Adaptive noise cancelling is a signal processing technique for suppressing interference corrupting a received signal where the interference is known and is accessible but unavoidable and where the target signal and the interference are unrelated.Kaunitz, J. (August 1972), "Adaptive Filtering of Broadband Signals as Applied to Noise Cancelling," Stanford Electronics Laboratories Rep. SU-SEL-3-038, Stanford University, Stanford, California, (Ph.D. dissertation) OCLC 15201972Widrow, B., Glover, J., R. McCool, J. M., Kaunitz, J., Williams, C. S., Hearn, R. H., Zeidler, J. R., Dong E. JR, and Goodlin, R. C. (December 1975) "Adaptive Noise Cancelling: Principles and Applications," Proc. IEEE, Vol. 63, DOI: 10.1109/PROC.1975.10036Widrow, B. and Stearns S. D. (1985) "Adaptive Signal Processing," Pearson Education, Inc. , 0130040290 OCLC 11159524 Examples of such situations include: a microphone attempting to receive speech near machinery or other noise sources in the environment, such as an aircraft cockpit a naval ship towing a sonar array where the ship's own noise masks a much weaker detected target signal obtaining a fetal electrocardiogram (ECG) where the presence of the mother's stronger ECG represents an unavoidable interference.
Conventional signal processing techniques pass the received signal, consisting of the target signal and the corrupting interference, through a filter that is designed to minimise the effect of the interference. The objective of optimal filtering is to maximise the signal-to-noise ratio at the receiver output or, as is the case with a Wiener filter, to produce the optimal estimate of the target signal in the presence of interference.
In contrast, adaptive noise cancelling relies on a second sensor, usually located near the source of the known interference, to obtain a relatively pure version of the interference, free from the target signal. This pure version of the interference and the sensor receiving it are called the reference.Kaunitz, J. and Widrow, B. (October 1973). "Noise Subtracting Filter Study," Stanford California: Stanford Electronics Laboratories., Ft. Belvoir Defense Technical Information Centre
The adaptive noise canceller consists of a self-adjusting adaptive filterKaunitz, J. (April 1971) "General Purpose Hybrid Adaptive Signal Processor," Stanford Electronics Laboratories, Stanford, California, SU-SEL-71-023, TR No. 6793-2 which automatically transforms the reference signal into an optimal estimate of the interference corrupting the target signal. This is then subtracted from the received signal, thereby cancelling (or minimising) the effect of the interference at the noise canceller output. The adaptive filter adjusts itself continuously and automatically to minimise the residual interference affecting the target signal at its output. The power of the adaptive noise cancelling concept is that it requires no detailed a priori knowledge of the target signal or the interference. The adaptive algorithm that optimises the filter relies only on ongoing sampling of the reference input and the noise canceller output.
Configuration and concept
The adaptive noise canceller configuration diagram on this section shows the target signal present at the primary sensor and the interference or noise source and its manifestations and at the primary and reference sensors respectively.
As and are the manifestations of the same interference source in different locations, these will usually differ significantly in an unpredictable fashion due to different transmission paths through the environment to the two sensors. So the reference cannot be used directly to cancel or reduce the interference corrupting the target signal . It must first be appropriately processed before it can be used to minimise, by subtraction, the overall effect of the interference at the noise canceller output.
An adaptive noise canceller is based on a self-optimising adaptive filter that has a variable transfer function shaped by adjustable parameters called . Using an iterative adaptive algorithm, the adaptive filter transforms the reference into an optimal estimate of the interference corrupting the target signal and the latter by subtraction, whilst leaving the target signal unchanged. So the output of the adaptive noise canceller shown above is:
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The power of the adaptive noise-cancelling approach stems from the fact that the algorithm driving the iterative adjustment of weights in an adaptive filter is a simple, fully automatic iterative process that relies only on an ongoing stream of measurements of the noise canceller output and the reference r(t) = nr(t). For example, the least-mean-squares (LMS) algorithm in the context of the usual tapped-delay-line digital adaptive filter (see below) leads to:
where the vector represents the set of filter weights at the iteration and the vector represents the last set of samples of the reference, which are the weight inputs. The adaptation constant determines the rate of adaptation and the stability of the optimal configuration.
Apart from the availability of a suitable reference signal, the only other essential requirement is that the target signal and the corrupting noise source are unrelated, that is uncorrelated, so that and for all values of , where the overbar represents time averaging.
Adaptive noise cancelling does not require detailed a priori knowledge of the interference or the target signal. However, the physical characteristics of the adaptive filter must be generally suitable for producing an adjustable frequency response or transfer function that will transform the reference signal nr(t) into a close estimate of the corrupting interference, ñp(t), through the iterative adjustment of the filter weights.
The adaptive noise cancelling approach, terminology and the proof of the concept, the first demonstrations that general broadband interference in a target signal can be reduced in practical situations using adaptive noise cancelling, were set out during 1971–72 at the Adaptive Systems Laboratory of the Stanford School of Electrical Engineering by Professor Bernard Widrow and John Kaunitz and documented in the latter's Ph.D. dissertation Adaptive Filtering of Broadband Signals as Applied to Noise Cancelling and related technical reports.
However, a subsequent 1975 paper published in the Proceedings of the IEEE by Widrow et al., Adaptive Noise Cancelling: Principles and Applications, is now the generally referenced introductory publication in the field. This paper sets out the basic concepts of adaptive noise cancelling and summarises subsequent early work and applications. Earlier unpublished efforts to eliminate interference using a second input are also mentioned. This paper remains the main reference for the adaptive noise cancelling concept and to date has been cited by over 3000 scientific papers and over 400 patents. The topic is also covered by a number of more recent books.
Genesis Adaptive noise cancelling evolved from the pioneering work on adaptive systems, adaptive filtering and signal processing carried out at the Adaptive Systems Laboratories in the School of Electrical Engineering at Stanford University during the 1960s and 70's under the leadership of Professor Bernard Widrow.
Adaptive filters incorporate adjustable parameters called weights, controlled by iterative adaptive algorithms, to produce a desired transfer function. Adaptive filters were originally conceived to produce the optimal filters prescribed by optimal filter theory during a training phase by adjusting the filter weights according to an iterative adaptive algorithm such as the LMS algorithm. During the training phase, the filter is presented with a known input and a training signal called a desired response.
The filter weights are adjusted by the adaptive algorithm, which is designed to minimise the mean-squared-error ξ, the difference between the adaptive filter output and the desired response:
where W represents the set of weights in vector notation and X(t) the set of weight inputs so y(t) = X(t)TW.
The above expression shows ξ to be a quadratic function of the weight vector W, a multi-dimensional paraboloid with a single minimum that can be reached from any point by descending along the gradient. Gradient descent algorithms, such as the original Least Means Squared algorithm, iteratively adjust the filter weights in small steps opposite the gradient. In the case of the usual digital tapped delay line filter, the vector Xk is simply the last set of samples of the filter input x(t) and the LMS algorithm results in:
Wk+1 = Wk - μekXk
where k represents the kth step in the iteration process, μ is the adaptation constant that controls the rate and stability of the adaptation process and ek and Xk are samples of the error and the input vector, respectively
At the completion of the training phase, the adaptive filter has been optimised to produce the desired optimal transfer function. In its normal operating phase such an optimised adaptive filter is then used passively to process received signals to improve the signal-to-noise ratio at the filter output under the assumed conditions. The theory and analysis of adaptive filters is largely based on this concept, model and terminology, and took place before the introduction of the adaptive noise cancelling concept around 1970.
Adaptive noise cancelling is an innovation that represents a fundamentally different configuration and application of adaptive filtering in those common situations where a reference signal is available by:
using the training mode of the filter as the operational mode, thus continually adjusting the filter during normal operation using the reference as the adaptive filter input using the primary input, the noise canceller input, containing the target signal and interference, as the desired response for the adaptation process using the noise canceller output, that is, the difference between the primary input and the output of the adaptive filter, as the error for adaptation.
Whilst the discussion of adaptive noise cancelling reflects the above terminology, it is clear from the above diagrams that the two are equivalent and the previously developed extensive adaptive filter theory therefore continues to apply in both situations.
In the adaptive noise cancelling situation, the received signal does not pass through the adaptive filter but instead becomes the 'desired response' for adaptation purposes. Since the adaptation process will aim to minimise the error, it follows that, in the noise canceller configuration, the adaptation process in effect aims to minimise the overall signal power at the noise canceller output - the error. So the adaptive filtering of the reference actually strives to suppress the overall signal power at the noise canceller output.
This counterintuitive concept can be understood by keeping in mind that the target signal s(t) and the interference n(t) are uncorrelated. So, in aiming to minimise the error, using a reference as input, which is related only to the interference, the best the adaptive filter can do, in generating an optimal estimate of the primary input, the desired response, is to generate the optimal estimate of the interference at the primary sensor ñp(t). This will result in minimising the overall effect of the interference at the noise canceller output whilst leaving the target signal s(t) unchanged.
The iterative adaptive algorithms used in adaptive filtering require only an ongoing sequence of sampling measurements at the weight inputs and the error. As digital adaptive filters are in effect tapped-delay-line filters, the operation of an adaptive noise canceller requires only on an ongoing sequence of sampling measurements of the reference and the noise canceller output.