EP2755405A1 - Zonal sound distribution - Google Patents

Abstract

Prior art creation of zonal reproduction systems suffer from performance and computational difficulties. A novel approach based on a cost function to optimise the cancellation and the target energy over a range of incoming plane wave directions is introduced, producing a planar sound field without explicitly specifying the propagation direction. The method produces consistent high contrast and a consistently planar target sound zone across the frequency range 80-7,000Hz.

Description

• The invention relates to methods and systems for obtaining a distribution of sounds in a listening space that provides zones of sound programmes that do not interfere with each other. This is obtained by means of a number of loudspeakers that are individually controlled and a number of microphones that are used to determine the resultant sound field, at least in a calibration setup, but according to requirement either for intermittent re-calibration or continuously for use with a continuously changing listening environment.
• Although it is believed that the following abbreviations are well-known in the present technical field, they are listed here:
• DOA: direction-of-arrival
• PM: pressure matching
• ACC: acoustic contrast control
• AEDM: acoustic energy difference maximization
• In the present text we distinguish between loudspeaker units, which are the individual electroacoustic units and loudspeakers, which may each consist of several such units with corresponding sound conduits and other acoustic elements.
• Various approaches have been investigated for the personal audio scenario, including for PC users, aircraft passengers, and users of mobile devices.
Background of the invention.
• Traditional loudspeaker stereophonic systems provide a sound field that generates a reasonably satisfactory directional perception on the line (or rather a vertical plane that encompasses such lines) that is equidistant from the loudspeakers, but if one loudspeaker is approached, the contribution of the other loudspeaker may become imperceptible. This is a very primitive zonal distribution of the sound that is useless for sharp division of the sound of sound programmes: it displays cross-talk. It is only mentioned here as an example of two sound sources/loudspeakers in different locations cooperating for a specific effect. It is the purpose of the invention to provide a sharp demarcation of the zone in which one programme only may be heard with as little crosstalk as possible from the programme in the neighbouring zone.
• Establishing the raw distribution pattern from a loudspeaker is a standard procedure using one or more microphones and it may be performed real-time and for this reason it may also be performed in a feedback loop. In this way, a desired sound pressure at any given frequency may be obtained at a spot where a monitoring microphone is placed. Using this manner of procedure to build up a complete sound zone is in itself very computation-intensive (a brute-force approach) and has the disadvantage of requiring the presence of one or several monitoring microphones whenever it it desired to perform the procedure. In a straight feedback setup, these computations have to occur continuously. The problems are compounded when neighbouring zones are intended to be provided with unrelated programme content.
• Personal sound zones have been proposed in the mid-1990s. Since then, array signal processing for the creation of sound zones has emerged as a key sub-topic of sound field control. Fundamentally, at least two regions must be created by the loudspeaker array - the target zone, where the sound pressure reaches a certain target level, and the dark zone, a region of cancellation where the audio programme delivered to the target zone is attenuated. An independent audio system then can be created by superposition.
• Techniques for obtaining this result have broadly fallen into two categories. One technique, with its heritage in wavefield synthesis, is to precisely specify the sound field controlled by the array. In this manner, a target sound field can be specified and the dark zone created by specifying attenuated weights for that region. Such control has been analysed based on sound field coefficient translation in 2D (using line sources) and 2.5D (using point sources), and by an optimised pressure matching (PM) to directly minimise the error between a discretised desired sound field and that reproduced by the array. Typically, a plane-wave is specified as the desired field, although any sound field could be synthesised.
• Alternatively, the energy in the zones can be controlled, either via a beamforming approach, or using an energy cancellation based optimisation approach. An optimised beamformer for focusing the energy in a particular direction, and acoustic contrast control (ACC), an energy cancellation method creating an extended region of significant attenuation have both been attempted. An alternative cancellation method known as acoustic energy difference maximization (AEDM) was proposed in M. Shin, S. Q. Lee, F. M. Fazi, P. A. Nelson, D. Kim, S. Wang., K. H. Park, and J. Seo, "Maximization of acoustic energy difference between two spaces," J. Acoust. Soc. Am., vol. 128, pp. 121-131, 2010, with a modified cost function to avoid the matrix inversion and allow for precise control of the array control effort.
• Owing to the nature of the respective cost functions, distinctive performance characteristics have emerged. The energy cancellation methods can produce excellent acoustic contrast (cancellation) between the zones, offering great potential for sound zone reproduction, yet the phase in the target zone is uncontrolled. Consequently, multiple plane wave components impinge on the zone from various directions, which may create highly selfcancelling waves or other undesirable audio artefacts. The synthesis approaches are able to resolve this issue, but often at the cost of some contrast performance and with high array effort. Accordingly, recent advances in sound zone work have included hybrid methods, which attempt to recreate a plane wave in the target zone whilst using an energy cancellation approach for the dark zone. However, in each case the target sound field must be specified by the designer. Whilst in some cases this may be necessary for the desired reproduction (e.g. for spatial audio), the specified plane wave is by no means the only satisfactory propagation pattern that the array could achieve. In fact, the required properties of the target zone for acceptable spatial quality are, for a single frequency, that it is planar and that the sound pressure level is homogenous across the zone. For reproduction over multiple frequencies, there is an additional requirement that the incoming plane wave directions are suitably aligned across frequency. Plane wave reproduction has commonly been regarded as the best way to create a target zone with these properties in the context of the sound zone problem, and synthesis approaches have been adopted where this is a particular requirement. Other methods have considered the manipulation of intensity in a single zone (with no corresponding cancellation region).
• One important field of application is the presentation of a plane wave in at least one zone of neighbouring zones. A plane wave simulates a sound source removed many wavelengths from the receiver. It is possible to filter the inputs to the individual loudspeaker elements in such a way that a plane wave is generated at the location of the listener, however again in this case it is a requirement that a number of omni-directional microphones are used in a feed-back or delayed feed-back configuration. The planarity of the sound field is a physical measure to assess the extent to which a reproduced sound field resembles a plane wave.
• It has been determined that with modem signal processing it is possible to utilise the combined radiation patterns of a certain number of loudspeaker units to completely control the instant sound pressure present at any point in a listening space, horizontally and vertically. The signals that are processed are sound programme signals, and the processing may take into account live contributions from monitoring microphones. Furthermore, use may be made of the psychoacoustic properties of the ear, including any precedence and masking effects. The signal processing may be considered as time varying filtering of the signals fed to each loudspeaker unit.
• One example of a signal processing approach may be found in US Patent 8,213,637 , which essentially describes a brute-force approach based on determining the impulse response from each loudspeaker in an array at each measurement position, determining a target impulse response at each measurement position and determining filter parameters based on an optimising criterion including weighted sums of powers of errors between compensated estimated impulse responses and target impulse responses in each listening region. This is a very computation-intensive approach that does not optimise a plane wave pressure distribution as such.
• We propose a novel cost function for sound zone optimisation, where the incoming plane wave direction with respect to the target zone is constrained over a range of angles, rather than a single one. In this way, the requirements set out above are fulfilled but the optimisation is free to find the best plane wave direction.
• An advantageous manner of structuring the huge amount of raw data is to base an optimisation of the filtering on the theory of constrained optimisation coupled with a numerical search in a multidimensional matrix of source and microphone combinations and applying source weights. Constrained optimisation is known from US Patents 7,949,727 and 8,224,854 and has not previously been utilised for filtering source input in order to obtain driving signals for loudspeaker units. Prior knowledge is applied by the geometry of the loudspeaker unit and microphone placements as well as any reflective surfaces. The variables that cannot be pre-stored comprise the listeners in the listening space, which mainly constitute absorbing qualities as well as the spatial location of the actual listening ears (the targets). If the listeners are more or less constrained in their location (such as in fixed seats of a theatre, or in an automobile), the modelling is simplified.
• One important field of application is the presentation of a plane delimitation of at least one zone towards neighbouring zones. It is possible to filter the inputs to the individual loudspeaker elements in such a way that a sharp plane delimitation is generated, which means that a proper zone has been established. However again in this case it is a requirement that a number of omni-directional microphones are used in a feed-back or delayed feed-back configuration.
• According to one aspect of the invention, the problems of the brute-force approach may be avoided by a procedure that is particular in that the sound field from a given loudspeaker unit is mapped as a two-component function of time, a first component being considered as slowly-varying to stationary, and a second component being considered as incremental deviations from said first components, the vector sum of sets of two components from each loudspeaker unit being calculated to provide annihilation of the sound signal outside a pre-defined border in the listening space.
Environment of the invention.
• A sound zone system comprises an array of loudspeaker units and a number of microphones sampling the sound field in each zone. For a single frequency, the source weight vector is written as q = [q ₁ q ₂ q_L ] ^T , where there are L sources and q_l describes the lth loudspeaker's complex source strength. The vectors of pressures at the microphones in each zone can likewise be written. Here, we consider two zones, A and B; p _A = [p ₁ p ₂ p_M ] ^T and p _B = [p ₁ p ₂ ··· p_M ] ^T, where there are M microphones in zone A and N in zone B, p_m is the complex pressure at the mth microphone in zone A and and p_n is the complex pressure at the nth microphone in zone B
• The plant matrices each contain the transfer functions between every loudspeaker and the microphones in one zone. For zone A it is defined as $${\mathit{G}}_A=\left(\begin{array}{cccc}{g}_{11}& g_{12}& \cdots & g_{1L}\\ g_{21}& g_{22}& \cdots & g_{2L}\\ ⋮& ⋮& \ddots & ⋮\\ g_{M1}& g_{M2}& \cdots & g_{\mathit{ML}}\end{array}\right),$$

  

  where g_ml is the transfer function between the mth microphone in zone A and the lth loudspeaker. The equivalent notation is used for G _B . The pressure vectors for each zone are populated by the summation of the contribution of each loudspeaker at each microphone, written in vector notation as p _A = G _A q and p _B = G _B q for zones A and B, respectively.
• Three evaluation metrics are introduced for evaluation of the novel cost function. These measure the achieved zone separation, the extent to which the target zone sound field exhibits characteristics of a plane wave, and the physical cost of cancellation.
• Acoustic contrast is the spatially averaged summary measure for sound zone performance, and is commonly used in the cancellation literature to describe system performance. For zone A defined by M microphones, the spatially averaged squared pressure is $${\bar{p}}_A^2=\frac{1}{M}{\displaystyle \sum _{m=1}^M}{p}_{A_m}^2,$$

  

  
  and can be more suitably expressed in decibels as the sound pressure level relative to the threshold of hearing, p_ref = 2×10^-5 Pa: $${\bar{p}}_{{\mathit{SPL}}_A}=10{\log }_{10}\left(\frac{{\bar{\mathit{p}}}_{\mathit{A}}^{\mathit{2}}}{{\mathit{p}}_{\mathit{ref}}^{\mathit{2}}}\right)\mathrm{.}$$

  
• Likewise, the pressures p _B and p _SPLB can be obtained. The acoustic contrast between target zone A and dark zone B is defined as the ratio of spatially averaged pressures in each zone due to the reproduction of program A: $${\mathit{contrast}}_{\mathit{AB}}={\bar{p}}_{{\mathit{SPL}}_A}-{\bar{p}}_{{\mathit{SPL}}_B}\mathrm{.}$$

  
• The ACC cost function, where the ratio of the spatially averaged sound pressure levels between the bright zone and the dark zone is maximised, represents the energy cancellation case. Introducing the indirect Tikhonov regularisation proposed in S. J. Elliott, J. Cheer, J.-W. Choi, and Y. Kim, "Robustness and regularization of personal audio systems.," IEEE Trans. Audio Speech Lang. Proc., vol. 20, no. 7, pp. 2123-2133, 2012, the cost function is written as a constrained optimisation problem based on minimising the dark zone pressure and constrained by the bright zone pressure and control effort: $$J={\mathbf{p}}_d^H{\mathbf{p}}_d+{\lambda }_1\left({\mathbf{p}}_b^H+{\mathbf{p}}_b-B\right)+{\lambda }_2\left({\mathbf{q}}^H\mathbf{q}-E\right),$$

  

  
  where the subscripts _d and _b denote assignment of the pressure vectors with respect to the dark and bright (target) zones, respectively, B is the target sound pressure in the bright zone, and E is the maximum allowed control effort.
• Taking the derivative of J and setting to zero, we obtain: $$\frac{\partial J}{\partial \mathbf{q}}=2\left[{\mathbf{G}}_d^H{\mathbf{G}}_d\mathbf{q}+{\lambda }_1{\mathbf{G}}_b^H{\mathbf{G}}_b\mathbf{q}+{\lambda }_2\mathbf{q}\right]=0,$$

  

  
  which can be rearranged as an eigenvalue problem of the form λ₁ q = Aq : $${\lambda }_1\mathbf{q}=-{\left({\mathbf{G}}_b^H{\mathbf{G}}_b\right)}^{-1}\left({\mathbf{G}}_d^H{\mathbf{G}}_d+{\lambda }_2\mathbf{I}\right)\mathbf{q}$$

  
• The minimum can be found by taking the eigenvector corresponding to the minimum eigenvalue of ${\left({\mathbf{G}}_b^H{\mathbf{G}}_b\right)}^{-1}\left({\mathbf{G}}_d^H{\mathbf{G}}_d+{\lambda }_2\mathbf{I}\right),$

  

  which is equivalent to taking the eigenvector corresponding to the maximum eigenvalue of ${\left({\mathbf{G}}_d^H{\mathbf{G}}_d+{\lambda }_2\mathbf{I}\right)}^{-1}\left({\mathbf{G}}_b^H{\mathbf{G}}_b\right)\mathrm{.}$

  

  The regularisation term λ₂ therefore regularises both the control effort and the numerical conditioning of the inversion of ${\mathbf{G}}_d^H{\mathbf{G}}_d\mathrm{.}$

  

  . In order to ensure the latter over all frequencies, the regularisation parameter is split such that λ₂=λ _min +λ _eff , where λ_min is first set to ensure that the condition number of $\left({\mathbf{G}}_d^H{\mathbf{G}}_d+{\lambda }_2\mathbf{I}\right)$

  

  is suitably controlled to avoid numerical errors and λ _eff is subsequently adjusted to ensure that E does not exceed the specified value.
• The reproduction error, often used in the sound field synthesis literature to quantify the performance of sound field synthesis methods, may rate a highly planar sound field very poorly if the plane wave direction does not coincide with the specified sound field. For sound zone reproduction at a single frequency, the absolute angle of the incoming plane wave is not important and the planarity property has been designed to test each plane wave component impinging on the microphone array. The energy distribution at the microphone array over each incoming plane wave direction w = [w₁ ··· w _i ] is given by $w_i=\frac{1}{2}{\psi }_i^{*}{\psi }_i,$

  

  where ()* denotes the complex conjugate, ψ=[ψ ₁ ··· ψ_i ] are the plane wave components at the ith angle, related to the observed microphone pressures by the steering matrix H whose elements are determined by super-directive beamforming about the microphone array, $$\mathit{\psi }=\mathbf{Hp},$$

  
• The elements of H could alternatively be calculated using a spatial Fourier decomposition approach. The planarity metric can now be defined as the ratio between the energy due to the largest plane wave component and the total energy flux of plane wave components: $${\mathit{planarity}}_A=\frac{{\sum }_i{w}_i{\mathbf{u}}_i\mathrm{.}{\mathbf{u}}_{\hat{i}}}{{\sum }_i{w}_i}$$

  

  
  where u _i is the unit vector associated with the ith component's direction, u _î is the sum of all components in the î th direction î = argmax _i w _i , and denotes the inner product.
• The control effort is the energy that the loudspeaker array requires in order to achieve the reproduced sound field. It is defined as the total array energy (sum of squared source weights) relative to a single monopole q_ref producing the same pressure in the target zone, and expressed in decibels as $${\mathit{effort}}_A=10{\log }_{10}\left(\frac{{\mathbf{q}}^H\mathbf{q}}{q_{\mathit{ref}}^2}\right)$$

  
• It is a necessity in any practical system to achieve a suitably low control effort. On the one hand, it is physically related to, whether a set of source weights are realisable through real loudspeakers. Yet in addition, limiting the control effort results in there being less sound energy overall in the enclosure, leading to improved robustness to reflections in reverberant rooms, and limits the white noise gain of the system, improving robustness to other kinds of errors such as measurement noise.
• As a sound field synthesis method, any phase distribution can be specified for PM. A complex pressure is specified at each microphone; in this case, a plane wave is specified propagating through the target zone, and a pressure amplitude of zero is specified for the dark zone positions. The optimisation cost function is written to minimise the error e _b = G _b q - d _b between the desired sound field d and reproduced sound field, with a control effort constraint for Tikhonov regularisation: $$J={\mathbf{e}}^H\mathbf{e}+\lambda \left({\mathbf{q}}^H\mathbf{q}-E\right)\mathrm{.}$$

  
• The solution can then be found for the optimal q: $$\mathbf{q}={\left({\mathbf{G}}^H\mathbf{G}+\lambda \mathbf{I}\right)}^{-1}{\mathbf{G}}^H\mathbf{d},$$

  

  
  where G = [G _A G _B ] ^T is the complete system plant matrix and λ = λ_min + λ_eff is split as above.
• For a hybrid solution combining PM and ACC, the pressure matching portion of the cost function is restricted to the reproduction of the dark zone, whilst the contrast control formulation is used for cancellation. Here, for consistency with the other methods, we again introduce Tikhonov regularisation instead of using the pseudo-inverse: $$J=\alpha {\mathbf{p}}_d^H{\mathbf{p}}_d+\left(1-\alpha \right)+{\mathbf{e}}_b^H{\mathbf{e}}_b+\lambda \left({\mathbf{q}}^H\mathbf{q}-E\right),$$

  

  
  where the error e _b = G _b q-d _b is now between the desired sound field and the reproduced field in the target zone only. The weighting α provides a tuning parameter between the pure ACC solution and the pure target PM solution, with the standard pressure matching approach (Eq. (11)) being equivalent to α = 0.5 [21]. The solution can be determined by finding the gradient of Eq. (13) and rearranging for the source weights: $$\mathbf{q}={\left[\alpha {\mathbf{G}}_d^H{\mathbf{G}}_d+\left(1-\alpha \right){\mathbf{G}}_b^H{\mathbf{G}}_b+\lambda \mathbf{I}\right]}^1\left(1-\alpha \right){\mathbf{G}}_b^H{\mathbf{d}}_b,$$

  

  
  and as above, where implemented, λ = λ_min +λ _eff.
Detailed description of the invention.
• The proposed cost function optimises the acoustic planarity by modification of the ACC cost function stated in Eq. (5). The elements of H from Eq. (8) can be written in full, with respect to the microphones in the target zone, as $${\mathbf{H}}_b=\left(\begin{array}{cccc}{h}_{11}& h_{12}& & h_{1M}\\ h_{21}& h_{22}& & h_{2M}\\ & & & \\ h_{I1}& h_{I2}& & h_{\mathit{IM}}\end{array}\right),$$

  

  where h_im is the steering vector between the ith angle of direction-of-arrival (DOA) with respect to the mth microphone in the zone. Using the super-directive (ACC) beamforming approach, H _b can be determined for each steering angle by grouping the plane wave components c in each direction (based on the plane-wave Green's function, $g_{i,c}=e^{\mathit{jk}{\mathbf{r}}_c\mathrm{.}{\mathbf{u}}_i}/M$

  

  ) into a passband P and stopband S: $${\mathbf{P}}_i=\left\{g_{p,c}\right\}$$

  

  $${\mathbf{S}}_i=\left\{g_{s,c}\right\},$$

  

  
  where p denotes passband range centred upon the ith angle and d denotes the stopband range. We can then obtain $${\mathbf{h}}_i=\mathrm{arg\; max}{\left({\mathbf{S}}_i^H{\mathbf{S}}_i+{\beta }_h\mathbf{I}\right)}^{-1}{\mathbf{P}}_i^H{\mathbf{P}}_i,$$

  

  
  and each row of H _b is populated by the corresponding h _i .
• H _b represents a mapping between the complex pressures at the microphones and the reproduced plane wave DOA distribution, as previously introduced in Eq. (8). Therefore, it presents us with an opportunity to include it in the cost function for the sound zone optimisation, and achieve some control of the available incoming DOA for the target zone. In order to do this, a weighting must be applied based on the acceptable range of incoming plane wave directions. Such a weighting can be specified in terms of the desired normalised energy distribution over DOA by means of a diagonal matrix Γ comprising weights between zero and one: $$\mathbf{\Gamma }=\left(\begin{array}{cccc}{\gamma }_1& 0& & 0\\ 0& {\gamma }_2& & 0\\ & & & \\ 0& 0& & {\gamma }_I\end{array}\right),$$

  

  
  where γ _i is the weighting applied for the ith steering angle.
• The planarity optimisation cost function can now be introduced: $$J={\mathbf{p}}_d^H{\mathbf{p}}_d+{\lambda }_1\left({\mathbf{p}}_b^H{\mathbf{H}}_b^H\mathbf{\Gamma }{\mathbf{H}}_b{\mathbf{p}}_b-B\right)+{\lambda }_2\left({\mathbf{q}}^H\mathbf{q}-E\right),$$

  

  
  and deriving the solution in the identical manner to Eq. (5 - 7) above, the optimal source weights can be found to be the eigenvector corresponding to the maximum eigenvalue of ${\left({\mathbf{G}}_d^H{\mathbf{G}}_d+{\lambda }_2\mathbf{I}\right)}^{-1}\left({\mathbf{G}}_b^H{\mathbf{H}}_b^H\mathbf{\Gamma }{\mathbf{H}}_b{\mathbf{G}}_b\right)\mathrm{.}$

  
• The optimisation is thus constrained to maximise the sound energy in the target zone from among the potential incoming DOAs allowed by Γ . The selection of r is clearly a significant factor. If the vector is filled with ones, then the cost function in Eq. (19) is no different from the contrast control formulation in Eq. (5) and identical performance is achieved. If, on the other hand, the vector is populated with zeros apart from a single target DOA, a plane wave impinging from the specified direction should be reproduced. The solution is efficient for planar reproduction. As no weighting is applied to the cancellation term, dark zone optimisation is always prioritised. When the range of allowable DOAs is suitably designed, the system is free to maximise the energy under this constraint, which is best achieved by the generation of a planar sound field, and thus the planarity is optimised. Furthermore, if r is kept identical over frequency, the similarity between adjacent frequency bins can be controlled and the spatial quality of the target zone kept to an acceptable level.
Examples.
• The operation and performance of the planarity optimisation algorithm is demonstrated in the following, by means of simulations. The simulations were conducted in Matlab, simulating a free-field lossless anechoic environment, with each source modelled as an ideal monopole. The free-field Green's Function was used to populate the plant matrices, giving the transfer function at each microphone due to a loudspeaker at distance r: $$g=\frac{\mathit{j\rho ckq}}{4\pi r}{\mathit{e}}^{-\mathit{jkr}},$$

  

  
  where ρ = 1.21 kg/m³, c = 342 m/s, and k is the wavenumber ω/c.
• The test geometry comprised a circular array of radius 1.2m of 48 loudspeaker units and 156 omnidirectional microphones spaced at 2.1cm and arranged to sample 30cm diameter circular zones. The microphones used for calculating the sound zone filters (setup) and those for obtaining predictions (playback) were kept spatially distinct or mismatched in order to assess a slightly wider spatial region than the specific points sampled for setup (becoming more independent with increasing frequency). The target sound pressure level was set to 76dB SPL, (achieved by scaling of the prototype source weight vector q), which has been shown to be a comfortable listening level and has been used during listening tests based on the sound zone interference situation. This imposes an upper limit on the achievable contrast scores as we do not allow sound pressure levels below 0dB.
• To set the regularisation conditions, the minimum regularisation parameter component λ _min was set to enforce a maximum matrix condition number of 10¹⁰, and the effort regularisation parameter component λ_eff adjusted, where necessary, to enforce a maximum effort of 20dB, with reference to a single monopole on the radius of the circle (q_ref, Eq. (10)).
• The plane wave for the PM and ACC-PM hybrid (herein simply referred to as ACC-PM) approaches was specified to travel from north to south (DOA 180°), and the weighting matrix Γ was set to constrain the incoming plane wave components between 120° and 240°. The weighting on the diagonal of r is indicated in Fig. 4 (top). The weighting α for ACC-PM was set to 0.9 to encourage good contrast performance.
• The planarity control method was applied to the array and Figure 2 shows the method's performance over frequency, alongside those obtained for ACC, PM and ACC-PM under the same conditions.
• The contrast performance is very good and very consistent across the extended midrange band of 50-7,000Hz. The term responsible for cancellation in the proposed planarity control (Eq. (19)) is unchanged from that in the ACC cost function (Eq. (5)) and the dark zone creation is therefore similar in each case, resulting in perfect cancellation as for ACC, and outperforming PM and ACC-PM.
• Likewise, the control effort performance tends towards that of ACC, which gives preferable performance by a small margin across the whole range, outperforming the planarity control by up to 6dB at the lowest frequencies but generally being within 3dB. Nonetheless, the effort is below 0dB for much of the frequency range, and it is consistently preferable to PM and ACC-PM under the same conditions.
• Finally, there is a good planarity performance across frequency. Under this metric, the synthesis metrics PM and ACC-PM naturally produce optimal scores for significant portions of the frequency range. However, with the exception of the low frequency performance (due to poor resolution of the planarity steering matrix in this region) and a narrow notch at 3.6kHz, the planarity scores are similar to PM and ACC-PM, and greatly improved from ACC, as the DOA constraint has removed the selfcancellation artefacts from the reproduced sound field.
• Perhaps the most striking characteristic of the planarity control method is its robustness as a function of frequency. Where PM and ACC-PM suffer from well documented limitations to the upper frequency of accurate reproduction, depending on the loudspeaker spacing and array radius, the planarity control is able to operate well above this limit. In fact, the aliasing problems for PM and ACC-PM can be observed in relation to each of the evaluation metrics: from the contrast the effect of aliasing lobes passing through the dark zone can be observed, and the corresponding control effort response noted. The planarity response is interesting at high frequencies for PM and ACC-PM, because a planar target field is still reproduced. Even under this metric, however, these methods falter around the aliasing frequency.
• The optimal contrast and planarity performance obtained using planarity control can be further clarified by studying the sound pressure level and phase maps shown in Fig. 3. We can now confirm that the planarity control produces an ACC-like dark zone, yet replaces the northsouth self-cancellation in the target zone with a planar field, and reduces the overall sound pressure in the enclosure as a consequence of the low effort score with relation to PM and ACC-PM.
• The properties of the sound field reproduced by the planarity control method are very relevant to potential users. For the cost function to be successfully realised, the plane wave directions would have to be constrained to a perceptually acceptable range of azimuths, and for spatial effects to be discerned, a single plane wave component reproduced. First, we consider the energy distribution over azimuth (with respect to the target zone) obtained for the window function used for the simulations mentioned above. We have seen from the planarity scores (Fig. 2, bottom) and the phase distributions in the enclosure (Fig. 3, bottom parts) that the planarity control method is capable of creating highly planar fields in the target zone, for single frequencies. However, these plots do not give us an indication of the range of incoming plane wave directions as a function of frequency. Therefore, in Fig. 4 the normalised energy distributions for multiple frequencies have been plotted across azimuth for planarity control, ACC and ACC-PM, at 100Hz spacing. This gives us a useful insight in to the planarity control's performance in relation to the existing methods. The target zone synthesis adopted in ACC-PM can be seen to successfully place the plane wave propagation to the specified direction, with a wider lobe at low frequency due to the poor beamformer resolution, and the higher frequency aliasing effects noticeable as side lobes. Conversely, ACC produces plane wave energy from a wide range of azimuths as well as self-cancellation patterns. It is likely that such a field would not create a very pleasurable listening experience. The distribution over frequency for planarity control can be noted to conform, for the most part, to the target window.
• To test the ability of the planarity control to reproduce a specific incoming plane wave direction, the window was set to allow a single azimuth (with a raised-cosine weighting to smooth the transition), and the direction varied. Three significant results are plotted in Fig. 5, at 1kHz, for specified directions of 90°, 146° (the optimal case for this frequency) and 180°. In the middle plot (180°), the planarity control method can be seen to accurately place the plane wave to arrive from the required direction (corresponding to north-south in Fig. 3), and for the optimal case this is achieved with additional side lobe suppression, although the width of the energy lobe for PM is slightly narrower. Yet for directions perpendicular to this (west-east propagation shown), which would require a beam to be placed across the dark zone, a highly self-cancelling pattern is instead reproduced and the peak in this direction is unsatisfactory. There is no variation in the contrast between these cases and the effort difference is minimal, yet if PM had been applied, the cancellation would have been poor and the effort very high, albeit with the specified plane wave component reproduced. An interesting property of the planarity control cost function is therefore exposed: that producing high contrast is the priority of the optimisation, and that where specification of the incident direction does not conflict with contrast performance, the energy can be placed precisely in the desired direction.
• The behaviour over frequency for a constrained window (146° ± 20° with a raised cosine weighting) is clarified by Fig. 6. At low frequencies, the compounding of poor beamformer resolution for both setup and evaluation results in very wide lobes, at mid frequencies up to the spatial aliasing limit (approximately 2kHz) the placement is satisfactory, and at high frequencies the behaviour is rather similar to that of ACC-PM, where side lobes emerge. Even so, the main energy components remain close to the specified window and good contrast and planarity are still achieved.
Conclusions.
• A method for optimising the planarity in the target zone, as well as producing significant cancellation between zones, has been demonstrated. The method has been shown to be comparable to the well-established acoustic control method in terms of contrast and control effort, and superior for creating a planar field in the target zone. It also outperforms the pressure matching approach and a state of the art hybrid between pressure matching and acoustic contrast control, particularly in terms of its ability to produce a good cancellation region above the spatial aliasing region, and a planar field around this limit. The resolution of the beamformer limits planarity performance at low frequencies below 300Hz. Definition of the weighting matrix r is very important for good performance. The ability of r to constrain incident plane wave directions over frequency has been demonstrated, and furthermore under the condition that it does not require propagation across the dark zone, a precise plane wave direction can be specified. The method therefore presents a compelling new alternative for sound zone system designers concerned about the spatial quality of an energy cancellation approach, giving flexibility to constrain the sound energy to impinge from a range of directions and the potential to reproduce a wave from a single direction.
Detailed description of figures.
• Fig. 1: Geometry of the sound zone system, where zone A is the target zone and zone B is the dark zone. The outer (dashed) circle represents the loudspeaker unit array, and the inner circle the reproduction radius with respect to the aliasing limit of the synthesis methods. The directions of plane wave incidence with respect to zone A are indicated.
• Fig. 2: Performance of planarity control (PC) with respect to ACC, PM and ACC-PM (α = 0:9), under the metrics of contrast (top), effort (middle) and planarity (bottom)
• Fig. 3: Sound pressure level (top row) and phase (bottom row) maps for PC, ACC and ACC-PM (α = 0:9). The target (left) and dark zones are indicated by the white circles. For the sound pressure level maps, white indicates a high sound pressure and black a low sound pressure
• Fig. 4: Energy distributions over azimuth for PC (top), ACC (middle) and ACC-PM (bottom), plotted at 100Hz intervals from 100-7,000Hz. The bold dot-dash line in the uppermost plot indicates the specified window along the diagonal of Γ, and the directions 90° and 180° correspond to incoming plane wave directions of west-east and north-south, respectively, in relation to Fig. 3.
• Fig. 5: Target vs. achieved energy distribution over azimuth at 1kHz, using planarity control to specify the DOA, for 90° (west-east) (top), 180° (north-south) (middle) and 146° (optimal) (bottom). Maximum contrast is achieved in each case. Energy reproduced by PM is included for reference (dot-dash line)
• Fig. 6: Target vs. achieved energy distributions over azimuth with lines plotted over frequency, for low (top), mid (middle) and high (bottom) frequency bands, using planarity control to constrain the DOA to a window around the optimal angle of 146°. Maximum contrast is achieved in each case.

Claims (3)

1. A method for zonal sound distribution optimisation for providing zones of sound programmes that do not interfere with each other by providing an essentially planar configuration of neighbouring sound fields, comprising a number of loudspeaker units that are capable of being individually controlled and a number of microphones for use in determining the resultant sound field, characterised in that the signals provided individually to the loudspeaker units are obtained by optimisation by means of constrained optimisation coupled with a numerical search in a multidimensional matrix of source and microphone combinations and the application of source weights and in that source signals are filtered by means of filtering functions operating on a basis of a pre-determined multidimensional matrix under the optimisation obtained by a cost function.
2. A method according to claim 1, characterised in that the signals to be provided individually to the loudspeaker units are obtained by means of a feedback from the microphones arranged in a pre-determined array at least in a calibration setup, with provisions for intermittent re-calibration or continuously for use with a continuously changing listening environment.
3. A method according to claim 1 or 2, characterised in that the sound field from a given loudspeaker unit is mapped as a two-component function of time, a first component being considered as slowly-varying to stationary, and a second component being considered as incremental deviations from said first components, the vector sum of sets of two components from each loudspeaker unit being calculated to provide annihilation of the sound signal outside a pre-defined border in the listening space.

Images