ADAPTIVE NOISE CANCELLING IN HEADSETS
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1 ADAPTIVE NOISE CANCELLING IN HEADSETS Per Rubak, Henrik D. Green and Lars G. Johansen Aalborg University, Institute for Electronic Systems Fredrik Bajers Vej 7 B2, DK-9220 Aalborg Ø, Denmark {pr, hdgr92, lgj }@kom.auc.dk 1 INTRODUCTION Noise reduction systems in headsets represent a succesful application of active noise cancellation. Up to now the major part of practical implementation is based on analog feedback principles. Bose and Sennheiser, among others, have developed active noise cancelling headsets (for use in cockpits and consumer headsets). In Japan Sony has developed a headset which is offered to business-class airline passengers. The analog feedback systems are able to provide about 15 db noise reduction up to about 500 Hz. The noise reduction will gradually go down to 0 db at about 1 khz. Therefore the conventional "analog solutions" have severe limitations. During the last years several research groups have been working on application of adaptive filtering within the field of active noise cancellation. 2 SYSTEM DESCRIPTION The noise signal at the entrance of the ear canal is estimated by filtering a reference noise signal. The reference signal x k, measured by a microphone mounted outside the ear cup, is transmitted through a FIR filter. The adaptive filter represents a parametric model of the transfer function of the ear cup. Adaptation of the filter coefficients is based on minimizing the mean square error-signal (from a microphone mounted inside the ear cup. A small loudspeaker is used to deliver the acoustic cancellation-signal. This signal is delivered in reverse phase compared to the unwanted noise signal we have to cancel. In figure 1 a model of the ANC-system is shown. G(z) represents the transfer function from the external sound field to the sound pressure inside the cup. Especially head movements should be considered. The convergence time of the adaptive algorithm is therefore of utmost importance
2 Figure 1: Adaptive Noise Cancelling system scenario H(z) is the transfer functions of the microphones (the two microphones are assumed to be identical). J(z) represents the transfer function for the loudspeaker (including the acoustical load impedance). This transfer function will normally contain a highpass function caused by an acoustical leak between the cup and head. This is important in relation to the lowfrequency performance of the ANC-system. I(z) represents an equalizing filter placed before the adaptive filter. This filter is intended to equalize the transfer function J(z). 3 ADAPTIVE FILTERING The aim of digital adaptive filtering is to adjust the required modification filter after each new sample arrival. The usual method is to employ FIR adaptive algorithms. Thus, the filter is always stable, and adjusting the filter coefficients is directly related to impulse response alterations. The algorithms considered in this paper are the Least Mean Square (LMS) and the Normalized Least Mean Square (NLMS). In both algorithms the coefficient update is based on the squared system error, i.e. the instant power of the difference between corrected signal and desired signal, see figure The headphone phase characteristic The headphone transfer function J(z) yields the corrected acoustical output. Unfortunately, J(z) is not a minimum phase function, i.e. it cannot be subject to inversion. The necessary invertibility is ensured by decomposing the transfer funtion J(z) into a minimum phase part J mp(z) and an excess phase part J ep(z) for which no reciprocal counterpart can be obtained. The microphone transfer function H(z) is invertible because it does not suffer from excess phase
3 3.2 The LMS algorithm The most simple adaptive FIR-filter, the LMS algorithm, is based on a filter coefficient update equation in which the difference between coefficients at time k and time k+1 is given by the negative gradient to the function that is to be minimized. This function, 2 denoted the performance function, is equal to the expected squared error E{e [k]}. The constant µ determines the rate of convergence, i.e. the time to reach the optimum Wiener solution that corresponds to the minimum of the performance function. Simplifying the expression above leads to the noisy gradient estimate LMS algorithm, where instead of + the instant error e[k] and the input sample vector x[k] are used: k When w is an L'th order filter, the applicable interval of µ is given by: 2 % x being the average power of the reference signal. If µ exceeds the upper limit, the convergence of the algorithm is no longer ensured. 3.3 The NLMS algorithm The theory behind this filter is not different from that of the LMS filter. Only now the step-size parameter µ is normalized to µ n, i.e. the power of x[k] is incorporated in the algorithm which takes the form: The instant power estimate of x[k] employs an exponential window defined by the forgetting factor 1 and is given by: - 3 -
4 The major advantages of the NLMS to the LMS algorithm is the fact that normalized stepsize enables comparison between simulations with different input signals and ensures that the maximum allowable actual stepsize never exceeds the upper limit. The price, however, is a slight increase in computational complexity. 4 SIMULATIONS AND RESULTS The performance of two algorithms, LMS and NLMS, was investigated for bandlimited (60Hz-3kHz) white and colored noise. A measured impulse response of the headphone was used in the simulations. It is our experience that reliable results are not obtained by using simplified models for the sound transmission and loudspeaker-ear transfer function. The ability of the two algorithms to cancel out noise was investigated using both floating point and fixed point simulations. Various approaches show that for the NLMS algorithm, optimum performance is reached by choosing the exponential window forgetting factor to For both algorithms convergence time lies in the interval 0.5 sec. to 5 sec. depending upon the length of the filter and the step-size parameter. Thus, simulations are performed using these quantities as parameters. A representative part of the Noise Reduction Ratio (NRR) results is listed beneath in the table. NNR is defined as: L = 1000 samples is used in these equations. Note that NRR is calculated after the filter adaptation is finished (stationary condition). signal LMS algorithm results NRR NLMS algorithm results NRR WHITE NOISE PINK NOISE L = 150, µ = db L = 130, µ = db L = 200, µ = db L = 190, µ = db L = 140, µ = db L = 150, µ = db L = 220, µ = db L = 220, µ = db Table 1: Noise Reduction Ratios from simulation - 4 -
5 The highlighted numbers are the maximum achievable "average" Noise Reduction Ratio. Fixed point simulations show that 19 bit variable representation is necessary to maintain the results found in floating point. 5 IMPLEMENTATION 5.1 Control Data Flow Graph of the algorithm To get a general view of how the algorithms are implemented, several Control Data Flow Graphs, abbreviated CDFG, of the LMS algorithm was constructed, as illustrated in figure 2. In the first box the constants and the variables are initialised. The loop starts with the new sample read from the converter. The new error estimate, ê, is calculated by means of the wiener weights, w, and the result is written to the converter. The new error sample is read and band pass filtered. In the last box, the wiener weights, w, are updated by means of the sampled error, e. More detailed CDFGs of the algorithm were constructed but are considered too extensive for this presentation. No Control Flow Begin LMS Initialize of variables x(k) = Read(M2) Calculate LMS Begin read and filter the error signal e(d) Update w k = k + 1 Yes k = L k = 0 Initialize of variables x(k) = Read(M2) Calculate LMS Update w Read k 1 Read k Data Flow Begin read and filter the error signal e(d) + Write k = '0' Write k Read L Figure 2: CDFG of the algorithm 5.2 The hardware architecture The ANC system requires four input channels and two output channels. I.e. to prevent noise in one ear cup, two input channels are necessary. So is the reference signal, x, the error signal, e, and one out channel for the estimated and inverted noise signal ê. The hardware system for right and left channels are identical as can be seen from figure
6 Figure 3: Block diagram of the ANC hardware architecture, where the signal processing can be performed by one or two DSPs depending on the number of input channels on the device. If the DSP system has four input channels it is only necessary to have one DSP. However, if the processor has the computational capacity to calculate both left and right channels it is possible to multiplex the input channels. Then it is not necessary to have four input channels, but two would be enough. The sampling frequency is 8 khz and with a processor latitude of 33 mips, there are 4125 instructions to calculate one sample. For testing purposes the ADSP-2181 easy kit lite, abbreviated EKL, from analog devices with two input channels and two output channels is chosen. I.e. two EKL boards are needed to complete the ANC-system. The final target hardware architecture however will be a dedicated ASIC (application specific integrated circuit). 5.3 Memory map of the ANC system Figure 4 illustrates the memory maps for the program memory and the data memory of the ANC program. The filter coefficients in the program memory and the variables in the data memory are implemented as ring buffers, this reduces the need for extra control instructions as shown in the CDFG in figure 3. The memory map of the ANC NLMS system is identical to figure 4, although there must be five more variables. As shown in figure 4, only a fraction of the memory is in use and naturally in an ASIC solution the need for memory is limited to less than 1kb. 5.4 The assembler program The assembler program is based on the CDFG in figure 3 and operates on the memory map illustrated in figure 4. Little effort has been put into optimising the assembler code because it is not necessary due to its simplicity. The program starts on interrupt from the A/D-converter, when input data are ready. Then data are read into the internal registers and internal data memory
7 Figure 4: Memory map of the ANC system 6 CONCLUSIONS It is possible to attenuate white noise by 19 db and colored noise by 17 db using the LMS and NLMS algorithm. These results were obtained with floating point simulation. Fixed point simulations have shown that these two algoritms gave satisfactory results using 19 bits. The optimum filter length is about taps (sampling frequency 8 khz).the step-size parameter should be selected very carefully. There is a trade-off between fast convergence (require large step size) and small stationary error (small step size). The NLMS algorithm was selected for real-time implementation. For the LMS algorithm the step size is dependent on the actual variance of the noise signal (not acceptable for practical applications). Convergence times in the range from 0.5 sec. to 5 sec. were calculated (depending on step size). For practical applications we believe that convergence times about 1-2 sec. are acceptable. Acknowledgement: The simulation material is widely based on the M.Sc. thesis by Flemming Pihl, [7]; his contribution is gratefully acknowledged
8 7 REFERENCES 1. Carme, C.E Method and apparatus for attenuating external origin noise reaching the eardrum, and for improving intelligibility of electro-acoustic communications. United States Patent No. 4,833, Gauger, D., et.al The Bose Headset System: Background, Description and Applications. Bose Corporation, Massachusetts. 3. Goodfellow, E.A. A Prototype Active Noise Reduction In-Ear Hearing Protector. Applied Acoustics, Vol. 42, Haykin, S Adaptive Filter Theory. Prentice-Hall Maxwell, D.W, et.al Performance characteristics of active hearing protection devices. Sound and Vibration, May Nelson, P.A (Second printing). Active Control of Sound. ACADEMIC PRESS Pihl, F Akustisk støjundertrykkelse i headset-baseret på digital signalbehandling (in Danish). M.Sc. Thesis, Aalborg University, June
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