8/7/2019 apd1

1/15

The Relation between the Amplitude Probability Distribution of anInterfering Signal and its Impact on Digital Radio Receivers

Kia Wiklundh

Abstract - New measurement methods are needed to characterize interference sources in

order to connect the radiated interference to performance degradation on digital

communication systems. Traditionally, standard emission requirements have focused on

protecting analog wireless services. However, developments in digital technology require

measurement methods adapted to protect digital radio communication services. The

amplitude probability distribution (APD) of an interference signal has been shown to be

correlated to the bit error probability of a disturbed digital radio receiver. However, a

general description of the APD of an interfering signal and its impact on a digital coherent

radio receiver has not been presented. The aim of this paper is to clarify this relation. A

method of incorporating the APD in conventional error expressions developed for digital

coherent radio receivers in additive white Gaussian noise is presented. Furthermore, therelation between the maximum error probability for different digital modulation schemes and

the APD is described, which allows definition of emission requirements on the APD.

Index Terms amplitude probability distribution, APD, error probability, non-Gaussian

interference

I. Introduction

Development in the direction of digital systems means that new methods of measuringinterference sources must be developed. The present emission requirements have beendeveloped to protect analog radio. These limits are defined as the maximum allowed level ofthe measured quasi-peak value of the radiated emission from the interference source.However, the levels measured by the quasi-peak detector are not correlated to the impact ofan interference source on a digital radio system. The quasi-peak detector was originallydeveloped to simulate the human perception of electromagnetic interferences on analog radioreceivers. Furthermore, the limits are only defined for the frequency band below 1 GHz. Asseveral radio services already operate beyond 1 GHz, there is a great need for newrequirements [5, 20].

The Amplitude Probability Distribution (APD) has been discussed as a possible measure ofthe radiated interference that would indicate the degradation of a digital radio receiver [32].The APD was used in the late 1960s and 1970s mainly to characterize interference sources[4,21,22] and in recent years has been discussed conserning its correlation to the bit error

probability (BEP) of digital radio systems. In particular, the relation between the APD and theimpact of microwave ovens on the performance of a certain digital receiver has previously

been presented in [1-3]. However, the literature lacks of a theoretical description of theconnection between the APD and the performance of digital communication systems. Thecorrelation has mainly been demonstrated by measurement, but in [1] a theoretical relation

between a microwave oven and a certain receiver is shown. As the same paper assumes noAWGN, the approach requires several new expressions for the BEP. Depending on the energy

of the contribution from the interference signal, different error expressions are required.Furthermore, error expressions for different receivers need to be derived to analyze the

8/7/2019 apd1

2/15

performance of a communication system with an arbitrary modulation method. The need for atheoretical description of the impact of a digital receiver and the APD of an interferencesource was also expressed as an issue that remains to be solved in [31].

To evaluate the impact of an interference signal on a digital radio receiver, the interference

signal needs to be characterized in such a way that it can be used in performance estimation.By tradition, interference signals are often modeled as Gaussian processes. Unfortunately, anapproximation of impulsive noise or pulse-modulated noise as additive white Gaussian noiseoften results in an underestimation of the resulting BEP of a victim receiver [33]. Hence,especially for these two types of interference, it is of great interest to consider the statisticalcharacter of the interference signal. Several papers model interference signals as impulsive ornon-Gaussian noise. In [6], a coherent Binary Shift Keying (BPSK) receiver subjected to aninterference signal with arbitrary amplitude probability density function (pdf) is considered;whereas the error probability for some receivers subjected to a class A interference (aninterference model for which the bandwidth is narrower than the radio receiver of interest) isexamined in [7-9]. The performance of impulsive interference in single-user systems and

multi-user systems, respectively, has been studied in [10-11]. Furthermore, the problem of acommunication system subjected to a non-Gaussian interference environment is treated in[12-14]. However, in these papers the digital radio receivers are assumed to be sub-optimizedto Gaussian noise and robust against deviations from Gaussian noise. For the special case witha receiver optimized for AWGN, these papers provide error expressions of this receiverdegraded by non-Gaussian noise. However, these performance expressions are complicatedand their usage in practical applications considering a Gaussian optimized receiver is notobvious.

The aim of this paper is to: clarify the relation between the APD measure of an interfering signal and its impact

on digital radio receivers. present a practical method for performance estimation of digital coherent radio

receivers in non-Gaussian interference by using classical results regarding the impactof interference on digital radio receivers.

present how the connection between the maximum BEP and the information providedby the APD applies to emission requirements.

The paper is partly based on results published by the author in [23-24]. The paper provides asystematic and practical method of incorporating the APD measure in conventional errorexpressions developed for AWGN. The method also makes it possible to consider the impact

of an arbitrary interference source in the general error expressions originally derived forAWGN. Furthermore, the relation between the maximum error probability of a digitalreceiver and the measured APD of an interference source is stated. This relation opens the

possibility to derive emission requirements for interference sources based on the APD. Therelation between the maximum BEP and the APD is supplemented with an illustration of itsuse for emission requirements and has not been published before. However, to estimate the

performance degradation of a digital receiver or to derive emission requirements by the use ofAPD, the bandwidth of the measurement receiver and the radio receiver must be similar.When the bandwidths differ, the APD measured cannot be used directly in these applications.In [25], a method of converting the APD measured by one bandwidth to another is presented.The method has been developed for a special group of signals, namely pulse-modulated noise,

which in many scenarios is a relevant type of interference. Reasons for choosing theseinterference models are given in [25].

8/7/2019 apd1

3/15

The paper is organized as follows. Section II presents a system model and describes the

problem. In Section III, a measured APD of an interference source is connected to thedegradation of a digital radio receiver due to the same interference. This is presented as asystematic method which incorporates the use of the APD measure in conventional error

expressions developed for AWGN. The method suggested paves the way for estimating the performance of digital communication systems in complex interference environments. Theapplicability of the method is then shown by an example. Section IV shows that the maximum

bit error probability (BEP) for a BPSK receiver is equal to a certain value of the APD. Thisproperty is then generalized for a variety of receivers. The relation obtained can be used todefine maximum emission limits for electrical equipment in terms of APD. By assuring thatthe measured APD of a interference source is lower than the proposed requirements, theimpact on the performance of a variety of receivers is guaranteed not to exceed a givenmaximum bit error probability. Section V concludes the paper.

II. Problem overview

A. General model of the problem

This paper discusses the relation between the measured APD of an interference signal and theperformance degradation on a digital radio receiver due to the same interference, see Fig. 1.Electrical equipment, such as micro-wave ovens, from which the radiated interference mighthave a non-Gaussian amplitude character, has been shown to severely affect the performanceof radio receivers. The key issue is to analyze the information the measured APD providesand connect it to parameters which are important when the performance of a receiver is to beestimated. The reverse problem is also of interest, i.e. to relate a certain level of the

performance measure BEP of the radio receiver to requirements on the APD of aninterference signal.

Electricalequipment

Measurement system

Radio system

APD detectorH(f)Filter

Performance measure, BEP dtFilter

1 2

APD

Detection and decision

8/7/2019 apd1

4/15

Figure 1: Overview of the problem; connect the measured APD of an interference source tothe performance degradation of a digital coherent radio receiver (1) and the reverse problem(2).

B. Radio system model

The receiver is assumed to be an ideal coherent digital receiver designed as a maximum-likelihood receiver for AWGN. The conventional performance measure of a digital radioreceiver is the BEP, which is defined as the probability that a transmitted bit is erroneouslydetected. An incorrect decision is generated when the contribution from an interfering signaladds to the desired signal such that the decision variable falls into an incorrect decision regionin the detector. The key issue when determining the impact of an interfering signal is to haveinformation about its envelope and phase in the decision device in the detector. Since theinterference signal can be regarded as uncorrelated with the desired signal, it is reasonable to

believe that the phase at the decision instant is uniformly distributed in the interval [ ]2,0 .We also assume that the system is memoryless between decision instants. This implies thatthe bit decisions can be considered as independent of each other. Hence, information aboutthe duration and arrival time of the impulses is of no importance. For the performanceanalysis, a first assumption is that the system does not use any error correcting codes.However, this is not a major restriction. Coded systems usually utilize interleaving, whichreorders the bits such that they become independent. In order to consider coded systems with

block codes and hard decisions, the performance degradation derived for uncoded systems canbe used as input for performance estimation of coded systems.

C. Interference signal

The radio system considered in this work is subjected to an interference environment, whichwill negatively influence the performance of the radio receiver of the intended signal. Theinterference sources, which constitute the interference environment, are assumed to be co-located with the receiver. The short distance to the receiver implies that electrical equipment,even with a moderate level of emission, can constitute a severe problem.

D. Measurement system model

The APD is defined as the part of time the measured envelope of an interfering signal exceedsa certain level [1]. We assume that the measured signal is ergodic and that the measurement ofthe APD is long enough to capture the signal properties. The relation between the )(APD r

R

and the probability density function of the envelope,R, is

)(1)(APD rFr RR = (1)

and

)(APD)()( rdr

drF

dr

drf RRR == , (2)

where ( )rFR and ( )rfR denote the cumulative distribution function (cdf) and probability

density function (pdf), respectively.

8/7/2019 apd1

5/15

An APD detector can be implemented by an envelope detector and a counter [16-18]. TheAPD can be estimated by a spectrum analyzer, where the signal is first converted to anintermediate frequency and band limited by a variable resolution bandwidth filter. The signalcan then be compressed by a log amplifier, after which the envelope is extracted by anenvelope detector [16].

To be able to use the information provided by the APD in the following analyses, someassumptions are necessary. The receiver structures of the APD detector and the analyzed radioreceiver have to be quite similar. This is normally the case for coherent digital radio receivers.APD gives information about the envelope statistics from the IF filter, which corresponds tothe required information for performance evaluation at the radio receiver. However, the

bandwidths of the measurement and the radio receiver need to be approximately the same. Ifthe bandwidths of the radio system and the measurement receiver differ significantly, amethod of modifying the APD is suggested in [25] for pulse-modulated interference.Furthermore, the APD needs to be measured at the frequency band the radio system works on.

III. Impact of an interfering signal on a digital coherent radio receiver

A. How to derive the BEP for a given APD

The traditional way of determining the error probability of a digital radio receiver is to assumethat the interference can be modeled as AWGN. For that kind of noise, error probabilityexpressions are often quite easily derived for different kinds of receivers. For other types ofnoise, there are no simple methods. But, as will be shown here, with information provided byan APD detector, even noise of a non-Gaussian nature can be incorporated with theconventional error probability expressions. The method is then demonstrated in an example.The key issue when determining the impact of an interfering signal on a coherent digital radio

receiver is information about the envelope and phase at the decision moment in the detector.For example, if we assume +1 was transmitted, the decision variable of a coherent BPSKreceiver in AWGN can be described as

nEy += b , (3)

where bE is the bit energy and n represents the additive Gaussian noise component, which

has zero mean and variance 202

N= . Thus, the performance is obtained as [27]

=

20

bb

N

EQP , (4)

where

( )

=v

dxx

vQ2

exp2

1 2 . (5)

For a BPSK receiver subjected to an interfering signal, the decision variable Yhas the

conditional expected value [ ] cos, b rErYE += and the variance 202 N= , wherecosr is the contribution from the interference. In detail, r and denote the envelope and

the phase, respectively, of the interference. Thus, the conditional error probability, adjustedfor the interfering signal, becomes

[ ]

+=

2

cos,errorbitPr

0

b

N

rEQr

. (6)

8/7/2019 apd1

6/15

By assuming that the phase in the moment of decision is uniformly distributed over [ ]2,0and by using the information from the APD, the error probability is obtained as

( )

ddrrfN

rEQP R

+=

2

0 0 0

bb

2

cos

2

1. (7)

At this stage, the information from the measured APD can be used to provide the probabilitydensity function of the envelope )(rfR . This is based on certain assumptions, e.g. that the

bandwidth of the measuring detector is approximately the same as that of the analyzed radio

receiver, see section IID. By modifying bE with cosb rE + in the conventional error

expression and then averaging over the envelope and phase, the influence of the interferenceis considered. This method can be generalized to other coherent digital modulation schemeswith bit-by-bit decisions. The method includes Gaussian noise, originated from thermal noisein the receiver. If only the interference is to be considered, which means that the thermalreceiver noise is neglected, 0N can be made arbitrarily small in practice. The method can be

summarized into the following steps:

1. Estimate )(rfR out of measured )(APD rR .

2. Adjust the decision variable with respect to the interference, e.g. substitute bE for

cosb rE + for coherent BPSK.

3. Use the error formula developed for AWGN and average for r and .

B. Example

The symbol error probability of a Quadriphase-Shift Keying (QPSK) modulated signal can bederived with the same approach used in section IIIA. In order to evaluate the influence on atwo-dimensional modulation scheme such as coherent QPSK, the contribution from theinterfering signal also has to be described in two dimensions. To demonstrate the method, weassume an interfering source that emits pulse-modulated Gaussian noise. Measurementequipment with an APD detector measures the interfering signal. The measured pulses have a

pulse width pT , which come periodically with a period time of T. This gives a duty factor of

TTp= .

The pulses and the noise between the pulses are characterized by Gaussian distributed noise

with the variance2

1 and2

2 , respectively. Nevertheless, the final pdf exhibits a non-

Gaussian distribution with the associated APD as

( ) ( )

+

=

2

2

2

2

1

2

2exp1

2expAPD

rrrR . (8)

This model often suits well as a model for signals radiated from electrical equipment [25].The APD has been calculated for this interfering signal with the current parameters

102

1 = , 12

2 = and 1.0= and is shown in Fig. 2. The APD

8/7/2019 apd1

7/15

100

101

106

105

104

103

102

101

100

Noise envelope, R

APD(r)

Figure 2: Calculated APD of pulse-modulated Gaussian noise with parametersdefined in the example.

does not indicate the order in which the envelope samples come in time. If the samples areswitched in time, they are still characterized by the same APD. It is worth noticing that aslong as the detector takes bit-by-bit decisions, which are used for signals without memory,this does not matter. Only the statistics of r and are of importance for the performance.

This implies that you can create an APD through a polynomial or a simple mathematicalmodel equal to a measured APD of a microwave oven, for example, and use the simplermodel when the impact is to be determined. With the previously described parameters and

100b =E , the bit error probability can be calculated, see Fig. 3. The figure also shows the bit

error probability in the absence of interference source when only thermal receiver noise is

present.

8/7/2019 apd1

8/15

4 2 0 2 4 6 8 10 12 14

105

104

103

102

101

100

Signaltonoise ratio, Eb/N0, [dB]

Biterrorprobability,

BEP

Disturbance consistingpulse modulated noise

No disturbance

Figure 3:Estimated bit error probability of a QPSK signal with and without interferingpulse-modulated Gaussian noise.

As QPSK symbols are mapped by two information bits, the symbol energy bs 2EE = , where

bE denotes the bit energy. Here the contribution from the interfering source to the decision

variable is defined with cos2s rE + instead of 2sE in the inphase channel and with

sin2s rE + instead of 2sE in the quadrature channel. By substituting 2sE with

cos2s rE + in the inphase channel and 2sE with sin2s rE + in the quadrature

channel, the conditional symbol error probability is obtained as [27]

( )

+

+

++

+=

2

sin2*

2cos2

2sin2

2

cos2,errorsymbolPr

0

s

0

s

0

s

0

s

N

rEQ

N

rEQN

rEQ

N

rEQr

. (9)

Finally, the expression is averaged over r and . By assuming that the phase is uniformly

distributed over [ ]2,0 at the moment of decision, by using the symmetry of the cosine andsine function and by assuming that the last term is relatively small, the symbol error

probability can be written as

8/7/2019 apd1

9/15

( )

+

2

0 0 0

s )(2

cos2

1

errorsymbolPr

ddrrfN

rEQ R

. (10)

Furthermore, by using the assumptions of Gray coded symbols, the bit error probability canbe approximated as [28]

( )errorsymbolPr2

1b =P . (11)

IV. Emission requirements on APD not to exceed a certain BEP

The information provided by the APD detector about an interference signal can be used toestimate the degradation on a radio receiver. However, we also want to reverse the problem inorder to restrict the maximum allowed APD. We will begin with the simplest modulation

method, BPSK, to illustrate the relation between the BEP and APD, and then proceed with ageneral approach.Adopting the assumptions of equal bandwidth mentioned in section IID, the APD of aninterference source can be used as an envelope estimate for the decision variable, from whichthe impact on a digital receiver can be estimated. By neglecting AWGN, we will see that it is

possible to find the direct relationship between a certain BEP and the APD that is useful whenderiving emission requirements.For a coherent BPSK receiver, the decision variable is

cosb rEy += , (12)

if we assume that a +1 was transmitted and no AWGN is present. Thus, the conditional error

probability conditioned on a certain phase is[ ]

[ ]

==

8/7/2019 apd1

10/15

Such reasoning makes it possible to define requirements on the APD based on requirementson a BEP level. The fact that the requirement corresponds to a worst case might lead tounnecessarily severe requirements on allowed radiated interference, which might result in toocostly products. The usefulness of the bound has therefore been investigated in [24], where itwas stated that the bound, perhaps in a modified version, is useful. In the example analyzed,

the discrepancy between the average BEP and maximum BEP was considered to beacceptably small.

By assuming statistical independence of the noise quadrature carriers, the relation between themaximum BEP and the APD can be generalized for other coherent modulation schemes bystudying the signal constellation. For signals that exhibit statistically dependent quadraturecomponents, it has been shown that the resulting BEP of a Quadrature Amplitude Modulation(QAM) system is only marginally affected by this property [29]. This means that the proposedrelation might be useful in practice also for situations when the quadrature components arestatistically dependent.

The distance between the closest symbols is defined as the minimum distance and is ofsignificance for the error probability of a coherent detector. The worst case symbol error

probability is achieved when the contribution from the interfering signal is directed toward theclosest symbol in the signal constellation. Considering the worst case, a symbol error occurswhen the envelope of the interference exceeds 2mind . This is due to the fact that the border

between decision regions is, in a conventional coherent receiver, located in the middlebetween two symbols. Therefore, the symbol error probability conditioned on a worst casephase value [ ] maxerrorsymbolPr can be obtained as

[ ]

=

>=

2APD2PrerrorsymbolPr

minmin

max

dd

r R . (15)

The expression shows that the symbol error probability is always less than or equal to theAPD for a certain value. This implies that the APD of a measured interference source for thevalue equal to 2mind must not exceed the maximum acceptable bit error rate. By letting the

measured APD for the value 2mind be less than the determined maximum allowed error rate,

the error rate will always be lower than or equal to what is acceptable. Such reasoning makesit possible to define requirements on the APD based on requirements on a BEP level.

Eq. (15) can be rewritten as [ ] )bwc APDerrorsymbolPr ER = , where takes differentvalues depending on the modulation scheme. The minimum distance for an M-ary Phase ShiftKeying (PSK) signal is [27]:

( )

=

MEMd

2cos1log2 b2min , (16)

where M denotes the number of symbols; for example 8=M results in 66.0= .

Furthermore, considering the number of bits that constitutes a symbol and assuming Grayencoded symbols, the BEP can be approximated from the symbol error probability as

presented in Table 1, [28]. The bounds are derived for different modulation schemes such as

PSK, Pulse Amplitude Modulated (PAM), QAM and Frequency Shift Keying (FSK).

8/7/2019 apd1

11/15

Table 1:Bounds derived for different modulation schemes

Mod. [ ]errorbitPr Relation maxb,P vs. APD2-PSK 1 Pr[symbol error] )bmaxb, APD EP 4-PSK 1 1/2* Pr[symbol error] )bmaxb, APD21 EP 8-PSK 0.66 1/3*Pr[symbol error] )bmaxb, 66.0APD31 EP 16-PSK 0.39 1/4*Pr[symbol error] )bmaxb, 39.0APD41 EP 4-PAM 0.63 1/2*Pr[symbol error] )bmaxb, 63.0APD21 EP 8-PAM 0.37 1/3*Pr[symbol error] )bmaxb, 37.0APD31 EP 16-QAM 0.63 1/4*Pr[symbol error] )bmaxb, 63.0APD41 EP 64-QAM 0.38 1/6*Pr[symbol error]

)bmaxb,38.0APD61 EP

2-FSK 0.71 Pr[symbol error] )bmaxb, 71.0APD EP 4-FSK 1 1/3*Pr[symbol error] )bmaxb, APD31 EP

For example, the bound of the BEP for a coherent BPSK receiver subjected to an interferencecan be interpreted as follows. If the measured bit energy at the detector is 1,bE , the maximum

BEP never becomes higher than )b,1b,1 APD EP = , whereas for a smaller bit energy b,2E theBEP is bounded by the larger value )b,2b,2 APD EP = , see Fig. 4.

b,1P

b,1Eb,2E

b,2P

Envelope r

APDR(r)

Figure 4: Schematic illustration of a BPSK system.

To demonstrate how the derived bounds on the BEP can be used for emission requirement, we

assume that the BEP is restricted never to become higher than 3101 , which corresponds to atypical requirement for voice transmission. For example, the subjective effect of bit errors for

voice transmission with pulse code modulation (PCM) is: 6101 not perceptible; 5101 single clicks; 4101 single but little distracting clicks; 3101 high density of clicks, which

8/7/2019 apd1

12/15

disturb each speech level; 2101 strong disturbing crackle with low intelligibility [30].Furthermore, the value of the bit energy at the detector must be determined. Here, we assume

that VE 10b = . Inserting the determined values of the maximum allowed BEP and the bit

energy in the bounds described in Table 1, the requirements can be implemented as a point in

the APD for every modulation scheme. To ensure that the error rate of a receiver that issubjected to an interfering signal does not exceed a certain error rate, the measured APD mustlay below the points, as illustrated in Fig 5. The figure shows measured data reported in [1]concerning radiated interference from two different microwave ovens: A: Inverter-type of 600W at 2.45 GHz and E: transformer-type of 500 W at 2.45 GHz. In the same figure, the

requirements, corresponding to a maximum BEP of 3101 and VE 10b = , are displayed

with circles. If the measured APD lays below all the points, the impact on different radiosystems in Table 1 are guaranteed not to exceed the permitted level of the BEP. We can seethat the microwave oven of transformer-type (E) fulfills the requirement both at 1 m and 3 m.This means that the radiated interference of this microwave oven will not cause a bit error rateworse than 3101 . However, the micro-wave oven of inverter-type (A) does not fulfil therequirement, and thus we cannot guarantee that the bit error rate is lower than therequirement, although the average BEP might be lower than the requirement. It is important tonote that the requirement only places restrictions on the APD levels in a specified noiseenvelope interval. In the example shown in Fig. 5, the APD is restricted between 6108.3 V

and 61010 V. For a higher or lower noise envelope, the interference can assume arbitraryAPD levels.

106

105

104

103

106

105

104

103

102

101

Noise envelope, E, [V]

APD(

Prob[e>E])

Measured data, MWO A, 1 mMeasured data, MWO E, 1 mMeasured data, MWO A, 3 mMeasured data, MWO E, 3 mRequirement acc. to Table 1

8/7/2019 apd1

13/15

Figure 5:Illustration of the bounds implemented in an APD graph with measuredradiated interference from two different microwave ovens at 1 m and 3 m [1]. The

requirements are calculated for a maximum BEP of 3101 when VE 10b = .

IV. Conclusions

It has previously been stated that the APD of an interference signal is strongly correlated tothe BEP of digital radio receivers. However, there the literature lacks of a theoreticaldescription of the relation between the APD of an interfering signal and the impact on adigital receiver. This paper summarizes [23,24] with the aim of clarifying the theoreticalrelation between the APD and the BEP. This paper presents a method of how to use theseresults in practical applications. It demonstrates that the APD provides the necessaryinformation about an interference signal to estimate its degradation of a digital coherent radio

receiver under certain conditions. Estimation of the impact of an arbitrary interference ondigital coherent receivers has been presented in [12-14]. However, analyzing the performanceof a receiver optimized to AWGN that is subjected to non-Gaussian interference constitutes aspecial case. These expressions are complicated and their use in practical applications is notobvious. This paper proposes a systematic method of incorporating the contribution of aninterfering signal, which might be non-Gaussian provided by an APD measurement system, inconventional error expressions developed for AWGN. The paper also suggests a possibleapproach to defining emission requirements on the APD in order to control radiatedelectromagnetic emission for the protection of radio communication systems.

References[1] Y.Yamanaka, T. Shinozuka, Measurement and estimation of BER degradation of PHS

due to electromagnetic disturbance from microwave ovens, Trans. IEICE, B-II, no. 11,Nov. 1996, pp 827-834 (translated into English).

[2] H. Kanemoto, S. Miyamoto, N. Morinaga, A study on modeling of microwave oveninterference and optimum reception, Proc. of 1998 IEEE Int. Symp. on EMC, Denver,Colorado, USA, Aug. 1998.

[3] T. Kowada, Y. Hayashi, K. Yamane, T. Shinozuka, Interference on wide-band digitalcommunication by disturbance in 2 GHz band, Proc. on 1999 Int. Symp. on EMC, May

1999.[4] A. D. Spaulding, C. J. Roubique, W. Q. Crichlow, Conversion of the Amplitude-

Probability Distribution Function for Atmospheric Radio Noise From One Bandwidth toAnother, J. Res. Bur. Stand. (Radio Propagation), sec. D, vol. 66, no. 6, 1962.

[5] Additional information on APD measuring equipment and draft CD for the amendmentto CISPR 16-1 Clause 6.2, CISPR/A/WG1, July 1998.

[6] A. S. Rosenbaum, F. E. Glave, An Error-Probability Upper Bound for Coherent Phase-Shift Keying with Peak-Limited Interference,IEEE Trans. on EMC, vol. COM-22, no.1, Jan. 1974.

8/7/2019 apd1

14/15

[7] A. D. Spaulding, D. Middleton, Reception in impulsive interference environment Part I: Coherent Detection, IEEE Trans. on Comm., vol.COM-25, no. 9, September1977, pp 910-923.

[8] S. Miyamoto, M. Katayama, N. Morinaga, Performance analysis of QAM systemsunder class A impulsive noise interference, IEEE Trans. on EMC, vol 37, no 2, May1995, pp 260-267.

[9] R. Prasad, A. Kegel, A. de Vos, Performance of Microcellular Mobile Radio in aCochannel Interference, Natural, and Man-Made Noise Environment, IEEE Trans. onVehicular Tech., vol. 42, no. 1, Feb. 1993.

[10] B. Aazhang, H. V. Poor, Performance of DS/SSMA Communications in ImpulsiveChannels Part I: Linear Correlation Receivers,IEEE Trans. on Comm, vol. COM-35,no. 11, Nov. 1987.

[11] T. Koizumi, Y. Inoue, M. Ohta, The effect of non-Gaussian noise on the performanceof binary CPSK system,IEEE Trans. on Comm., vol. COM-26, Feb. 1978.

[12] T. berg, M. Mettiji, Robust Detection in Digital Communication, IEEE Trans. onComm., vol. 43, No. 5, May 1995.

[13] A. Spaulding, Locally Optimum and Suboptimum Detector Performance in a Non-Gaussian Interference Environment,IEEE Trans. on Comm., vol. COM-33, no. 6, June1985.

[14] P. K. Enge, D. V. Sarwate, Spread-Spectrum Multiple-Access Performance ofOrthogonal Codes: Impulsive Noise, IEEE Trans. on Comm., vol. 36, no. 1, Jan. 1988.

[16] J. R. Hoffman, M. G. Cotton, et. al., Measurements to Determine Potential Interferenceto GPS Receiver from Ultrawideband Transmission Systems, NTIA Report 01-384,

Febuary, 2001.[17] M. Uchino, Y. Hayashi, T. Shinozuka, R. Sato, Development of low-cost high-

resolution APD measuring equipment, Proc. on 1997 Int. Symp. on EMC, Beijing,May, 1997, pp 253-256.

[18] M. Uchino, T. Shinozuka, R. Sato, Development of APD measuring equipment and itsfaculty. Proc. on 1998 Int. Symp. on EMC, Denver, Aug., 1998.

[20] P. J. Kerry, EMC standards Quo Vadis?, Proc. on the 2003 IEEE Int. Symp. onEMC, Istanbul, Turkey, May, 2003.

[21] R. A. Shephard, Measurements of amplitude probability distributions and power of

automobile ignition noise at HF, IEEE Trans. on Vehicular Tech., vol. VT-23, no. 3,Aug. 1974.

[22] M. Mettiji, T. berg, Noise amplitude probabilty distribution in the 900 MHzfrequency band, Proc. on International Conference of Communication Systems

ICCS90, pp. 819-823, Singapore, November, 1990.

[23] K. Wiklundh, A method to determine the impact from disturbing electrical equipmenton digital communication systems, Proceedings on EMC Europe 2002, Sorrento, Italy,Spet., 2002.

[24] K. Wiklundh, A new approach to derive emission requirements on APD in order toprotect digital communication systems, Proceedings of the 2003 IEEE Int. Symp. onEMC, Istanbul, Turkey, May, 2003.

8/7/2019 apd1

15/15

[25] K. Wiklundh, Bandwidth conversion of the APD for pulse modulated interference,Technical report R009/2003, Chalmers University of Technology, Sweden, October,2003 eller ta licavhandlingen?

[26] A. D. Spaulding, D. Middleton, Reception in impulsive interference environment Part I: Coherent Detection, IEEE Trans. on Comm., vol.COM-25, no. 9, Sept. 1977,

pp. 910-923.

[27] J. G. Proakis, Digital Communications, 3rd ed. McGraw-Hill International Editions,1995.

[28] S. Haykin,Digital Communications, John Wiley & Sons, Inc., 1988.

[29] S. Miyamoto, M. Katayama, N. Morinaga, Performance analysis of QAM systemsunder class A impulsive noise interference, IEEE Trans. on EMC, vol. 37, no. 2, May1995, pp 260-267.

[30] A. Knobloch, H. Garbe, Critical review of converting spectral data into prospective biterror rates, Proc. on 2002 Int. Symp. on EMC, Minnesota, August, 2002, pp. 173-178.

[31] Y. Yamanaka, T. Shinozuka, Statistical Parameter measurement of unwanted emissionfrom microwave ovens, Proc. IEEE Int. Symp. on EMC, 1995, pp. 57-61.

[32] Additional information on APD measuring equipment and draft CD for the amendmentto CISPR 16-1 Clause 6.2, CISPR/A/WG1, July, 1998.

[33] K. Wiklundh, Impact of some interfering signals on an MSK receiver under fadingconditions, Proc. of IEEE MILCOM00, Los Angeles, USA, October, 2000.