to be performed, which in practice correspond to large amounts of RAM, or taps, or excessive power consumption associated with the number of computations required.

Furthermore, filters employing the Volterra series rely on polynomial functions, and are not well equipped to mitigate distortions that, in practice, are not necessarily well approximated by continuous polynomials.

As a result, systems with nonlinear signal distortions resulting from ADC or DAC components in combination with components that introduce memory effects in the signal are not well mitigated by filters employing the Volterra series.

Nevertheless, even though memory polynomials are less complex than Volterra series, the price to pay for the omission of the cross-terms is a significant decline in performance, and they are equally limited to continuous polynomial forms.

The digital and analog components can achieve only limited accuracy, and nonlinear distortions with memory effects are commonplace.

As linear power amplifiers approach the end of their dynamic range, saturation can occur, which induces a departure from a linear behavior, or response, thus, if left unattended, leading to distortions, or otherwise departures from the intended signal shaping.

Additionally, high baud rate digital transmission systems tend to suffer from memory effects, which manifest as intersymbol interference (ISI).

This can result in loss, change, or other impairments to information even before transmission (e.g., directly at the output of the DP-MZM).

Unfortunately, the presence of nonlinearities within circuitry of electrical and optical transmitters can reduce the ability to correct impairments at the receiver.

Such attempted solutions often act on memoryless nonlinearity, and can thus be incapable of correcting impairments to the transmission signal that result from system memory effects.

However, these solutions are often unsatisfactory because, in addition to the frequency response (e.g., the linear response of the system), transmitters often possess a nonlinear nature of the response that is inherent in the amplitude cosine transfer function of the transmitter.

However, these solutions are unsatisfactory because they neglect the system memory of the nonlinear response of the optical transmitters.

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