The Relation between the Amplitude Probability Distribution of an Interfering Signal and its Impact on Digital Radio Receivers. I.

Transcription

1 The elation etween the Amplitude Proaility Ditriution of an Interfering Signal and it Impact on Digital adio eceiver Kia Wiklundh Atract - New meaurement method are needed to characterize interference ource in order to connect the radiated interference to performance degradation on digital communication ytem. Traditionally, tandard emiion requirement have focued on protecting analog wirele ervice. However, development in digital technology require meaurement method adapted to protect digital radio communication ervice. The amplitude proaility ditriution (APD of an interference ignal ha een hown to e correlated to the it error proaility of a ditured digital radio receiver. However, a general decription of the APD of an interfering ignal and it impact on a digital coherent radio receiver ha not een preented. The aim of thi paper i to clarify thi relation. A method of incorporating the APD in conventional error expreion developed for digital coherent radio receiver in additive white Gauian noie i preented. Furthermore, the relation etween the maximum error proaility for different digital modulation cheme and the APD i decried, which allow definition of emiion requirement on the APD. Index Term amplitude proaility ditriution, APD, error proaility, non-gauian interference I. Introduction Development in the direction of digital ytem mean that new method of meauring interference ource mut e developed. The preent emiion requirement have een developed to protect analog radio. Thee limit are defined a the maximum allowed level of the meaured quai-peak value of the radiated emiion from the interference ource. However, the level meaured y the quai-peak detector are not correlated to the impact of an interference ource on a digital radio ytem. The quai-peak detector wa originally developed to imulate the human perception of electromagnetic interference on analog radio receiver. Furthermore, the limit are only defined for the frequency and elow 1 GHz. A everal radio ervice already operate eyond 1 GHz, there i a great need for new requirement [5, ]. The Amplitude Proaility Ditriution (APD ha een dicued a a poile meaure of the radiated interference that would indicate the degradation of a digital radio receiver [3]. The APD wa ued in the late 196 and 197 mainly to characterize interference ource [4,1,] and in recent year ha een dicued conerning it correlation to the it error proaility (BEP of digital radio ytem. In particular, the relation etween the APD and the impact of microwave oven on the performance of a certain digital receiver ha previouly een preented in [1-3]. However, the literature lack of a theoretical decription of the connection etween the APD and the performance of digital communication ytem. The correlation ha mainly een demontrated y meaurement, ut in [1] a theoretical relation etween a microwave oven and a certain receiver i hown. A the ame paper aume no AWGN, the approach require everal new expreion for the BEP. Depending on the energy of the contriution from the interference ignal, different error expreion are required. Furthermore, error expreion for different receiver need to e derived to analyze the

2 performance of a communication ytem with an aritrary modulation method. The need for a theoretical decription of the impact of a digital receiver and the APD of an interference ource wa alo expreed a an iue that remain to e olved in [31]. To evaluate the impact of an interference ignal on a digital radio receiver, the interference ignal need to e characterized in uch a way that it can e ued in performance etimation. By tradition, interference ignal are often modeled a Gauian procee. Unfortunately, an approximation of impulive noie or pule-modulated noie a additive white Gauian noie often reult in an underetimation of the reulting BEP of a victim receiver [33]. Hence, epecially for thee two type of interference, it i of great interet to conider the tatitical character of the interference ignal. Several paper model interference ignal a impulive or non-gauian noie. In [6], a coherent Binary Shift Keying (BPSK receiver ujected to an interference ignal with aritrary amplitude proaility denity function (pdf i conidered; wherea the error proaility for ome receiver ujected to a cla A interference (an interference model for which the andwidth i narrower than the radio receiver of interet i examined in [7-9]. The performance of impulive interference in ingle-uer ytem and multi-uer ytem, repectively, ha een tudied in [1-11]. Furthermore, the prolem of a communication ytem ujected to a non-gauian interference environment i treated in [1-14]. However, in thee paper the digital radio receiver are aumed to e u-optimized to Gauian noie and rout againt deviation from Gauian noie. For the pecial cae with a receiver optimized for AWGN, thee paper provide error expreion of thi receiver degraded y non-gauian noie. However, thee performance expreion are complicated and their uage in practical application conidering a Gauian optimized receiver i not oviou. The aim of thi paper i to: clarify the relation etween the APD meaure of an interfering ignal and it impact on digital radio receiver. preent a practical method for performance etimation of digital coherent radio receiver in non-gauian interference y uing claical reult regarding the impact of interference on digital radio receiver. preent how the connection etween the maximum BEP and the information provided y the APD applie to emiion requirement. The paper i partly aed on reult pulihed y the author in [3-4]. The paper provide a ytematic and practical method of incorporating the APD meaure in conventional error expreion developed for AWGN. The method alo make it poile to conider the impact of an aritrary interference ource in the general error expreion originally derived for AWGN. Furthermore, the relation etween the maximum error proaility of a digital receiver and the meaured APD of an interference ource i tated. Thi relation open the poiility to derive emiion requirement for interference ource aed on the APD. The relation etween the maximum BEP and the APD i upplemented with an illutration of it ue for emiion requirement and ha not een pulihed efore. However, to etimate the performance degradation of a digital receiver or to derive emiion requirement y the ue of APD, the andwidth of the meaurement receiver and the radio receiver mut e imilar. When the andwidth differ, the APD meaured cannot e ued directly in thee application. In [5], a method of converting the APD meaured y one andwidth to another i preented. The method ha een developed for a pecial group of ignal, namely pule-modulated noie, which in many cenario i a relevant type of interference. eaon for chooing thee interference model are given in [5].

3 The paper i organized a follow. Section II preent a ytem model and decrie the prolem. In Section III, a meaured APD of an interference ource i connected to the degradation of a digital radio receiver due to the ame interference. Thi i preented a a ytematic method which incorporate the ue of the APD meaure in conventional error expreion developed for AWGN. The method uggeted pave the way for etimating the performance of digital communication ytem in complex interference environment. The applicaility of the method i then hown y an example. Section IV how that the maximum it error proaility (BEP for a BPSK receiver i equal to a certain value of the APD. Thi property i then generalized for a variety of receiver. The relation otained can e ued to define maximum emiion limit for electrical equipment in term of APD. By auring that the meaured APD of a interference ource i lower than the propoed requirement, the impact on the performance of a variety of receiver i guaranteed not to exceed a given maximum it error proaility. Section V conclude the paper. A. General model of the prolem II. Prolem overview Thi paper dicue the relation etween the meaured APD of an interference ignal and the performance degradation on a digital radio receiver due to the ame interference, ee Fig. 1. Electrical equipment, uch a micro-wave oven, from which the radiated interference might have a non-gauian amplitude character, ha een hown to everely affect the performance of radio receiver. The key iue i to analyze the information the meaured APD provide and connect it to parameter which are important when the performance of a receiver i to e etimated. The revere prolem i alo of interet, i.e. to relate a certain level of the performance meaure BEP of the radio receiver to requirement on the APD of an interference ignal. Meaurement ytem Electrical equipment Filter H(f APD detector APD 1 Filter dt Performance meaure, BEP Detection and deciion adio ytem

4 Figure 1: Overview of the prolem; connect the meaured APD of an interference ource to the performance degradation of a digital coherent radio receiver (1 and the revere prolem (. B. adio ytem model The receiver i aumed to e an ideal coherent digital receiver deigned a a maximumlikelihood receiver for AWGN. The conventional performance meaure of a digital radio receiver i the BEP, which i defined a the proaility that a tranmitted it i erroneouly detected. An incorrect deciion i generated when the contriution from an interfering ignal add to the deired ignal uch that the deciion variale fall into an incorrect deciion region in the detector. The key iue when determining the impact of an interfering ignal i to have information aout it envelope and phae in the deciion device in the detector. Since the interference ignal can e regarded a uncorrelated with the deired ignal, it i reaonale to elieve that the phae at the deciion intant i uniformly ditriuted in the interval [,π]. We alo aume that the ytem i memoryle etween deciion intant. Thi implie that the it deciion can e conidered a independent of each other. Hence, information aout the duration and arrival time of the impule i of no importance. For the performance analyi, a firt aumption i that the ytem doe not ue any error correcting code. However, thi i not a major retriction. Coded ytem uually utilize interleaving, which reorder the it uch that they ecome independent. In order to conider coded ytem with lock code and hard deciion, the performance degradation derived for uncoded ytem can e ued a input for performance etimation of coded ytem. C. Interference ignal The radio ytem conidered in thi work i ujected to an interference environment, which will negatively influence the performance of the radio receiver of the intended ignal. The interference ource, which contitute the interference environment, are aumed to e colocated with the receiver. The hort ditance to the receiver implie that electrical equipment, even with a moderate level of emiion, can contitute a evere prolem. D. Meaurement ytem model The APD i defined a the part of time the meaured envelope of an interfering ignal exceed a certain level [1]. We aume that the meaured ignal i ergodic and that the meaurement of the APD i long enough to capture the ignal propertie. The relation etween the APD and the proaility denity function of the envelope,, i and APD f = 1 F (1 d d = F = APD, ( dr dr where F ( r and f ( r denote the cumulative ditriution function (cdf and proaility denity function (pdf, repectively.

5 An APD detector can e implemented y an envelope detector and a counter [16-18]. The APD can e etimated y a pectrum analyzer, where the ignal i firt converted to an intermediate frequency and and limited y a variale reolution andwidth filter. The ignal can then e compreed y a log amplifier, after which the envelope i extracted y an envelope detector [16]. To e ale to ue the information provided y the APD in the following analye, ome aumption are neceary. The receiver tructure of the APD detector and the analyzed radio receiver have to e quite imilar. Thi i normally the cae for coherent digital radio receiver. APD give information aout the envelope tatitic from the IF filter, which correpond to the required information for performance evaluation at the radio receiver. However, the andwidth of the meaurement and the radio receiver need to e approximately the ame. If the andwidth of the radio ytem and the meaurement receiver differ ignificantly, a method of modifying the APD i uggeted in [5] for pule-modulated interference. Furthermore, the APD need to e meaured at the frequency and the radio ytem work on. III. Impact of an interfering ignal on a digital coherent radio receiver A. How to derive the BEP for a given APD The traditional way of determining the error proaility of a digital radio receiver i to aume that the interference can e modeled a AWGN. For that kind of noie, error proaility expreion are often quite eaily derived for different kind of receiver. For other type of noie, there are no imple method. But, a will e hown here, with information provided y an APD detector, even noie of a non-gauian nature can e incorporated with the conventional error proaility expreion. The method i then demontrated in an example. The key iue when determining the impact of an interfering ignal on a coherent digital radio receiver i information aout the envelope and phae at the deciion moment in the detector. For example, if we aume +1 wa tranmitted, the deciion variale of a coherent BPSK receiver in AWGN can e decried a y = E + n, (3 where E i the it energy and n repreent the additive Gauian noie component, which ha zero mean and variance σ = N. Thu, the performance i otained a [7] E P = Q, (4 N where 1 x Q( v = exp dx. (5 π v For a BPSK receiver ujected to an interfering ignal, the deciion variale Y ha the conditional expected value E [ Y r, ϕ] = E + r coϕ and the variance σ = N, where r coϕ i the contriution from the interference. In detail, r and ϕ denote the envelope and the phae, repectively, of the interference. Thu, the conditional error proaility, adjuted for the interfering ignal, ecome [ ] E + r coϕ Pr it error r, ϕ = Q. (6 N

6 By auming that the phae in the moment of deciion i uniformly ditriuted over [,π] and y uing the information from the APD, the error proaility i otained a π 1 E r ϕ P Q + co = f ( r dr dϕ. (7 π N At thi tage, the information from the meaured APD can e ued to provide the proaility denity function of the envelope f (r. Thi i aed on certain aumption, e.g. that the andwidth of the meauring detector i approximately the ame a that of the analyzed radio receiver, ee ection IID. By modifying E with E + r coϕ in the conventional error expreion and then averaging over the envelope and phae, the influence of the interference i conidered. Thi method can e generalized to other coherent digital modulation cheme with it-y-it deciion. The method include Gauian noie, originated from thermal noie in the receiver. If only the interference i to e conidered, which mean that the thermal receiver noie i neglected, N can e made aritrarily mall in practice. The method can e ummarized into the following tep: 1. Etimate f (r out of meaured APD.. Adjut the deciion variale with repect to the interference, e.g. utitute E for E + r coϕ for coherent BPSK. 3. Ue the error formula developed for AWGN and average for r and ϕ. B. Example The ymol error proaility of a Quadriphae-Shift Keying (QPSK modulated ignal can e derived with the ame approach ued in ection IIIA. In order to evaluate the influence on a two-dimenional modulation cheme uch a coherent QPSK, the contriution from the interfering ignal alo ha to e decried in two dimenion. To demontrate the method, we aume an interfering ource that emit pule-modulated Gauian noie. Meaurement equipment with an APD detector meaure the interfering ignal. The meaured pule have a pule width T p, which come periodically with a period time of T. Thi give a duty factor of α = T p T. The pule and the noie etween the pule are characterized y Gauian ditriuted noie 1 with the variance σ and σ, repectively. Neverthele, the final pdf exhiit a non- Gauian ditriution with the aociated APD a ( ( r + r APD r = α exp 1 α exp. (8 σ 1 σ Thi model often uit well a a model for ignal radiated from electrical equipment [5]. The APD ha een calculated for thi interfering ignal with the current parameter σ 1, σ 1 and α =. 1and i hown in Fig.. The APD 1 = =

7 APD(r Noie envelope, Figure : Calculated APD of pule-modulated Gauian noie with parameter defined in the example. doe not indicate the order in which the envelope ample come in time. If the ample are witched in time, they are till characterized y the ame APD. It i worth noticing that a long a the detector take it-y-it deciion, which are ued for ignal without memory, thi doe not matter. Only the tatitic of r and ϕ are of importance for the performance. Thi implie that you can create an APD through a polynomial or a imple mathematical model equal to a meaured APD of a microwave oven, for example, and ue the impler model when the impact i to e determined. With the previouly decried parameter and E = 1, the it error proaility can e calculated, ee Fig. 3. The figure alo how the it error proaility in the aence of interference ource when only thermal receiver noie i preent.

8 1 1 1 Bit error proaility, BEP No diturance Diturance coniting pule modulated noie Signal to noie ratio, E/N, [db] Figure 3: Etimated it error proaility of a QPSK ignal with and without interfering pule-modulated Gauian noie. A QPSK ymol are mapped y two information it, the ymol energy E = E, where E denote the it energy. Here the contriution from the interfering ource to the deciion variale i defined with E + r coϕ intead of E in the inphae channel and with E + r inϕ intead of E in the quadrature channel. By utituting E with E + r coϕ in the inphae channel and E with E + r inϕ in the quadrature channel, the conditional ymol error proaility i otained a [7] E ( + r coϕ Pr ymol error r, ϕ = Q N E + + r inϕ E r coϕ + Q Q. (9 N N E + r inϕ * Q N Finally, the expreion i averaged over r and ϕ. By auming that the phae i uniformly ditriuted over [,π] at the moment of deciion, y uing the ymmetry of the coine and ine function and y auming that the lat term i relatively mall, the ymol error proaility can e written a

9 Pr ( ymol error 1 π π E + r coϕ Q N f. (1 dr dϕ Furthermore, y uing the aumption of Gray coded ymol, the it error proaility can e approximated a [8] 1 P = Pr( ymol error. (11 IV. Emiion requirement on APD not to exceed a certain BEP The information provided y the APD detector aout an interference ignal can e ued to etimate the degradation on a radio receiver. However, we alo want to revere the prolem in order to retrict the maximum allowed APD. We will egin with the implet modulation method, BPSK, to illutrate the relation etween the BEP and APD, and then proceed with a general approach. Adopting the aumption of equal andwidth mentioned in ection IID, the APD of an interference ource can e ued a an envelope etimate for the deciion variale, from which the impact on a digital receiver can e etimated. By neglecting AWGN, we will ee that it i poile to find the direct relationhip etween a certain BEP and the APD that i ueful when deriving emiion requirement. For a coherent BPSK receiver, the deciion variale i y = E + r coϕ, (1 if we aume that a +1 wa tranmitted and no AWGN i preent. Thu, the conditional error proaility conditioned on a certain phae i Pr it errorϕ = Pr [ ] [ E + r coϕ < ϕ : π ϕ 3π ], (13 E = = f dr APD coϕ E coϕ For thi kind of receiver, we get an interpretation of the APD function. The value of the APD i directly correlated to the conditional error proaility. Thi i an intereting fact, ecaue there would normally not e any imple connection etween a maximum allowed error rate and a maximum allowed APD when a Gauian noie i alo preent. If we aume the wort poile phae value, ϕ = π, it i poile to otain a relation etween the maximum it error proaility and the APD a P, max = Pr[ E r < ] = APD ( E. (14 Thi phae value aumption mean that the interfering ignal will work detructively entirely againt the deired ignal. It contitute a wort cae of the interference and will reult in the maximum error proaility. The expreion how that the it error proaility i alway le than or equal to the APD for E. It implie that the APD of a meaured interference ource for E mut not exceed the maximum acceptale it error rate. By letting the meaured APD for E e le than the determined maximum allowed error rate P,requirement, the error rate will to alway e lower than or equal to the acceptale one.

10 Such reaoning make it poile to define requirement on the APD aed on requirement on a BEP level. The fact that the requirement correpond to a wort cae might lead to unnecearily evere requirement on allowed radiated interference, which might reult in too cotly product. The uefulne of the ound ha therefore een invetigated in [4], where it wa tated that the ound, perhap in a modified verion, i ueful. In the example analyzed, the dicrepancy etween the average BEP and maximum BEP wa conidered to e acceptaly mall. By auming tatitical independence of the noie quadrature carrier, the relation etween the maximum BEP and the APD can e generalized for other coherent modulation cheme y tudying the ignal contellation. For ignal that exhiit tatitically dependent quadrature component, it ha een hown that the reulting BEP of a Quadrature Amplitude Modulation (QAM ytem i only marginally affected y thi property [9]. Thi mean that the propoed relation might e ueful in practice alo for ituation when the quadrature component are tatitically dependent. The ditance etween the cloet ymol i defined a the minimum ditance and i of ignificance for the error proaility of a coherent detector. The wort cae ymol error proaility i achieved when the contriution from the interfering ignal i directed toward the cloet ymol in the ignal contellation. Conidering the wort cae, a ymol error occur when the envelope of the interference exceed d min. Thi i due to the fact that the order etween deciion region i, in a conventional coherent receiver, located in the middle etween two ymol. Therefore, the ymol error proaility conditioned on a wort cae Pr ymol error can e otained a phae value [ ] max Pr d d = r >. (15 min min [ ymol error] Pr = APD max The expreion how that the ymol error proaility i alway le than or equal to the APD for a certain value. Thi implie that the APD of a meaured interference ource for the value equal to d min mut not exceed the maximum acceptale it error rate. By letting the meaured APD for the value d min e le than the determined maximum allowed error rate, the error rate will alway e lower than or equal to what i acceptale. Such reaoning make it poile to define requirement on the APD aed on requirement on a BEP level. Eq. (15 can e rewritten a Pr[ ymol error] wc= APD ( β E, where β take different value depending on the modulation cheme. The minimum ditance for an M-ary Phae Shift Keying (PSK ignal i [7]: π ( M E 1 co d min = log, (16 M where M denote the numer of ymol; for example M = 8 reult in β =. 66. Furthermore, conidering the numer of it that contitute a ymol and auming Gray encoded ymol, the BEP can e approximated from the ymol error proaility a preented in Tale 1, [8]. The ound are derived for different modulation cheme uch a PSK, Pule Amplitude Modulated (PAM, QAM and Frequency Shift Keying (FSK.

11 Tale 1: Bound derived for different modulation cheme Mod. β Pr [ it error] elation P, max v. APD -PSK 1 Pr[ymol error] P, max APD( E 4-PSK 1 1/* Pr[ymol error] P, max 1 APD( E 8-PSK.66 1/3*Pr[ymol error] P, max 1 3APD(. 66 E 16-PSK.39 1/4*Pr[ymol error] P, max 1 4APD(. 39 E 4-PAM.63 1/*Pr[ymol error] P, max 1 APD(. 63 E 8-PAM.37 1/3*Pr[ymol error] P, max 1 3APD(. 37 E 16-QAM.63 1/4*Pr[ymol error] P, max 1 4APD(. 63 E 64-QAM.38 1/6*Pr[ymol error] P, max 1 6APD(. 38 E -FSK.71 Pr[ymol error] P, max APD(. 71 E 4-FSK 1 1/3*Pr[ymol error] P 1 3 ( E, max APD For example, the ound of the BEP for a coherent BPSK receiver ujected to an interference can e interpreted a follow. If the meaured it energy at the detector i E, 1, the maximum BEP never ecome higher than P,1 = APD( E,1, wherea for a maller it energy E, the BEP i ounded y the larger value P, = APD( E,, ee Fig. 4. APD (r P, P,1 E, E,1 Envelope r Figure 4: Schematic illutration of a BPSK ytem. To demontrate how the derived ound on the BEP can e ued for emiion requirement, we 3 aume that the BEP i retricted never to ecome higher than 1 1, which correpond to a typical requirement for voice tranmiion. For example, the ujective effect of it error for 6 5 voice tranmiion with pule code modulation (PCM i: 1 1 not perceptile; ingle click; 1 1 ingle ut little ditracting click; 1 1 high denity of click, which

12 ditur each peech level; 1 1 trong dituring crackle with low intelligiility [3]. Furthermore, the value of the it energy at the detector mut e determined. Here, we aume that E = 1µ V. Inerting the determined value of the maximum allowed BEP and the it energy in the ound decried in Tale 1, the requirement can e implemented a a point in the APD for every modulation cheme. To enure that the error rate of a receiver that i ujected to an interfering ignal doe not exceed a certain error rate, the meaured APD mut lay elow the point, a illutrated in Fig 5. The figure how meaured data reported in [1] concerning radiated interference from two different microwave oven: A: Inverter-type of 6 W at.45 GHz and E: tranformer-type of 5 W at.45 GHz. In the ame figure, the 3 requirement, correponding to a maximum BEP of 1 1 and E = 1µ V, are diplayed with circle. If the meaured APD lay elow all the point, the impact on different radio ytem in Tale 1 are guaranteed not to exceed the permitted level of the BEP. We can ee that the microwave oven of tranformer-type (E fulfill the requirement oth at 1 m and 3 m. Thi mean that the radiated interference of thi microwave oven will not caue a it error rate 3 wore than 1 1. However, the micro-wave oven of inverter-type (A doe not fulfil the requirement, and thu we cannot guarantee that the it error rate i lower than the requirement, although the average BEP might e lower than the requirement. It i important to note that the requirement only place retriction on the APD level in a pecified noie 6 envelope interval. In the example hown in Fig. 5, the APD i retricted etween V 6 and 1 1 V. For a higher or lower noie envelope, the interference can aume aritrary APD level APD (Pro[e>E] Meaured data, MWO A, 1 m Meaured data, MWO E, 1 m Meaured data, MWO A, 3 m Meaured data, MWO E, 3 m equirement acc. to Tale Noie envelope, E, [V]

13 Figure 5: Illutration of the ound implemented in an APD graph with meaured radiated interference from two different microwave oven at 1 m and 3 m [1]. The 3 requirement are calculated for a maximum BEP of 1 1 when E = 1µ V. IV. Concluion It ha previouly een tated that the APD of an interference ignal i trongly correlated to the BEP of digital radio receiver. However, there the literature lack of a theoretical decription of the relation etween the APD of an interfering ignal and the impact on a digital receiver. Thi paper ummarize [3,4] with the aim of clarifying the theoretical relation etween the APD and the BEP. Thi paper preent a method of how to ue thee reult in practical application. It demontrate that the APD provide the neceary information aout an interference ignal to etimate it degradation of a digital coherent radio receiver under certain condition. Etimation of the impact of an aritrary interference on digital coherent receiver ha een preented in [1-14]. However, analyzing the performance of a receiver optimized to AWGN that i ujected to non-gauian interference contitute a pecial cae. Thee expreion are complicated and their ue in practical application i not oviou. Thi paper propoe a ytematic method of incorporating the contriution of an interfering ignal, which might e non-gauian provided y an APD meaurement ytem, in conventional error expreion developed for AWGN. The paper alo ugget a poile approach to defining emiion requirement on the APD in order to control radiated electromagnetic emiion for the protection of radio communication ytem. eference [1] Y.Yamanaka, T. Shinozuka, Meaurement and etimation of BE degradation of PHS due to electromagnetic diturance from microwave oven, Tran. IEICE, B-II, no. 11, Nov. 1996, pp (tranlated into Englih. [] H. Kanemoto, S. Miyamoto, N. Morinaga, A tudy on modeling of microwave oven interference and optimum reception, Proc. of 1998 IEEE Int. Symp. on EMC, Denver, Colorado, USA, Aug [3] T. Kowada, Y. Hayahi, K. Yamane, T. Shinozuka, Interference on wide-and digital communication y diturance in GHz and, Proc. on 1999 Int. Symp. on EMC, May [4] A. D. Spaulding, C. J. ouique, W. Q. Crichlow, Converion of the Amplitude- Proaility Ditriution Function for Atmopheric adio Noie From One Bandwidth to Another, J. e. Bur. Stand. (adio Propagation, ec. D, vol. 66, no. 6, 196. [5] Additional information on APD meauring equipment and draft CD for the amendment to CISP 16-1 Claue 6., CISP/A/WG1, July [6] A. S. oenaum, F. E. Glave, An Error-Proaility Upper Bound for Coherent Phae- Shift Keying with Peak-Limited Interference, IEEE Tran. on EMC, vol. COM-, no. 1, Jan

14 [7] A. D. Spaulding, D. Middleton, eception in impulive interference environment Part I: Coherent Detection, IEEE Tran. on Comm., vol.com-5, no. 9, Septemer 1977, pp [8] S. Miyamoto, M. Katayama, N. Morinaga, Performance analyi of QAM ytem under cla A impulive noie interference, IEEE Tran. on EMC, vol 37, no, May 1995, pp [9]. Praad, A. Kegel, A. de Vo, Performance of Microcellular Moile adio in a Cochannel Interference, Natural, and Man-Made Noie Environment, IEEE Tran. on Vehicular Tech., vol. 4, no. 1, Fe [1] B. Aazhang, H. V. Poor, Performance of DS/SSMA Communication in Impulive Channel Part I: Linear Correlation eceiver, IEEE Tran. on Comm, vol. COM-35, no. 11, Nov [11] T. Koizumi, Y. Inoue, M. Ohta, The effect of non-gauian noie on the performance of inary CPSK ytem, IEEE Tran. on Comm., vol. COM-6, Fe [1] T. Öerg, M. Mettiji, out Detection in Digital Communication, IEEE Tran. on Comm., vol. 43, No. 5, May [13] A. Spaulding, Locally Optimum and Suoptimum Detector Performance in a Non- Gauian Interference Environment, IEEE Tran. on Comm., vol. COM-33, no. 6, June [14] P. K. Enge, D. V. Sarwate, Spread-Spectrum Multiple-Acce Performance of Orthogonal Code: Impulive Noie, IEEE Tran. on Comm., vol. 36, no. 1, Jan [16] J.. Hoffman, M. G. Cotton, et. al., Meaurement to Determine Potential Interference to GPS eceiver from Ultrawideand Tranmiion Sytem, NTIA eport 1-384, Feuary, 1. [17] M. Uchino, Y. Hayahi, T. Shinozuka,. Sato, Development of low-cot highreolution APD meauring equipment, Proc. on 1997 Int. Symp. on EMC, Beijing, May, 1997, pp [18] M. Uchino, T. Shinozuka,. Sato, Development of APD meauring equipment and it faculty. Proc. on 1998 Int. Symp. on EMC, Denver, Aug., [] P. J. Kerry, EMC tandard Quo Vadi?, Proc. on the 3 IEEE Int. Symp. on EMC, Itanul, Turkey, May, 3. [1]. A. Shephard, Meaurement of amplitude proaility ditriution and power of automoile ignition noie at HF, IEEE Tran. on Vehicular Tech., vol. VT-3, no. 3, Aug [] M. Mettiji, T. Öerg, Noie amplitude proailty ditriution in the 9 MHz frequency and, Proc. on International Conference of Communication Sytem ICCS 9, pp , Singapore, Novemer, 199. [3] K. Wiklundh, A method to determine the impact from dituring electrical equipment on digital communication ytem, Proceeding on EMC Europe, Sorrento, Italy, Spet.,. [4] K. Wiklundh, A new approach to derive emiion requirement on APD in order to protect digital communication ytem, Proceeding of the 3 IEEE Int. Symp. on EMC, Itanul, Turkey, May, 3.

15 [5] K. Wiklundh, Bandwidth converion of the APD for pule modulated interference, Technical report 9/3, Chalmer Univerity of Technology, Sweden, Octoer, 3 eller ta licavhandlingen? [6] A. D. Spaulding, D. Middleton, eception in impulive interference environment Part I: Coherent Detection, IEEE Tran. on Comm., vol.com-5, no. 9, Sept. 1977, pp [7] J. G. Proaki, Digital Communication, 3 rd ed. McGraw-Hill International Edition, [8] S. Haykin, Digital Communication, John Wiley & Son, Inc., [9] S. Miyamoto, M. Katayama, N. Morinaga, Performance analyi of QAM ytem under cla A impulive noie interference, IEEE Tran. on EMC, vol. 37, no., May 1995, pp [3] A. Knoloch, H. Gare, Critical review of converting pectral data into propective it error rate, Proc. on Int. Symp. on EMC, Minneota, Augut,, pp [31] Y. Yamanaka, T. Shinozuka, Statitical Parameter meaurement of unwanted emiion from microwave oven, Proc. IEEE Int. Symp. on EMC, 1995, pp [3] Additional information on APD meauring equipment and draft CD for the amendment to CISP 16-1 Claue 6., CISP/A/WG1, July, [33] K. Wiklundh, Impact of ome interfering ignal on an MSK receiver under fading condition, Proc. of IEEE MILCOM, Lo Angele, USA, Octoer,.