APPLICATION NOTE One Technology Way P.O. Box 9106 Norwoo, MA 02062-9106, U.S.A. Tel: 781.329.4700 Fax: 781.461.3113 www.analog.com Microphone Array Beamforming by Jera Lewis INTRODUCTION All MEMS microphones have an omniirectional pickup response, which means that they respon equally to souns coming from any irection. Multiple microphones can be configure in an array to form a irectional response, or a beam pattern. A beamforming microphone array can be esigne to be more sensitive to soun coming from one or more specific irections than soun coming from other irections. Microphone beamforming is a rich, complex topic. This application note is only intene to cover the basic concepts an array configurations, incluing broasie summing arrays an ifferential enfire arrays. It covers esign consierations, spatial an frequency responses, an avantages/isavantages of ifferent array configurations. EXPLAINING DIRECTIONALITY AND POLAR PLOTS Directionality escribes the pattern in which the output level of the microphone or array changes when the soun source changes position in an anechoic space. All Analog Devices, Inc., MEMS microphones are omniirectional (or omni), which means that they are equally sensitive to soun coming from all irections, regarless of the orientation of the microphone. Figure 2 shows a 2-axis polar plot of an omniirectional microphone s response. This plot looks the same regarless of whether the microphone s port is oriente in the x-y, x-z, or y-z plane. 30 33 500Hz 1kHz 5kHz 2 In this application note, any reference to the front of the array as the on-axis irection is the irection of the esire auio pickup an is labele as in polar plots. The rear of the array is at 18 an the sies refer to the space in-between, centere on 9 an 27. All polar plots inclue in this application note are normalize to the response level. All equations involving the frequency an wavelength of soun use the relationship, c = f λ, where c is 343 m/sec, the spee of soun in air at 2C. Figure 1 shows the relationship between frequency an wavelength for soun waves uner these conitions. The Formula for Calculating Design Parameters section at the en of this application note lists equations for calculating the array esign parameters use here. WAVELENGTH (m) 100 10 1 0.1 0.01 20 100 1k 10k 20k FREQUENCY (Hz) Figure 1. Frequency vs. Wavelength for Soun Waves in Air 3 6 10478-002 27 9 24 12 21 15 18 Figure 2. Omniirectional Microphone Response Plot 10478-001 Rev. A Page 1 of 8
TABLE OF CONTENTS Introuction... 1 Explaining Directionality an Polar Plots... 1 Broasie Arrays... 3 Enfire Arrays... 4 Microphone Matching... 7 Application Note Effects of Array Processing on System Noise...7 Placement of Multiple Microphones...7 Avance Beamforming...7 Comparison...7 Formula for Calculating Design Parameters...8 REVISION HISTORY 5/12 Rev. 0 to Rev. A Changes to Figure 14... 6 1/12 Revision 0: Initial Version Rev. A Page 2 of 8
Application Note BROADSIDE ARRAYS A broasie microphone array is one in which a line of microphones is arrange perpenicular to the preferre irection of soun waves (see Figure 3). In this figure, is the spacing between the two elements of the array. The soun from the broasie of the array is what is usually esire to be picke up. AN-1140 Above the frequency at which perfect attenuation occurs, the frequencies will alias an the polar response starts to show nulls at other angles. At this point, the sie attenuation starts to ecrease again. For example, in Figure 4 the 3 khz signal (light blue line) is being aliase. 500Hz 1kHz 2kHz 3kHz 3 3 6 2 6 9 9 12 12 Figure 3. 2-Microphone Broasie Array Broasie arrays can be implemente with basic processing; the microphones in the array are simply summe together. The ownsie to this type of array is that it can only attenuate soun coming from the sie of the array. The rear-facing response always matches the front response since there is nothing ifferentiating pressure waves approaching the microphones from the front an the rear ue to the axisymmetry of the array. A broasie array is useful in applications where there is not much soun incient from behin or above an below the array, such as for a television mounte on a wall. In a 2-microphone broasie array, there are two minima in the response at 9 an 27. The signal attenuation at these points is very frequency-epenent. The response approaches perfect cancellation as the half-wavelength of the incient frequency approaches the spacing between the microphones. For an array with two microphones space 75 mm apart, theoretically there is a perfect null at approximately 2.3 khz (343 m/sec (0.075 m 2) 2.3 khz). 10478-003 15 18 Figure 4. Response of a 2-Microphone Broasie Array with 75 mm Spacing Frequency Response A broasie beamformer has a flat frequency response on-axis since it is simply summing the signals from two microphones receiving the same signal. Figure 5 shows the normalize response of a 2-microphone broasie beamformer with 75 mm spacing. Off-axis, this figure clearly shows the nulls in the response. MAGNITUDE (B) 10 5 0 5 10 15 20 25 30 45 9 15 10478-004 35 40 100 1k 10k FREQUENCY (Hz) Figure 5. Normalize Frequency Response of a Broasie Beamformer at Different Incient Angles 10478-005 Rev. A Page 3 of 8
Broasie Arrays with More Elements Broasie arrays with more than two elements can also be constructe by simply aing aitional microphones in line with the original two, as is shown in Figure 6. Higher numbers of microphones in broasie arrays can achieve greater attenuation of soun from the sies of the array. Figure 7 shows the response of a 3-microphone broasie array with 75 mm spacing between elements. In this array, the soun from the sies is attenuate by 6 B, whereas it was only attenuate by 3 B in the 2-microphone broasie array. However, aliasing (cloverleaf pattern) occurs at even lower frequencies now because the total istance between all elements has been increase from 75 mm to 150 mm. Application Note ENDFIRE ARRAYS An enfire array consists of multiple microphones arrange in line with the esire irection of soun propagation. When the front microphone in the array (the first that soun propagating on-axis reaches) is summe with an inverte an elaye signal from the rear microphone(s), this configuration is calle a ifferential array. Figure 8 shows a 2-microphone enfire ifferential array with istance () between the microphones an the rear microphone elaye by n samples before the subtraction (or, invert-an-sum) block. This can be use to create carioi, hypercarioi, or supercarioi pickup patterns, where the soun from the rear of the array is greatly attenuate. 500Hz 1kHz 2kHz 3kHz 9 6 12 Figure 6. 3-Microphone Broasie Array 3 2 3 10478-006 6 9 12 Figure 8. 2-Microphone Enfire Array When both the istance between microphones an the time elay are properly selecte, for frequencies less than the aliasing frequency the response of a elay-an-sum beamformer is a carioi, or heart-shape, pattern (see Figure 9). A carioi pattern has no signal attenuation to the front of the array an theoretically completely cancels the soun incient to the array at 18. The signals on the sies of a first-orer (2-microphone) elay-an-sum beamformer are attenuate by 6 B. 3 Z n 3 10478-008 15 18 Figure 7. Response of a 3-Microphone Broasie Array with 75 mm Spacing Between each Microphone Spacing microphones closer together in a broasie array raises the aliasing frequency, but reuces the attenuation at lower frequencies. This trae-off must be consiere when esigning a broasie array. Aliasing can be further reuce by applying ifferent weighting coefficients to iniviual microphones in a multi-microphone broasie array. The main response angle of roasie arrays can also be steere to something other than the front of the array with elays on the outputs of iniviual microphones. Calculation of these coefficients an elays an the resulting polar patterns is beyon the scope of this application note. 15 10478-007 6 9 12 2 6 9 12 15 15 18 Figure 9. Response of a 2-Microphone Enfire Carioi Beamformer 10478-009 Rev. A Page 4 of 8
Application Note The soun picke up by the ifferent microphones in the enfire array iffers only in the arrival time, assuming farfiel propagation that can be approximate by a plane wave. To create a carioi pickup pattern, the signal from the rear microphones shoul be elaye by the same time that it takes the soun waves to travel between the two microphone elements. This gives the system esigner two egrees of freeom in esigning an enfire beamformer: the istance between the microphones an the elay applie in the processor. In many auio applications, the choice of elay time is quantize by the sampling rate (f S ). If a DSP s elay is quantize by the perio of a single sample, then when f S = 48 khz that minimum elay is 21 μs. At 2C, the spee of soun in air is 343 m/sec, so a soun wave travels about 7 mm in 21 μs. Fractional sample elays can be implemente with ifferent filters such as elaye sync filters, allpass filters, an FFT filterbanks, but this sort of processing is more in-epth than what is covere here. As with the broasie array, the spacing between the microphones etermines the first null in the esire irection response. The closer the microphones are space to each other, the higher in frequency this null is (an therefore wier banwith). The further apart they are space, the longer the physical length of the array is, possibly conflicting with the inustrial esign limitations. Again assuming f S = 48 khz, a 3-sample elay results in an acoustical time elay of about 63 μs. This is the time it takes soun to travel about 21 mm, which is the spacing between microphone elements for a carioi pattern. The half-wavelength of an 8.2 khz soun wave is 21 mm, so this is the null frequency. Figure 10 shows the response of the same enfire configuration shown in Figure 9, but here the response at 10 khz is also shown. Along with the null in the rear, two aitional nulls at about ±52 are also present. 10KHz 1kHz 6 3 2 3 6 AN-1140 Matching the istance between microphones with the electrical elay is critical to goo performance of the beamforming array. Figure 11 shows the effect of varying the physical istance between microphones while keeping the elay constant. For this example, a 3-sample elay is again use, which correspons to a istance of about 21 mm to achieve a carioi response pattern (f S = 48 khz). When the istance between microphones is less than 21 mm, the rear null is much less pronounce an the response is in a subcarioi pattern. When the physical istance is greater than 21 mm, the resulting pattern is a hypercarioi, with two rear nulls space equally from the 18 point. This may be esirable in applications where the esire rejection is not exactly to the rear, but may be more sprea out, as the attenuation to the sies is also greater than that of a carioi response. 9 14mm 19mm 21mm 23mm 28mm 33mm 6 12 3 2 Figure 11. Effect of Varying Microphone Distance in an Enfire Beamformer Frequency Response The ifferential array beamformer oes not have a flat frequency response, but rather has a high-pass filter response characteristic up to the null frequency. The response of a firstorer beamformer (two microphone elements) rises with frequency at 6 B/octave an flattens above the aliasing frequency. At the null frequency, the array theoretically has no output because the elaye signal exactly matches the signal from the front microphone. 3 15 15 18 6 12 9 10478-011 9 9 12 12 15 15 18 Figure 10. Frequency Aliasing in a 2-Microphone Enfire Beamformer 10478-010 Rev. A Page 5 of 8
Application Note Figure 12 shows the frequency magnitue response of a 2-microphone ifferential array beamformer at ifferent incient angles. In this plot, the 0 B point is the output level of a single omniirectional microphone. This beamformer is set up with 21 mm spacing an a 3-sample elay, so the on-axis null appears at about 8.2 khz. On axis, the response is rising at 6 B/octave up to the point where the quarter-wavelength of the incient signal matches the length between the two microphones. After this point, the response ecreases to the null point an increases back to a maximum again at the ¾-wavelength point. Along with the on-axis null at the point where the spacing between array elements matches the halfwavelength of the incient signal, there are aitional nulls at successive multiples of that half-wavelength. MAGNITUDE (B) 10 5 0 5 10 15 20 25 30 35 45 9 135 18 40 100 1k 10k FREQUENCY (Hz) Figure 12. Frequency Response of an Enfire Beamformer at Different Incient Angles Notice that the response for a signal incient at 9 is 6 B below that of the signal at, an it has its maximum output level at the on-axis null frequency. An equalization (EQ) filter is typically applie to the output of a ifferential beamforming algorithm to flatten the response. The null frequency shoul be selecte so that it oes not interfere with frequencies of interest, but not so high that low frequencies are attenuate more than is esire. In an enfire ifferential array with a single sample elay (f S = 48 khz) an 7 mm microphone spacing, the null frequency is at about 24.5 khz an if the microphone spacing is 84 mm with a 6- sample elay, the aliasing frequency will be 4.2 khz. A esign typically requires the null frequency to be somewhere between these two examples, so that it is not so low that the null interferes with the banwith of human speech, or so high that the low-frequency response is highly attenuate. With these requirements in min, the istance between the two microphones is typically chosen to match a elay of between two to four samples. Again, this is all assuming f S = 48 khz. All of these calculations scale linearly with the sampling rate. 10478-012 Higher-Orer Enfire Arrays Higher-orer ifferential array beamformers can be forme by aing aitional microphones in line with the first two. This results in more rejection of souns from the rear an sie, but oes, of course, require a longer physical istance in which the beamformer nees to be built. Figure 13 shows an example of such secon-orer (3-microphone) enfire beamformer. A secon-orer enfire beamformer can achieve 12 B of attenuation to the sies with the same null to the rear of the array, as shown in Figure 14. Here, the blue line is the response of the first-orer (2-microphone) beamformer an the re line shows the response of the secon-orer beamformer. Figure 13. Secon-Orer Differential Beamforming Array 2-MICROPHONE ENDFIRE 3-MICROPHONE ENDFIRE 9 6 12 3 Z n 2 Figure 14. Comparison of First-Orer an Secon-Orer Enfire Beamformers This same line of thinking can be extene to even higherorer enfire beamformers, at the obvious expense of array size. Z n 15 15 18 3 Z n 6 12 10478-013 9 10478-014 Rev. A Page 6 of 8
Application Note MICROPHONE MATCHING Goo performance from a microphone beamformer requires that the sensitivity an frequency response of the ifferent elements of the array be closely matche. Differences in these two parameters between ifferent array elements result in a breakown of the array s esire response. Nulls may not be as sharp an the array s irectionality may not be properly oriente. The sensitivity an frequency response of Analog Devices MEMS microphones are closely matche, so they make an excellent choice for use in beamforming arrays. EFFECTS OF ARRAY PROCESSING ON SYSTEM NOISE The effects on the SNR epen on the array configuration an processing, an may result in an increase or a ecrease of the system SNR for ifferent array topologies. It is important to select microphones with the highest SNR specification to maximize the overall system performance. On axis, the broasie beamformer s output is analogous to simply summing two ientical signals to improve SNR. In a broasie summing array, the self noise from multiple microphones is ae together in power terms, resulting in a 3 B increase in noise per oubling of the number of microphones. In this case, the signal level oubles for a 6 B increase, while the noise sums incoherently for a 3 B increase in overall level. This results in a 3 B improvement of SNR. Off axis, this beamformer s signal output is not flat, as seen in Figure 5. At the off-axis incient angles, the SNR is reuce from the on-axis peak because of the reuce signal levels. The effect on SNR of a ifferential array is more complex an is not quantitatively evaluate here. The on-axis frequency response of a 2-microphone ifferential array beamformer is 6 B for frequencies with a wavelength twice the microphone spacing (about 4.1 khz in the example shown in Figure 12). Aroun this frequency, the ifference between the array s signal output an its noise is higher than each iniviual microphone s, but the signal/noise relationship across all frequencies is more ifficult to calculate. AN-1140 PLACEMENT OF MULTIPLE MICROPHONES The linear istance between the soun ports of microphones in an array is only one path that shoul be consiere when builing a microphone array. Even though the Analog Devices MEMS microphones are very thin evices, there is still some nonzero height that shoul be consiere in the array esign. The acoustic center at the iaphragm of an Analog Devices MEMS microphone is 0.57 mm above the soun port. Along with the thickness of the PCB on which the microphone is mounte, this istance shoul also be consiere when choosing the spacing between microphones. If all microphones are mounte in the same way (same PCB, same soun port length), then this is not a problem. ADVANCED BEAMFORMING This application note is intene to cover the basics of microphone beamforming an is in no way an exhaustive overview of this fiel of processing. Arrays with ifferent numbers of microphones an ifferent configurations are obviously possible, an the level of sophistication in the signal processing algorithms can be extene far beyon the simple algorithms escribe in this application note. More avance algorithms can be use for voice tracking an beam steering, even with small numbers of microphones. The arrays covere here are all linearly-space, but more avance higher-orer beamformers can be built with varying spacing between each pair of microphones in the array. This sort of configuration changes the null an aliasing frequencies an signal-to-noise ratio between the ifferent microphones an can potentially result in an array with less noise an a wier usable frequency response. COMPARISON Table 1 shows the relative avantages an isavantages of broasie an enfire beamformers. Table 1. Comparison of Broasie an Enfire Beamforming Arrays Array Configuration Avantage Disavantage Broasie Summing Enfire Differential Shallow array epth Processing is easy to implement (simple sum) Better off-axis attenuation Smaller overall size Lower off-axis attenuation Small spacing between microphones is neee to prevent aliasing Deeper array epth More processing complexity (signal elay require) Attenuate low frequency response Rev. A Page 7 of 8
FORMULA FOR CALCULATING DESIGN PARAMETERS Variables : istance in meters c: spee of soun in air, in m/sec (343 m/sec at 2C) t: time in secons n: number of samples of elay in DSP. t D : time elay in secons f S : sampling frequency in hertz f NULL : frequency of the null in hertz Distance Soun Travels in a Specifie Time = c t Application Note Microphone Spacing to Match an n-sample Delay = n c/f S Time Delay for an n-sample Delay t D = n/f S On-Axis Null Frequency in a Differential Array f NULL = ½ c/ 2012 Analog Devices, Inc. All rights reserve. Traemarks an registere traemarks are the property of their respective owners. AN10478-0-5/12(A) Rev. A Page 8 of 8