hybrid digital–analog transmission for wireless acoustic sensor networks

7
Hybrid DigitalAnalog transmission for wireless acoustic sensor networks Matthias Rüngeler n , Peter Vary Institute of Communication Systems and Data Processing (IND), RWTH Aachen University, Aachen, Germany article info Article history: Received 24 January 2014 Received in revised form 24 May 2014 Accepted 8 July 2014 Keywords: Hybrid DigitalAnalog (HDA) Purely digital transmission Saturation due to quantization noise Maximum Ratio Combining (MRC) abstract A crucial task of a Wireless Acoustic Sensor Network (WASN) is the transmission of the acoustic signal to a central fusion node. Due to different microphone locations, the microphones may experience different or even varying radio channel qualities. Usually, the design of the digital transmission scheme is governed by the worst-case radio channel. For given radio resources, the end-to-end audio quality is specified by the compromise between the fidelity of the audio encoder and the required error protection capabilities of the channel encoder. The quantization noise of the audio encoder limits the end-to-end SNR even for increasing radio channel qualities. In the fusion node, the decoded signals are combined (fusion algorithm) and the overall output audio quality is limited due to the quantization noise even for error free transmission. In this paper it is shown that this unfavorable behavior can be avoided by using a Hybrid Digital-Analog (HDA) transmission concept. The key feature of HDA is that the audio output quality improves with increasing channel qualities. For typical fusion algorithms the HDA system supersedes purely digital transmission for all radio channel qualities. & 2014 Elsevier B.V. All rights reserved. 1. Introduction One key task of a Wireless Acoustic Sensor Network (WASN) is the wireless transmission of an audio signal from several microphones to a fusion node for further processing. The microphones may be positioned at differ- ent distances to the fusion node and therefore experience different individual radio channel qualities. Cost and com- plexity constraints and the possible lack of a feedback channel to each of the microphones impede the adaptation of each transmission link to its individual radio channel quality. Therefore, each transmitter is usually designed for the worst case radio channel to ensure reliable transmis- sion without adaptation. Each of these transmission links can be regarded as a point-to-point communication for which well known techniques may be employed, separate source and channel coding and an intermediate binary representation of the source signal lead to asymptotically optimal solutions [1]. For a given, fixed radio channel quality, or for systems which can adapt to the instantaneous radio channel quality, this approach is widely used in practice. For a fixed, non-adaptive transmission system, which operates at a channel quality above the design channel quality, all bits are transmitted without error and the end-to-end SNR of the audio signal is limited by the unavoidable quantiza- tion noise introduced in the source encoder. A further improvement of the radio channel quality does not further improve the end-to-end SNR. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/sigpro Signal Processing http://dx.doi.org/10.1016/j.sigpro.2014.07.005 0165-1684/& 2014 Elsevier B.V. All rights reserved. n Correspondence to: Institute of Communication Systems and Data Processing (IND), RWTH Aachen University, Muffeter Weg 3a, 52074 Aachen, Germany. E-mail addresses: [email protected] (M. Rüngeler), [email protected] (P. Vary). URL: http://www.ind.rwth-aachen.de (P. Vary). Signal Processing ] (]]]]) ]]]]]] Please cite this article as: M. Rüngeler, P. Vary, Hybrid DigitalAnalog transmission for wireless acoustic sensor networks, Signal Processing (2014), http://dx.doi.org/10.1016/j.sigpro.2014.07.005i

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Page 1: Hybrid Digital–Analog transmission for wireless acoustic sensor networks

Contents lists available at ScienceDirect

Signal Processing

Signal Processing ] (]]]]) ]]]–]]]

http://d0165-16

n CorrProcessAachen

E-mvary@in

URL

PleasSign

journal homepage: www.elsevier.com/locate/sigpro

Hybrid Digital–Analog transmission for wirelessacoustic sensor networks

Matthias Rüngeler n, Peter VaryInstitute of Communication Systems and Data Processing (IND), RWTH Aachen University, Aachen, Germany

a r t i c l e i n f o

Article history:Received 24 January 2014Received in revised form24 May 2014Accepted 8 July 2014

Keywords:Hybrid Digital–Analog (HDA)Purely digital transmissionSaturation due to quantization noiseMaximum Ratio Combining (MRC)

x.doi.org/10.1016/j.sigpro.2014.07.00584/& 2014 Elsevier B.V. All rights reserved.

espondence to: Institute of Communicatioing (IND), RWTH Aachen University, Muff, Germany.ail addresses: [email protected] (P. Vary).: http://www.ind.rwth-aachen.de (P. Vary).

e cite this article as: M. Rüngeler, P.al Processing (2014), http://dx.doi.o

a b s t r a c t

A crucial task of a Wireless Acoustic Sensor Network (WASN) is the transmission of theacoustic signal to a central fusion node. Due to different microphone locations, themicrophones may experience different or even varying radio channel qualities. Usually,the design of the digital transmission scheme is governed by the worst-case radio channel.For given radio resources, the end-to-end audio quality is specified by the compromisebetween the fidelity of the audio encoder and the required error protection capabilitiesof the channel encoder. The quantization noise of the audio encoder limits the end-to-endSNR even for increasing radio channel qualities. In the fusion node, the decoded signalsare combined (fusion algorithm) and the overall output audio quality is limited due to thequantization noise even for error free transmission. In this paper it is shown that thisunfavorable behavior can be avoided by using a Hybrid Digital-Analog (HDA) transmissionconcept. The key feature of HDA is that the audio output quality improves with increasingchannel qualities. For typical fusion algorithms the HDA system supersedes purely digitaltransmission for all radio channel qualities.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

One key task of a Wireless Acoustic Sensor Network(WASN) is the wireless transmission of an audio signalfrom several microphones to a fusion node for furtherprocessing. The microphones may be positioned at differ-ent distances to the fusion node and therefore experiencedifferent individual radio channel qualities. Cost and com-plexity constraints and the possible lack of a feedbackchannel to each of the microphones impede the adaptationof each transmission link to its individual radio channel

n Systems and Dataeter Weg 3a, 52074

(M. Rüngeler),

Vary, Hybrid Digital–Arg/10.1016/j.sigpro.201

quality. Therefore, each transmitter is usually designed forthe worst case radio channel to ensure reliable transmis-sion without adaptation.

Each of these transmission links can be regarded asa point-to-point communication for which well knowntechniques may be employed, separate source and channelcoding and an intermediate binary representation of thesource signal lead to asymptotically optimal solutions [1].For a given, fixed radio channel quality, or for systemswhich can adapt to the instantaneous radio channelquality, this approach is widely used in practice. For afixed, non-adaptive transmission system, which operatesat a channel quality above the design channel quality, allbits are transmitted without error and the end-to-end SNRof the audio signal is limited by the unavoidable quantiza-tion noise introduced in the source encoder. A furtherimprovement of the radio channel quality does not furtherimprove the end-to-end SNR.

nalog transmission for wireless acoustic sensor networks,4.07.005i

Page 2: Hybrid Digital–Analog transmission for wireless acoustic sensor networks

Fusion node

cSNR1

cSNR2cSNRi

cSNRL

u1

u2 ui

uLu1

u2 ui uLs

sa

sbna nb

Mic 1

Mic 2 Mic i

Mic L

Fig. 1. Target sound sources (sa; sb;…) and undesired noise sources(na;nb;…) form an acoustic scene. Several microphones capture audiosignals ui and transmit them to a fusion node where the signals arereceived as u i . Each transmission link 1r irL experiences a differentradio channel quality cSNRi and the output of the fusion node is s .

M. Rüngeler, P. Vary / Signal Processing ] (]]]]) ]]]–]]]2

Hybrid Digital–Analog transmission systems tackle thischallenge for point-to-point communication. In [2] it isshown that an additional transmission of the quanti-zation error using continuous-amplitude means leads toan improvement of the end-to-end SNR with increasingchannel quality. In [3,4] the design of HDA systems usingwell known digital channel codes is elaborated and it isshown how for every purely digital transmission system asuperior HDA system can be designed, while the numberof channel uses, i.e., the transmission bandwidth on thechannel, and the transmission power is kept constant.Especially for WASN with many microphones and fixedtransmission systems which have to cope with differentradio channel qualities, HDA transmission systems are ofspecial interest. For each microphone the same fixed HDAsystem design can be used while the end-to-end SNR isimproving with increasing radio channel quality.

At the fusion node, an audio signal processing algo-rithm (fusion algorithm) combines the received micro-phone signals to recover an improved audio signal or theposition of the audio source. In any case, the quality of theoutput of the fusion algorithm is dependent on the SNRof the received signals. Depending on the type of fusionalgorithm, different dependencies may occur, in somecases the worst signal may dictate the output quality, inother cases the best signal.

Using purely digital transmission systems, the inputquality is bounded by the quantization noise and hence,the output quality of the processing in the fusion node islimited by the errors introduced at the beginning of thetransmission chain. Using Hybrid Digital–Analog transmis-sion, some microphone signals are received with a betterSNR, depending on their radio channel quality which maylead to an improved quality of the output signal of thefusion node.

In Section 2 the system model with an arbitrary fusionalgorithm is considered whose output quality may dependin different ways from the input SNR of the receivedmicrophone signals. In Section 3 the design of the HDAsystem is revised and its performance for one example isdepicted. Section 4 gives simulation results comparingpurely digital and HDA transmission systems for differentdependencies of the output quality on the input qualitiesfor a WASN. Section 5 concludes this paper.

2. System model

2.1. Fusion node and noisy transmission

In the acoustic scene shown in Fig. 1, there may beseveral target sound sources (sa; sb;…) and undesirednoise sources (na;nb;…). For each of the L microphones,there is an individual acoustic transfer function Ti with1r irL which models the acoustic influence of the sceneon the signals before being captured as one of the micro-phone signals ui:

ui ¼ Tiðsa; sb;…;na;nb;…Þ ð1ÞThe microphone signal ui is a vector formed by samples ofthe waveform captured by microphone i. Each microphonesignal is transmitted over the radio link using the same

Please cite this article as: M. Rüngeler, P. Vary, Hybrid Digital–ASignal Processing (2014), http://dx.doi.org/10.1016/j.sigpro.201

type of transmission system. At the fusion node, for eachmicrophone the audio signal u i is received.

The distortion which is introduced by the transmissiondepends on the transmission system (e.g., purely digital orHybrid Digital–Analog) and the channel quality (cSNRi)which may be different on each individual radio link.

The fusion algorithm Fð�Þ combines the received signals(ui) and obtains an estimate s of the desired target signal s:

s ¼ Fðu1; u2;…; uLÞ¼ ~sþeþd¼ sþd ð2Þ

The fusion algorithm may perform beamforming, derever-beration, noise reduction, source separation, etc. The target(clean) signal of the fusion algorithm is ~s while the influenceof the undesired noise sources (na;…) is modeled by theerror e. The scope of this paper is the analysis of thedistortion d in the output signal of the fusion node whichis introduced by the transmission. The actual performance ofthe particular fusion algorithm or the influence of capturednoise is not considered here, thus, the signals ~s and e arecombined to s. This way, the output of the fusion node ismodeled by s and a term d which is dependent on thetransmission system and the radio channel quality.

2.2. Generic purely digital transmission

A generic purely digital transmission system is depictedin Fig. 2. A continuous-amplitude source vector ui frommicrophone i forming one frame with M symbols whichcould be the captured discrete-time, continuous-amplitudesamples or parameters of an audio or speech codec. Thereare several A/D and D/A converters depicted which use sucha high resolution that the influence of the conversion willbe neglected in the following. The digital encoder, whichincludes the source and channel coding as well as the

nalog transmission for wireless acoustic sensor networks,4.07.005i

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M. Rüngeler, P. Vary / Signal Processing ] (]]]]) ]]]–]]] 3

modulator, produces an N dimensional channel vector yD;i. Incontrast to the A/D convertors in Fig. 2, the distortionintroduced by the quantizer in the digital source encoderis taken into account in the following. An Additive WhiteGaussian Noise (AWGN) channel adds a Gaussian noisevector with the variance σ2

n;i per dimension which leads tothe following radio channel SNR cSNRi for microphone i:

cSNRi ¼Ef‖yD;i‖2g

σ2n;i

: ð3Þ

The digital decoder decodes the received vector zD;i forthe current frame to the estimate uD;i of the initially capturedsymbols.

The end-to-end parameter SNR for each radio linktransmission is described by

pSNRi ¼Ef‖ui‖2gMSEi

¼ Ef‖ui‖2gEf‖ui� uD;i‖2g

ð4Þ

where MSE is the mean square error between the sourcesymbols and the decoded symbols.

2.3. Generic Hybrid Digital–Analog transmission

Fig. 3 shows the Hybrid Digital–Analog transmissionsystem. Here an HDA encoder transforms the source vectorui into two output vectors. The first vector ydH;i is generatedusing the same methods as in a purely digital system. Thisvector is transmitted in the Digital branch. The secondvector yaH;i contains a continuous-amplitude refinement totransmit the source vector with a higher fidelity than ydH;ipermits. This vector contains analog symbols which aregenerated using digital signal processing and subsequentD/A conversion. These symbols are transmitted as analogsamples in the pseudo analog branch with a certaincomputational precision (e.g., 16 bit fixed point or evenfloating point), therefore the word “pseudo” which isomitted in the following. In the digital branch, the channelsymbols are formed of discrete sets as generated bymodulations such as BPSK or QPSK. In the pseudo analogbranch, the channel symbols may take all values which theD/A convertor is able to generate.

The dimensions of the channel vectors in the digital (D)and the analog (A) branch add up to N¼DþA, hence the

Fig. 2. Purely digital transmission system with a

Fig. 3. Hybrid Digital–Analog (HDA) transmission system

Please cite this article as: M. Rüngeler, P. Vary, Hybrid Digital–ASignal Processing (2014), http://dx.doi.org/10.1016/j.sigpro.201

HDA system relies on the same number of channel uses(same bandwidth) as the purely digital system. The vectorsare transmitted via an AWGN channel and the HDAdecoder estimates the purely digital source representationudH;i and the pseudo analog refinement ua

H;i. Adding upthese two vectors yields the overall estimate uH;i of theinitially captured symbols. Again, all depicted A/D and D/Aconvertors introduce only negligible distortions, yet theeffects of the quantizer in the digital part of the HDAencoder are not negligible. The cSNRi and the pSNRi of theHDA system are defined as in the purely digital case.

2.4. Combining the microphone signals in fusion node

A set of possibly different radio channel qualities cSNRi

(1r irL) for the microphone transmission links is called“scenario” in the following. For further assessment, notonly one scenario is considered. The scenarios are modeledusing a statistical description of the channel qualitieswhile the quality of the radio links is time invariant ineach scenario.

At the fusion node all microphone signals are receivedwith an individual pSNRi which depends on the channelquality cSNRi of the corresponding radio link i and the MSEiof the employed transmission system. The pSNRi dependsvia (4) on the MSEi, which may be higher or lower, depend-ing on the effectiveness of the transmission system and theindividual radio channel quality. As stated in (2) a fusionalgorithm uses the received microphone signals to generatethe estimate s of the target signal which is the sum of thetarget signal s and undesired components d. Dependingon the application, there may be more and different targetsignals, but the considerations taken here can easily beextended to the more general case.

The quality fSNR (“fusion” SNR) of the output signal ofthe fusion node can be defined as follows:

fSNR¼ Ef‖s‖2gfMSE

¼ Ef‖s‖2gEf‖s� s‖2g ¼

Ef‖s‖2gEf‖d‖2g ð5Þ

The quality in fSNR and hence the distortion fMSE ofthe output signal of the fusion node depends on thedistortion (MSEi) of the received microphone signals and

source vector captured by microphone i.

with a source vector captured by microphone i.

nalog transmission for wireless acoustic sensor networks,4.07.005i

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M. Rüngeler, P. Vary / Signal Processing ] (]]]]) ]]]–]]]4

the properties of the fusion algorithm. Table 1 lists severaltypes of dependencies the fusion algorithms may exhibit.

All types correspond to the behavior of existing fusionalgorithms or represent behaviors which complete thetable. The “mean” type is motivated by its simplicity whilethe output distortion is the average of the distortions ofthe received microphone signals. The algorithm of the“minSNR” type produces a fusion signal which is domi-nated by the quality of the worst input signal to the fusionnode (worst input has the minimum pSNRi and maximummean square error (MSEi)) while for the “maxSNR” typethe quality of the best input dominates. The “Cohadd” typecorresponds to the behavior of a coherent addition of noisysignals which corresponds to the behavior of a delay andsum beamformer. Algorithms such as the MultichannelWiener Filter [5] achieve, under certain circumstances, acombination following Maximum Ratio Combining (“MRC”type). One example of the “add” type is the Elko beam-former [6]. Here, the uncorrelated quantization andchannel noise of all input signals is added up.

Table 1Typical types of characteristics of the distortion fMSE at the output ofthe fusion node. Different fusion algorithms exhibit different types ofdependencies of the output quality on the quality of the input signals.The expectation is taken over the considered scenarios. The MSEi refersto the mean square error of microphone signal i.

Type fMSE¼

mean E1L

∑L

i ¼ 1MSEi

( )

minSNR E max1r ir L

ðMSEiÞ� �

maxSNR E min1r ir L

ðMSEiÞ� �

Cohadd E1

L2∑L

i ¼ 1MSEi

( )

MRC E ∑L

i ¼ 1

1MSEi

!�18<:

9=;

add E ∑L

i ¼ 1MSEi

( )

Fig. 5. HDA transmission system with code rates rccmD ¼ ℓvH =ðN�AÞ ¼ ℓvH =D in

Fig. 4. Purely digital transmission sys

Please cite this article as: M. Rüngeler, P. Vary, Hybrid Digital–ASignal Processing (2014), http://dx.doi.org/10.1016/j.sigpro.201

3. Realization of the purely digital and HybridDigital–Analog transmission system

Fig. 4 shows a conventional purely digital transmissionsystem. In the following, the A/D and D/A conversionblocks and the indices i to indicate the microphonenumber are omitted for simplicity. The source emitscontinuous-amplitude and discrete-time source symbolsu forming one frame with dimension 1�M following theprobability density function (pdf) pðuÞ. The symbols couldbe the captured discrete-time, continuous-amplitude sam-ples of an audio signal or even parameters of any sourceencoder. The entries of the vector u are quantized (Q) anda bit-mapper (BM) generates ℓvD source bits, yielding thevector vD. Subsequently, a digital channel encoder fol-lowed by a digital modulator transforms the source bitsinto N real-valued symbols forming the vector yD with asymbol power of EfyD2g ¼ 1 averaged over all vectorentries yD. Modulation schemes using complex-valuedsymbols (e.g., QPSK, 8PSK) may also be considered bynoting the equivalence between one complex symbol andtwo real symbols. Since channel coding and modulation(ccm) is combined as one step, the ratio between thenumber of bits ℓvD and the number of real symbols N isdenoted by the rate

rccmD ¼ ℓvD

N: ð6Þ

Moreover, the ratio between the number of real sourcesymbols and real channel symbols is given by rD ¼M=N.

Additive white Gaussian noise (AWGN) n with varianceσ2n per dimension disturbs the channel symbols, thereby

yielding the received symbols zD. After demodulation, chan-nel decoding and reconstruction of quantization levels, uD

gives an estimate of the initial source symbols u. In case ofhard decision demodulation and channel decoding thereconstruction of quantization levels is a maximum like-lihood (ML) estimator. If soft decision demodulation anddecoding is employed, also maximum a posteriori (MAP) orminimum mean square error (MMSE) estimation can beused. In this paper an ML estimator is employed.

the digital branch and rmappH ¼M=ðN�DÞ ¼M=A in the analog branch.

tem with code rates rccmD ¼ ℓvDN .

nalog transmission for wireless acoustic sensor networks,4.07.005i

Page 5: Hybrid Digital–Analog transmission for wireless acoustic sensor networks

M. Rüngeler, P. Vary / Signal Processing ] (]]]]) ]]]–]]] 5

Fig. 5 illustrates the HDA transmission system [3]. Thegeneral idea is to use a conventional digital transmissionsystem for u which is differently designed, though, andadditionally transmit the quantization error ua

H by usingcontinuous-amplitude (pseudo analog) discrete-time pro-cessing. The upper branch of the hybrid encoder anddecoder is the digital branch and the lower branch thepseudo analog, or in short analog branch. All operations,also in the analog branch, are conducted using digitalsignal processing. The discrete-time continuous-amplitudesymbols are represented with a precision depending onthe digital processor.

The digital branch is a purely digital transmissionsystem; per frame of M source symbols u, the number ofreal channel dimensions used by the digital branch is D.The analog branch utilizes A40 channel uses. Thus, thenumber of channel uses per HDA frame is

N¼DþA ð7Þwith DoN and the code rate of the channel coding andthe modulation in the digital branch is

rccmH ¼ ℓvH

N�A¼ ℓvH

D: ð8Þ

In order to compare both systems, the respectivenumbers of channel uses (N) in the purely digital systemand in the HDA system are kept equal.

In the hybrid encoder, scalar quantization Q may beapplied to the elements of frame u. Alternatively a vectorquantizer might be applied to the complete frame or partsof the frame. Then a bit-mapper (BM) generates the sourcebits vH. Subsequently, the quantized source representationudH is decoded in the transmitter. The distortion

uaH ¼ u�ud

H introduced by the quantizer is processed inthe analog branch. The analog mapper uses thecontinuous-amplitude function f ð�Þ to map the entries ofthe ua

H to the entries of yaH with length A and averagepower EfðyaHÞ2g ¼ 1:

yaH ¼ f ðuaHÞ: ð9Þ

The function f ð�Þ can also be defined to work on severalentries of ua

H in one step and also output multiple entriesof yaH. The ratio between the input and the output dimen-sions of the block is

rmappH ¼ M

N�D¼M

A: ð10Þ

This mapping f ð�Þ could be a linear amplification or anonlinear function with a rate of rmapp

H ¼ 1 or in case of amapping yielding one complex symbol for one real inputsymbol rmapp

H ¼ 1=2. In this paper a scaling with rmappH ¼ 1 is

employed.After multiplexing the modulated symbols from the

digital and the analog branch and transmitting over theAWGN channel, the received symbols are demultiplexedand conveyed to the digital and analog decoding branches.

The analog demapper then gives uaH as the estimate

of the quantization error which can be facilitated usingseveral methods such as ML, MMSE and linear minimummean square error (LMMSE) estimators. The ML estimatorjust inverts the effect of (9) whereas the LMMSE estimatoradditionally weights the received symbols before the

Please cite this article as: M. Rüngeler, P. Vary, Hybrid Digital–ASignal Processing (2014), http://dx.doi.org/10.1016/j.sigpro.201

inversion with cSNR=ð1þcSNRÞ [7,8]. The MMSE estimatoradditionally considers the source and noise pdf andcalculates the conditional expectation Efua

HjzaHg. The out-puts of the analog and digital branches are added,whereby u gives the final estimate of the source symbols.

For a fair comparison between the purely digital andthe HDA transmission systems, the transmission powershould be equal and also the number of channel uses (N)should be the same. It may be clear that with additionalchannel uses for the analog branch, the HDA systemperforms better than a purely digital system. But for a faircomparison with a fixed overall number of channel uses N,the number of channel uses D for the digital branch has tobe lowered by D¼N�A. In [3] it has been shown how forany purely digital a superior HDA system can be designed.The fidelity of the quantizer of the HDA system and thusthe number of bits which need to be transmitted islowered, such that the channel coding rate of the digitalchannel encoder in the purely digital system is higher thanor the same as the channel coding rate in the digitalbranch of the HDA system. The number of quantizationbits of the HDA system cannot be lowered too much, sincethen loss in fidelity due to coarser quantization cannotbe compensated anymore by the analog branch [3].If additionally an LMMSE estimator is used as the analogdemapper in the analog branch, the performance of theHDA system is superior or equal to the purely digitaltransmission system at all channel qualities. Especially inthe context of unknown radio channel qualities, or withchannel qualities which may be higher than expectedwhile designing the system, the HDA system exhibits thevery desirable property to increase the end-to-end pSNRwith rising channel qualities.

The LMMSE (and also the MMSE) estimator in theanalog branch needs the current channel quality. Since,depending on the digital channel coding and modulation,the channel quality is obtained anyways, e.g., using pilots,this channel quality can also be used for the analog branch.In case of non-perfect estimation of the channel quality,the LMMSE estimator exhibits the nice property of gracefuldegradation; therefore, the loss in performance is notsignificant.

Fig. 6 shows the performance of a purely digitaltransmission system and an HDA transmission systemwith an LMMSE estimator in the analog branch. Bothsystems use the same number of channel uses (N¼ 880),the same transmission power, and encode the same sourcevectors with length M¼ 80. The source could be an audiosignal with a sampling rate of 16 kHz, partitioned to 5 msblocks. This leads to frames with the size M¼ 80. Forsimplicity, the pdf of the source is assumed to be Gaussianand in [3] it is shown that also for other pdfs, the HDAsystems are superior to purely digital transmission. Thedigital transmission system employs a scalar Lloyd Maxquantizer (LMQ) with FD ¼ 6 bits per symbol leading to amaximum pSNR of 31.9 dB due to the quantization noise. Thechannel code uses a rate-12 recursive systematic con-volutional code with the generator polynomial f1;15=13g8 —

the same code which is used in LTE [9]. Puncturing is used toachieve a coding rate of rccmD ¼ 0:55. Binary phase shiftkeying (BPSK) is employed as the modulation. The HDA

nalog transmission for wireless acoustic sensor networks,4.07.005i

Page 6: Hybrid Digital–Analog transmission for wireless acoustic sensor networks

M. Rüngeler, P. Vary / Signal Processing ] (]]]]) ]]]–]]]6

system employs a quantizer with only F ¼ 5 bits per symbolwhich leads to an even more robust channel coding rate ofrccmH ¼ 0:5. The HDA system exhibits a superior performancefor all channel qualities. In contrast to the saturation of thepurely digital system, the HDA system increases its perfor-mance for improved channel qualities.

For audio and speech coding, usually the correlation inthe signal is exploited by linear prediction or by transformcoding. In [4] it is shown that HDA systems also show asuperior performance in the context of transform coding.

4. Simulation results

In order to evaluate the performance of WASNs, theradio channel qualities cSNRi of the individual microphonelinks have to be chosen. In wireless communication a log-normal distribution of the channel quality is frequentlyobserved which is characterized by a normal distributionof the cSNR in the logarithmic domain. The mean channelquality in dB of all links is set by cSNRjdB and the varianceby Γ in the logarithmic domain across the radio links inthe different scenarios. The channel qualities cSNRi in dB

Fig. 6. Performance of Hybrid Digital–Analog and purely digital trans-mission. Gaussian source vector withM¼ 80, Lloyd Max quantization andconvolutional coding with puncturing and BPSK modulation. The analogbranch uses an LMMSE estimator in the analog demapper. Both simula-tions employ N ¼ 880 channel uses and quantizer with word lengthsFH and FD respectively. ℓvH ¼M � FH ; ℓvD ¼M � FD .

10 5 0 5 10 15 20 250

20

40

60

cSNR dB

fSNRdB

Fig. 7. Performance in fSNR of the output signal of the fusion node with of L¼Γ ¼ 5. As a reference, the performance of just one microphone is also depictedtransmission.

Please cite this article as: M. Rüngeler, P. Vary, Hybrid Digital–ASignal Processing (2014), http://dx.doi.org/10.1016/j.sigpro.201

for all L radio links are then modeled by

cSNRijdB ¼N ðcSNRjdB ;ΓÞ; 1r irL: ð11ÞIn Fig. 7 the performance in fSNR of the output signal of

different fusion algorithms with L¼ 4 microphones for amean radio channel quality cSNRjdB between �10 dB and50 dB and a variance Γ ¼ 5 is depicted. As a reference, theperformance of the transmission with just one micro-phone with the corresponding cSNR is also shown whichis equivalent to the curves in Fig. 6.

The curves with the worst performance correspond to thecombination type “minSNR”. Here the microphone with thelowest pSNR determines the performance of the combinedsignal. The performance of the “maxSNR” combination typedepends on the microphone with the best transmissionquality and therefore, in contrast to the “minSNR” type, showsan even better performance than using just one microphone.The “MRC” type combines all received signals in dependenceof their individual cSNRi. This type supersedes all othercombination types. E.g., for the digital transmission systemwith a channel quality for which the transmission quality hasalready saturated, the combination types “minSNR” and“maxSNR” show the same performance as using just onemicrophone, since all individual microphones achieve thesame fSNR. But the “MRC” type achieves a gain of 6 dBcompared to the performance of just one microphone.

The comparison of different combination types formicrophone signals is not in the focus of this study.The main focus is the comparison of purely digital andHybrid Digital–Analog (HDA) transmission in the contextof WASNs. Fig. 7 clearly shows that the HDA system alwayssupersedes the purely digital transmission systems for thesame combination type. Especially for channel qualities inwhich the performance of the purely digital transmissionsystem saturates due to the unrecoverable noise intro-duced by the quantizer, the HDA transmission systemexhibits its advantages.

In Fig. 8 the performance in fSNR of the output signalof different fusion algorithms and a varying number L ofmicrophones for a mean radio channel quality cSNRjdB ¼15 dB and a channel quality variance Γ ¼ 5 is depicted. Asexpected, for just one microphone (L¼ 1), the performancefor all combination types is equal. Still, the pSNR in Fig. 6

30 35 40 45 50

HDA one micHDA MRCHDA maxSNRHDA minSNRDigital one micDigital MRCDigital maxSNRDigital minSNR

4 microphones for a mean radio channel quality cSNRjdB and a variance. For all combination types, the HDA system outperforms purely digital

nalog transmission for wireless acoustic sensor networks,4.07.005i

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0 2 4 6 8 10

20

40

Microphones (L)

fSNRdB

HDA MRCHDA maxSNRHDA meanHDA minSNRDigital MRCDigital maxSNRDigital meanDigital minSNR

Fig. 8. Performance in fSNR of the output signal of the fusion node forvarying number L of microphones for a mean radio channel qualitycSNRjdB ¼ 15 dB and a variance Γ ¼ 5. For all combination types, the HDAsystem outperforms purely digital transmission. The gray lines indicateneighboring markers, not interpolated values.

M. Rüngeler, P. Vary / Signal Processing ] (]]]]) ]]]–]]] 7

for cSNR¼ 15 dB is not achieved, since in Fig. 8 thechannel quality is varied according to (11) with Γ ¼ 5.Two combination types are shown which benefit from anincreased number of microphones: the “maxSNR” and the“MRC” type.

The “MRC” type gains most, as well for the HDA as forthe digital transmission, when using more microphones.For the HDA transmission system, the gain in fSNR usingL¼ 10 microphones instead of just one is remarkable28 dB. Another notable observation is that the HDAtransmission with only 2 microphones supersedes theperformance of 10 microphones with purely digitaltransmission.

The “maxSNR” combination type leads to a gain for theHDA system for additional microphones, since with moremicrophones the probability of a high cSNRi is increasedand thus also the performance of the best microphone. Incase of a purely digital transmission system, an increasedchannel quality is not rewarded with an improved fSNR,since the performance of the purely digital system hasalready saturated. Thus, the “maxSNR” type does notbenefit from more microphones with a purely digitaltransmission system.

When averaging the performance of all microphones(“mean”), the performance is independent of the amountof microphones, both for the HDA and for the digitalsystem. With the “minSNR” and the “add” (not depicted)type, the performance of the output signal of the fusionnode decreases with more microphones.

Independent of the combination type, it can be observedthat again the systems using the HDA transmission showa superior performance to the purely digital transmission.Even with the “maxSNR” type, purely digital transmissiondoes not lead to a gain with additional microphones, butHDA transmission enables an additional gain for an increasednumber of microphones.

Please cite this article as: M. Rüngeler, P. Vary, Hybrid Digital–ASignal Processing (2014), http://dx.doi.org/10.1016/j.sigpro.201

5. Conclusion

Usually, microphones in Wireless Acoustic Sensor Net-works (WASNs) use the same type of transmission systemto transmit their acoustic signals to a fusion node. The linkfrom each microphone experiences a different radio chan-nel quality due to a different distance to the fusion node,while the transmission system cannot adapt to the radiochannel quality because of a missing feedback channelor cost, latency or complexity constraints. Purely digitaltransmission systems cannot exceed a certain end-to-endSNR due to the inherent quantization noise which isdictated by the overall design for the worst case radiochannel quality. One of the strengths of a Hybrid Digital–Analog (HDA) transmission system is the constant improve-ment of the end-to-end SNR for an increased radio channelquality, also for non-adaptive transmitters.

Independent of the behavior of the fusion algorithm interms of output quality in dependence of the quality ofthe received microphone signals, the HDA transmissionsystem supersedes purely digital transmission. It gainsmost when the fusion algorithm can translate an improvedinput quality to an increased output quality.

Especially for WASNs with the inherent wide range ofradio channel qualities of the wireless link to the indivi-dual microphones, HDA transmission leads to an improvedperformance compared to purely digital transmission.

References

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