Automatic Noise Floor Spectrum Estimation in the Presence

Michael J. Ready, Michael L. Downey, and Leo J. Corbalis
Applied Signal Technology

This paper describes a technique for automatically estimating the noise floor spectrum in the presence of signals. The technique works equally well for both flat and non-flat noise floor spectrums. The technique is based on applying morphological binary image processing operators to a binary image of the received power spectrum. It is related to rank-order filters but is more computationally efficient. The performance is illustrated on the detection of radio signals.

This paper introduces an automated algorithm for estimating the noise floor spectrum in the presence of signals. It works equally well for both flat and non-flat noise floor spectra. The method is based on treating the power spectrum as a binary image and applying binary morphological image processing operators to determine the noise floor spectrum. Mathematical morphology is an algebraic system of nonlinear operators that has been used to decompose complex 2-D shapes into different parts [2].

Estimating the noise floor spectrum with image processing techniques is motivated by the fact that the humans are good at estimating the noise floor spectrum by “eyeballing” a spectral plot. Intuitively, we separate the spectral humps from the noise floor spectrum by eliminating those parts of the spectrum shape that are due to signals and visually draw in the noise floor spectrum.

Accurate noise floor spectrum estimation is important in a number of signal detection problems as well as system noise floor characterization. Figure 1 shows an example. A radio receiving stations is thousands of feet from the antenna. In this case, the RF signals must be amplified many times before it “hits” the signal detector.

In many cases, the noise floor spectrum is set by active components in the receiving system, usually a low-noise amplifier (LNA) right behind the sensor. Ideally, the noise floor spectrum would be flat so that signal detection threshold can be “straight-lined” across the spectrum. In practical systems, however, the noise floor spectrum may not be flat. The non-flat response is caused by impedance mismatches and non-flat response of passive and active components in the receiving system (e.g., slope roll-off of sensors, cables and waveguides and non-flat amplitude and group delay response of amplifiers and mixers).

Figure 1. Example of equipment configuration that could lead to a nonflat noise floor spectrum.

Figure 2 shows an example of a received signal spectrum. In this instances, the noise floor spectrum is not flat. In fact, the noise floor changes as much as 7 dB over 80 MHz making “straight line” threshold detection useless, especially since some signals have low SNR.

Figure 2. Received signal spectrum showing nonflat noise floor.

Detecting the emergence of signals of unknown bandwidth and carrier frequency in a frequency band of interest much wider than the signal of interest is a common problem in many fields [1]. A common signal detection technique is based on measuring the power spectrum over the bandwidth of interest and comparing the received signal power spectrum with the noise power spectrum plus a threshold. The threshold level provides a tradeoff between the probability of correct detection, false alarm and missed detection. The performance of this approach generally requires an accurate estimate of the receiving system noise floor spectrum. One way of establishing the noise floor spectrum is to measure it when the signals are not present. This generally requires taking the receiving system off-line and perfoming lengthy and tedious calibration procedures.

There are many reasons that motivate automatic noise floor spectrum estimation when signals are present and the system is on-line including:

This paper is divided into three sections. Overview of Morphological Image Processing reviews the relevant morphological binary image operators. Applying Morphological Image Processing to Estimating the Noise Floor Spectrum describes the application of the morphological operators to automatic estimation of the noise floor. Performance Example illustrates the noise floor spectrum estimator performance via a signal detection problem.

Morphological image processing decomposes complex image shapes into different parts. The proposed noise floor spectrum estimation techniques described in this paper use morphological techniques applied to a 2 dimensional (2-D) bit image of the power spectrum. Before describing the noise floor spectrum estimator, the morphological processing operators are reviewed.

Morphological image processing is based primarily on set theory. The techniques used for noise floor spectrum estimation are based on two morphological binary operators: “binary erosion and dilation”. Erosion

is the intersection of sets and dilation

is the union of sets. Figure 3 illustrates how these two operators work. The image A consist of pixels that are either “on” (shown as shaded element) or “off.” The kernel K can consist of any binary shape. The one most useful for purposes here is a rectangular shape consisting of N pixels, where N=2 in the example below.

Figure 3. Example of morphological binary image processing.

To erode the signal, the kernel K is moved over the image A much like a 2-D convolution. An eroded image pixel is “on” whenever the image pixels aligning with the kernel pixels are all “on”, otherwise it is “off”. The images at the upper right shows the result of eroding A by K. The image is eroded in the sense that there are fewer pixels “on” than in the original image.

To dilate the image, whenever the origin pixel in the kernel K aligns with an image pixel that is “on”, the output image pixels corresponding to the kernel are turned “on”. The images at the lower right shows the result of dilating A by K. The image is dilated in the sense that there are more pixels “on” than in the original image.

Image shapes can be isolated by first eroding then dilating the image as shown in Figure 4. This operation is called “opening” (O) an image. Its easy to see that opening an image with the kernelK simply isolates that part of the image that has the same shape as K.

Figure 4. Result of first eroding then dilating (called opening) an image.

The opening operation forms the basis of the noise floor spectrum estimation technique as illustrated in Figure 7. The kernel

is defined as a 1 x N horizontal rectangle N pixels wide. The image A is a binary image of a simplified power spectrum where the pixels below the spectral values (Y-axis) at each frequency (X-axis) are “on” (black) while the pixels above are “off” (white). The image is successively opened (that is, eroded then dilated) with kernels

. Focusing on the opening with

shows that the kernel eliminates signal peaks that are one pixel wide. Subsequent passes with larger kernels eliminate peaks that are N-1 pixels wide. Notice that the successive opening operations eliminate signals that have bandwidth less than N-1 pixels. A natural question is how wide should the kernel be in order to produce the noise floor spectrum.

Figure 5 shows an algorithm for determining when the “opening” process has converged. An iterative process is used because the bandwidth of the signals of interest are unknown. After each opening, the total power of the resulting power spectrum is computed and compared to the power of the previously opened spectrum. If the power of the two is (approximately) equal, then the noise floor spectrum estimate is assumed to have converged. Otherwise, the process continues.

Figure 5. Algorithm for determining when the spectrum estimate has converged.

The image-based noise floor estimation technique described here is similar to rank-order filtering that has been commonly used by industry. The rank-order filter R(N,m) is shown in Figure 6. The input signal spectrum is taken N frequency bins at a time and sorted in decreasing order. The filter output is the

value in the sort. A well-known rank-order filter is the median filter which takes the middle value, R(N,N/2).

Figure 6. Block diagram of rank-order filter R(N,m).

Rank-order filters can be related to the erosion and dilation operators as follows:

This can be seen by performing the rank-order filtering operation on the spectrum-like signal in Figure 7.

Figure 7. Results of successive openings with larger kernels used on a spectrum-like image.

One key implementation tradeoff between morphological binary image processing and rank-order filtering is computations and memory. The morphological operations require only 1-bit processing while rank-order filtering requires fixed or floating point sorting operations on a vector containing the spectrum values. On the other hand, morphological images may require more memory than a fixed or floating point spectrum vector depending on the image size and resolution.

The noise floor spectrum estimator performance is illustrated on a live example for signal detection from a radio receiving site. Figure 8 shows a block diagram of the signal detection problem that includes the morphological image processing-based noise floor spectrum estimator.

Figure 8. Block diagram of the signal detection problem with the morphological image processing-based noise floor spectrum estimator.

The signal receiving system is separated from the sensor (an antenna in this case) by about 1 mile of transmission line with 26 distributed amplifiers to overcome the signal loss. Figure 9 shows the signal spectrum at the output of the spectrum estimation block. The band of interest is about 100x – 100,000x wider than the signals of interest. Only a portion of the band of interest is shown. The noise floor spectrum is not flat across the band of interest because of the combined frequency response of the amplifiers and transmission line.

Figure 9. Signal spectrum of input to signal detection block with the noise floor spectrum estimate shown (based on the techniques described in this paper).

The spectrum plot shows that the noise floor spectrum rolls about 7 dB over the range shown. The estimated noise floor spectrum matches the spectral estimate that would be produced by “eyeballing” a spectral plot very well. In addition, the signals have only 5–10 dB SNR. Straight line thresholding on this signal would cause severe misdetections.

Figure 10 shows the signal spectrum after the estimated noise floor is subtracted from the received spectrum. Ideally, the noise floor should be flat and zero. In other words, when the spectrum plot is viewed, it should appear that the noise floor spectrum is flat, and it is. Thus, after subtracting out the noise floor, the signal can be easily detected by comparing the received spectrum to a straight-lined threshold. The performance of the signal detection algorithm is dependent on the statistics of the noise and signal and not covered in this paper.

Figure 10. Signal spectrum after the estimated noise floor is subtracted.

The noise floor spectrum estimation technique described in this paper has been applied to many different radio detection experiments. Results indicate greater than 99% correct detection with signals as low as 4 dB with a very low false detection rate.

Image morphological processing can be used for estimating a system’s noise floor spectrum in the presence of signals. Morphological processing separates the signals from the noise floor spectrum much the way the “eye” does with spectral plots by separating shapes. It has been used successfully for a number of real scenarios resulting in high probability of detection (>99% for live applications), even for signals with SNR’s as low as 3–4 dB. It is related to rank-order filters but is likely more computationally efficient. Moreover, morphological binary image processing mimics visual intuition.