An experimental study of signal-to-noise ratio losses due to OR-ing

An experimental study of signal-to-noise ratio losses due to OR-ing William A. Struzinski Code 3213, Naval Underwater Systems Center, New London, Connecticut 06320 Jerrold C. Bloom Code 3253, Naval Underwater Systems Center, New London, Connecticut 06320 {Received 1 June 1983; accepted for publication 16 August 1983) OR-ing experiments have been conducted on the Naval Underwater Systems Center Acoustic Display Research Facility. The objective of the experiments is to determine the signal-to-noise ratio loss when OR-ing N bins of data and to compare these results with some of the recently published theoretically derived losses. This paper discusses the details of the OR-ing experiment hardware and software, as well as the results obtained to date. PACS numbers: 43.60.Gk INTRODUCTION In previous theoretical studies, 1-12 mathematical mod- els were developed to characterize the performance of var- ious signal processing systems containing an OR-ing device, a device that picks the single channel with the most energy. However, experimental data are sparse. Therefore, a study was initiated to experimentally determine the signal-to-noise ratio {SNR} loss when OR-ing N channels of data. I. EXPERIMENTAL HARDWARE AND SOFTWARE The facility used for the subject experiments was the Naval Underwater Systems Center Acoustic Display Re- search Facility. This facility contains a Ramtek graphic dis- play system with cursor and hard copy printout capabilities. The display system is interfaced to a VAX 11/780 computer. The experimental software was designed to be flexible, so that different parameters could be varied at the inception of an experiment. The specifications for each experiment are as follows: 1. multi-display format; i.e., a spectral display With no OR-ing and a spectral display with OR-ing displayed simul- taneously, but viewed independently, 2. 944 frequency bins horizontally, 3. simulated data; spectrally white noise having a Gaus- sian amplitude probability density function in each bin, and signal plus noise bins having Gaussian amplitude probability density functions, and 4. random number of signals of various SNR's posi- tioned in frequency in a random fashion. In addition to the above specifications, various types of signals are of interest. The signals of interest are {1 }. static signal {frequency rate = 0} spanning one bin, {2}. static signal {frequency rate- 0} spanning two bins, and {3}. sinusoidal frequency modulation signal spanning one bin. The subsequent results will be devoted to the first type of signal; that is, a static signal spanning one bin. The subject work is based on a paper presented at the 105th Meeting of the Acoustical Society of America held in Cincinnati, Ohio, during 9 May-13 May 1983. Prior to display, the OR-ed and un-OR-ed data are quantized into eight levels {3 bits} with the quantizer step size being specified at the beginning of an experiment. In order to maintain a 50% marking density {percentage of data area that is written} for both the OR-ed and un-OR-ed cases, the quantizer step size is adjusted for the OR-ed case, based upon the theoretically computed mean and standard devi- ation of the noise-only distribution. The detection probability for each input SNR, PD, and the per bin false alarm probability, Pt, are computed in ac- cordance with Eqs. {1} and {2} PD -- Number of successful detections per SNR {1) Total number of chances per SNR Number of false alarms (944/N bins •( trials ){z operators) trial ]\ y operator = N {Number of false alarms) {2} 944yz bins where N is the number of bins OR-ed, and a detection is defined as an operator calling signal present given signal present. In summary, the following parameters are variables, and are entered at the beginning of each experiment: signal type, input SNR's to the OR-ing device, number of bins OR- ed, quantizer step size, number of statistically independent lines on the display, number of operators, and number of trials per operator. Figure 1 provides an example of a spectral display with no OR-ing, along with a spectral display for a four to one OR with 64 statistically independent lines on the display. For this example, the input SNR's of the signals are 0 and 1 dB. An examination of this figure clearly shows that OR-ing yields a performance loss. II. EXPERIMENTAL PROCEDURE The first phase of the experiments consisted of two runs: (1} two bins OR-ed and {2} four bins OR-ed. For each run, the signal of interest was a static signal spanning one bin. The quantizer step size was one-third the standard devi- 1418 J. Acoust. Soc. Am. 74 (5), November 1983 1418 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 137.189.170.231 On: Fri, 19 Dec 2014 17:36:44 :• -:" ,•': ' GAUSSIAN PDF '"• ..... ' • ......... • ................ '" •:" • ........... ' ........... ' "• ......... LINES 64 il ................ j ....................................................................................... 944 BINS ...................................... Tt FIG. 1. Spectral display for no OR-ing and for four bins OR-ed. 'i -•-•--236 BiNS--• 0.98 - 0.7 0.6 0.5 0.4 SNR -3.5 dB --4dB -4.5 dB -5 dB -6 dB -7 dB -8 dB FIG: 2. Experimental receiver operating characteristic curves for no OR-ing. 0.1 10-6 0.98 - 0.95 - 0.9- 0.8- 0.7- 0.6- 0.5- 0.4- 0.3- 0.2- 0.1- -2 dB --3 dB -4 dB i I i 10 '6 10 '5 10 '4 10 '3 FALSE ALARM PROBABILITY, PF FIG. 3. Experimental receiver operating characteristic curves for two bins OR-ed. • 1419 J. Acoust. Soc. Am., Vol. 74, No. 5, November 1983 W.A. Struzinski and J. C. Bloom: SNR losses due to OR-ing 1419 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 137.189.170.231 On: Fri, 19 Dec 2014 17:36:44 0.98- 0.95 - 0.9-- 0.8- 0.7- 0.6- 0.5- 0.4- 0.3- 0.2- 10-6 1.5 dB 1.0 dB -0.25 dB -0.5 dB 1•)'5 1•)'4 1•)-3 FALSE ALARM PROBABILITY, PF FIG. 4. Experimental receiver operating characteristic curves for four bins OR-ed. ation of the noise, and there were 64 statistically independent lines on the display. Both runs employed four operators. The experimental procedure was as follows: {1} Each operator viewed the spectral display for the OR-ed and un-OR-ed cases independently of one another. When viewing each display, the operator positioned the cur- sor on the information that he considered signal. The opera- tor then pressed the enter switch for each signal. All correct hits, misses, and false alarms were recorded in the computer. The operator was given a 5-min time limit for each display, and he received no information as to how many signals were present. {2} Each operator repeated step {1} above a second time. On the second trial, the input SNR's to the OR-ing device were the same, but the number of signals and their bin loca- tions were different. {3} After four operators completed steps {1) and (2}, the computer printed out the detection probability for each SNR and the per bin false alarm probability. This was done for both the OR-ed and un-OR-ed cases. {4} Steps {1}-(3} were repeated seven more times. The input SNR's to the OR-ing device were not necessarily the same in each case, and different operators were used. III. RESULTS Figures 2-4 depict the experimental receiver operating characteristic curves. These curves were generated by per- forming a least squares fit to the experimental data points. •3 We now desire to compare the experimental data with some of the recently published theoretically derived data. 6'9 Table I provides this comparison for a detection probability of 0.5 and for false alarm probabilities of 10 -4 and 10 -6. The experimental results for the input SNR to the OR-ing device were obtained from Figs. 2-4 using an interpolation. The experimental hardware did not have a square law device preceding the OR-ing device. Therefore, the experi- mental SNR loss relative to the detector input (SNR•oss } was obtained from Eq. {3}, SNR•os• = (SNR•v>• -- SNR•v=• )/2 (dB), (3) where SNR•v> • = required input SNR to. the OR-ing device for N bins OR-ed SNR•v= • =requtred input SNR to the OR-ing device for no OR-ing (N = 1 ). An examination of Table I reveals that there is less than TABLE I. Comparison between experimental and theoretical results for 64 statistically independent lines on the display. Input SNR(dB) to the OR-ing device PD PF N Exp. Theor. A SNRoR (dB) SNR,o,, (dB) A SNR,os, (dB) between relative to the between cxp. and detector input cxp. and theor. Exp. Theor. theor. 0.5 10 -4 1 -- 7.06 -- 6.59 0.5 10 -4 2 -- 3.13 -- 3.56 0.5 10 -4 4 --0.09 --0.73 0.5 10 -6 1 --4.00 --4.73 0.5 10 -6 2 -- 1.63 -- 1.80 0.5 10 -6 4 1.37 0.88 0.47 ......... 0.43 1.97 1.51 0.46 0.64 3.48 2.93 0.55 0.73 ......... 0.17 1.19 1.47 0.28 0.49 2.68 2.81 0.13 1420 J. Acoust. Soc. Am., Vol. 74, No. 5, November 1983 W. A. Struzinski and J. C. Bloom: SNR losses due to OR-ing 1420 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 137.189.170.231 On: Fri, 19 Dec 2014 17:36:44 a 0.75-dB difference in the input SNR to the OR-ing device and less than a 0.6-dB difference in the SNR loss between the experimental and the theoretical results. Therefore, there is relatively good agreement between the experimental and the theoretical results. IV. SUMMARY OR-ing experiments were conducted on the Naval Un- derwater Systems Center Acoustic Display Research Facili- ty. Experimental performance data were obtained for a static signal spanning one bin, and it was determined that there was good agreement between the experimental and the theo- retical results. Experimental performance data will be ob- tained for a sinusoidal frequency modulation signal span- ning one bin as well as for a static signal spanning two bins, and the results will be presented at a future date. •"Loss of S/N Ratio in Peak Detecting N Channels of Data," ASW Tech- nical Note, Hughes Aircraft Co., Fullerton, CA, 12 February 1968. 2j. j. Dow, B. M. Brown, and N. A. Reeder, "A Performance Comparison of Three Narrowband Data Reduction Techniques, "Traeor Report T70- AU-7382-C, Tracor Inc., Austin, TX (1970). 3A. H. Nuttall, "Signal-to-Noise Ratio Requirements for Greatest-of De- vice Followed by Integrator," NUSC Technical Memorandum No. TC- 13-75, Naval Underwater Systems Center, New London, CT (24 July 1975). 4A. H. Nuttall, "Input Deflection Requirements for Quantizers Followed by Greatest-of Device and Integrator," NUSC Technical Memorandum No. 781174, Naval Underwater Systems Center, New London, CT (24 August 1978) •W. A. Struzinski, "OR-ing Loss Data for Square Law Detectors Followed by an OR-ing Device and an Accumulator," J. Acoust. Soc. Am. 72, 191- •95 (•982). 6W. A. Struzinski, "OR-ing Loss for Quantizers Followed by an OR-ing Device and an Accumulator," IEEE Trans. Acoust. Speech, Signal Pro- cess. ASSP-30, 668-671 (1982). 7W. A. Struzinski, "OR-ing Loss Model for Implementation in Signal Pro- cessing Systems for Data Display," Proceedings ICASSP 83, 579-581 (1983). 8A. H. Nuttall, "Detection Performance Characteristics for a System with Quantizers, OR-ing, and Accumulator," J. Acoust. Soc. Am. 73, 1631- 1642(1983). 9W. A. Struzinski, "Optimizing the Performance of a Quantizer," J. Acoust. Soc. Am. 73, 1643-1647 (1983). løW. A. Struzinski, "Integration and Signal-to-Noise Ratio Requirements for a Signal Processing System Containing an OR-ing Device," IEEE Trans. Acoust. Speech, Signal Process, ASSP-31, 651-656 (1983). •W. A. Struzinski, "Performance Model for Square Law Detectors Fol- lowed by Accumulators and an OR-ing Device,"IEEE Trans. Acoust. Speech, Signal Process, ASSP-31, 759-761 (1983). •2W. A. Struzinski, "A Method for Treating Statistically Dependent Inputs to an OR-ing Device," J. Acoust. Soc. Am. 74, 143-145 (1983). •3The experimental data points and associated error bars have been omitted from the figures for purposes of figure clarity. 50% of the data points were within one standard error of estimate from the regression curves. 1421 J. Acoust. Soc. Am., Vol. 74, No. 5, November 1983 W.A. Struzinski and J. C. Bloom: SNR losses due to OR-ing 1421 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 137.189.170.231 On: Fri, 19 Dec 2014 17:36:44