EVALUATION OF CONSTANT ENVELOPE OFFSET QUADRATURE PHASE SHIFT KEYING TRANSMITTERS WITH A SOFTWARE BASED SIGNAL ANALYZER

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1 EVALUAIO OF COSA EVELOPE OFFSE QUADRAURE PHASE SHIF KEYIG RASMIERS WIH A SOFWARE BASED SIGAL AALYZER Item ype text; Proceeding Author Jefferi, Robert P. Publiher International Foundation for elemetering Journal International elemetering Conference Proceeding Right Copyright International Foundation for elemetering Download date 06/07/08 0:40:7 Link to Item

2 EVALUAIO OF COSA EVELOPE OFFSE QUADRAURE PHASE SHIF KEYIG RASMIERS WIH A SOFWARE BASED SIGAL AALYZER Robert P. Jefferi YBRI Corporation ABSRAC Off-line oftware baed ignal analyi can be a valuable tool for detailed examination of tranmitter ignal characteritic. hi paper decribe the Advanced Range elemetry (ARM) Contant Envelope (CE) offet quadrature phae hift keying (OQPSK) modulation analyzer. It wa developed exprely for evaluation of FQPSK-B, FQPSK-JR and haped OQPSK tranmitter ignal. Rationale for it creation, underlying aumption, computation method, and example of it data product are preented. KEYWORDS FQPSK-B, FQPSK-JR, SOQPSK-G, oftware receiver, modulation analyzer IRODUCIO In 004 the United State Department of Defene (DoD) Range Commander Council added FQPSK-JR [] and SOQPSK-G modulation to it telemetry tandard, recognizing FQPSK-JR and SOQPSK-G a inter-operable alternative to FQPSK-B modulation []. hee technique are notable for good radio frequency (RF) pectrum efficiency and compatibility with non-linear amplifier (LA). he DoD ARM project ponored initial development of airborne tranmitter (X) and companion detection equipment for thee waveform. One challenge ha been detailed X ignal quality evaluation, epecially in light of three modulation alternative. RF power pectrum and additive white Gauian noie (AWG) detection performance meaurement are traightforward with tandard laboratory equipment and uitable demodulator. However, RF power pectra and bit error probability (BEP) data will not normally reveal ubtle X defect. Many tet equipment manufacturer produce vector ignal analyzer deigned for detailed examination of widely ued modulation method. Linear ytem in particular have a rich et of metric like error vector FQPSK refer to Feher Quadrature Phae Shift keying.

3 magnitude (EVM) and it pin-off metric to diagnoe ubtle problem. o date, thee manufacturer have not programmed their intrument to undertand 4-ary CE OQPSK ignal. hi void wa partially filled when the Jet Propulion Laboratory (JPL) completed a oftware receiver for FQPSK ignal [3]. It demodulate hort egment of X RF ignal captured by digitizing ocillocope and produce EVM and EVM-related ignal analyi product. Unfortunately, EVM i of limited value becaue CE OQPSK tranmitter uually incorporate a LA. LA model ufficiently precie to predict intra-ymbol amplitude value in the context of EVM are not available. In order to bypa thee limitation, the JPL oftware receiver wa changed to emphaize generic meaurement reflecting performance characteritic common to all CE OQPSK ignal. EVM analyi wa removed and the graphical uer interface (GUI) wa modified to incorporate the data product decribed below. he demodulator, Cota loop, and digital tranition timing loop (DL) ymbol timing loop were retained. REFERECE SIGAL AD RECEIVER FILERS ranmitter are viewed a cloed ytem. he only ignal available for evaluation i that emanating from the RF port. X ignal are compared to an idea linearly amplified CE OQSK reference ignal that i baed on the contant envelope FQPSK-JR half-ymbol wavelet et deigned by Formeiter and Jefferi []. However, FQPSK-JR pot-wavelet aembly filter and interpolation filter are omitted yielding the power pectrum hown in figure. hi point of reference ha four deirable feature. It i contant modulu at all poible ample intantt doe not produce any inter-ymbol interference (ISI)t doe not produce zero-croing (phae) jitter, and it i eaily decribed with cloed form equation. Otherwiet poee the eential attribute of all relevant CE OQPSK variant.e., uppreed carrier double ideband RF ignaling that emerge within conventional coherent QPSK demodulator a an OQPSK ignal with the peculiar characteritic of binary in-phae (I) and quadrature phae (Q) channel ymbol waveform poeing two poible mean energy level per tate at mid-ymbol ampling intant. hu, we conider thi bai ignal to offer the bet ynchronization and detection performance potential poible in a coherent, ample and hold (SH) detection cheme. FIGURE Reference Power Spectrum he oftware analyzer repreent a nearly ideal ingle ymbol coherent SH detector with the baic tructure hown in figure. Figure 3 how the reference ignal in three contellation form. Figure 3a i a conventional QPSK contellation. Baeband in-phae (I) and quadrature phae (Q) ignal are ampled imultaneouly at mid-ymbol after removing the bit interval (τ b ) inter-channel delay.

4 pre-d FILER I(t) S(t) co(ω c t) in(ω c t) CARRIER RECOVERY (COSAS LOOP) SYMBOL IMIG RECOVERY MID-SYMBOL CLOCK SYMBOL CLOCK pre-d FILER Q(t) FIGURE - Analyzer Structure ote the 6 point peculiar to thee waveform. he OQPSK contellation in 3b i conidered a more ueful preentation for diagnotic. Inter-channel delay i retained. I and Q are ampled midymbol and at ymbol end point. In thi domain the reference ha eight mean target vector (V) end point that lie on a circle. However, ISI and memory preent in the real ignal caue the V at odd multiple of 45 degree to plit into pair o that mean V appear. he third graph (3c) i a ingle dimenion hitogram of I and Q ignal at their repective mid-ymbol ampling intant. hi i the ample et actually proceed by independent I and Q deciion circuit in a SH demodulator. ote that 4 level are aociated with each channe a pair of high energy or outer tate level and a pair of low energy or inner tate level. From the tandpoint of product tetingt i unfortunate that thee modulation were adopted without tandardization of detection filter. Accordingly, commercial demodulator tend to be proprietary in thi regard. With the expre purpoe of chooing a reaonable non-proprietary compromie applicable to all igna detection filter employed here are traightforward equiripple, linear phae, finite impule repone approximation to ideal low pa filter. he wide repone curve in figure 4 i the pre-detection (pre-d) filter. It bandwidth/ymbol period product i Bτ =. 4. It i ued to capture ignal feature with negligible ditortion. It wide bandwidth i jutified becaue the tet i conducted at very high ignal to noie ratio, noie and ditortion introduced by the tet equipment i negligible, and there are no interfering ignal. he narrow repone curve i the final detection filter with normalized bandwidth Bτ = Simulation baed on the technique developed by Lee [4] have hown the detection filter to be a reaonable compromie between noie bandwidth and detection lo. It i not optimum in any ene, but doe create a conitent evaluation domain for X ignal. AALYZER OPERAIO AD DAA PRODUCS A Q Q (0,) (A,A) A I or Q - -A A I I 0 -A - (a) - QPSK (b) - OQPSK (c) - DECISIO VIEW FIGURE 3 - Contellation Variation 3

5 Signal are ampled with the equipment hown in figure 5. A random binary data equence i applied to a X under tet (U) at ome deired bit rate. he ignal i attenuated and tranlated to a convenient intermediate frequency (IF), typically 70 MHz, with a high quality mixer and low noie local ocillator (LO). A digitizing ocillocope ample the IF ignal. ormally, M ample are taken at a ample rate of 00M ample/econdntentionally aliaing the ignal to a carrier frequency of 30 MHz. Sample block are tranferred by computer network to the analyzer oftware hot. FIGURE 4 Detection Filter With the exception of ample rate and detection filter deigngnal are proceed in much the ame manner a well deigned commercial SH demodulator. Offet are identified and removed from the baeband ignal. Inter-channel amplitude (gain) imbalance i identified and amplitude are adjuted to produce conitent caling. Howevern order to extract detailed information, ample file are proceed in two ditinct phae at a ample rate of f = 0 ample per ymbol (p), which i ubtantially higher than rate ued in practical demodulator. A Simulink model demodulate the ample block. he operator ee three dynamic diplay window. An ocillocope window how progreion of Cota loop phae, DL phae, and DL loop error power veru equivalent real time. Eye diagram and a contellation catter diagram linked to the pre-d filter are alo preented. Collectively, thee diplay clearly indicate ample block integrity and whether or not the ignal contain anomalie eriou enough to caue erratic demodulator behavior. Carrier loop bandwidth i et to the leer value of 0.00R or 0 khz, where R i the ymbol rate. DL bandwidth i et at the leer value of R or 5 khz. hee value are conitent with the range ued in ome commercial product for operation between and 0 Mb/ and have been hown to work well in thi application. Upon DL ynchronization, the model capture ample panning 4000 contiguou bit period and tore 3 vector. I and Q ample are a complex time erie DAA/CLOCK GEERAOR LO Worktation U DIGIIZIG OSCILLOSCOPE FIGURE 5 - ranmitter et Equipment 4

6 z nt f z ( n) = I nt f + jq nt f () where ubcript denote pre-d filter ample. he nd vector i a mid-ymbol ample pointer for the I channel. he 3 rd i a bit boundary ample pointer. Proceing then tranfer to a erie of Matlab cript. Phae tart by creating the normalized vector z ( n) = I ( n) + jq ( n) wherein offet are removed and amplitude are caled a decribed below. he ynchronization vector are ued to ort z ( n ) into real valued OQPSK contellation e, coordinate et C fc, where the V ubet are indexed by a combination of upercript and ubcript. he e denote energy level (e=h denote high energy point, e=l denote inner point). he denote the ign of the current ample. he letter f i the filter group aociation (f= denote pre-d filter ample, f=r denote pot detection filter ample). c=i indicate that the I channel coordinate i the ample being preented to deciion circuit.e., the current ample, and c=q the oppoite cae. I and Q are paed through the final detection filter to create the deciion ample vector e, z R ( n) = I R ( n) + jqr ( n). Pot-detection filter mid-ymbol ample group C R,c are extracted from zr ( n) to repreent ymbol amplitude ample that a hardware S&H demodulator preent to deciion circuit. wo group of analyi product are created. he firt group, aociated with z nclude tabular and graphic preentation of: Euclidean ditance lo of the inner Vgnal to noie ratio of inner V ample, phae trajectory deviation, and zero croing jitter. he econd group, derived from z R, include predicted detection performance at BEP benchmark value and noie margin. ormalized offet and gain imbalance are alo preented. Graphic diplay of eye pattern, pre-d contellation, detector ample ditribution, RF power pectrum, and baeband power pectrum are available. DISACE LOSS AD SIGAL DEVIAIO RAIO (SDR) Euclidean ditance of the inner V trongly dominate deciion error occurrence at high ignal to noie ratio. hereforegnal examination focue on the inner contellation point in term of geometric ditance and ymbol-to-ymbol deviation of amplitude from mean value. Signal power i normalized in the conventional manner.e., given an average RF ignal power P at the demodulator input then P τ E = E b () where E i energy expended in a ymbol interval and E b i energy expended in a bit interval. hen the reference ignal inner Carteian ditance i. Euclidean ditance lo λ and SDR i computed for I with the equation: 5

7 , 0log min C i λi SDR I S 0log 0log l L, = +, + i L l + L i l+ i l + L l + l L i L i + [ C ( l) ] + [ C ( l) ] l + l L i L i + + [ C ( l) C ] + [ C ( l) C ] l= i l= l= l= (3) (4) Over-bar denote mean value and L i the number of ubet member. Q channel value are computed imilarly. Filtered CE OQPSK produce lower bound on λ and SDR due to inherent ISI. hee bound change when an LA i preent. able (ee appendix for all table) lit practical lower bound for linear and LA cae. Linear imulation were baed on ideal 0 p 70 MHz IF ample et created in Matlab. he LA baeline were obtained with laboratory grade X emulator driving a linear amplifier hard into aturation. ote that the LA erve a a normalizing component in the ene that lo and SDR figure for all three technique nearly converge. Real tranmitter produce larger value due to phae noie and a hot of poible defect. BEP, RASMIER LOSS, AD OISE MARGI Symbol detection in I and Q i treated a independent binary deciion procee. he claic formula for ymbol error probability P in a binary phae hift keying (BPSK) ytem i ued to project BEP. Given a ingle ymbol obervation interva P i given by [5]: P = erfc E 0 = erfc E b 0 = erfc d 0 (5) where erfc i the complimentary error function, 0 / i the power pectral denity of AWG introduced between the X and detection filter, and d repreent the Euclidean ditance between deciion amplitude. Strictly peaking, equation (5) i only valid for optimum detection. However, ueful projection of detection performance can be realized by replacing E or E b with appropriate root mean quare (rm) value in thi application. he reference ignal poee eight unique ymbol interval baeband waveform [6]. Without lo of generality, we et reference ignal caling for peak outer tate amplitude of unity which place all reference ignal V endpoint on a unit radiu circle a in figure 3b. he BEP etimation tart with an ordered et γ { γ γ γ } =,,..., J of bit energy to noie denity ratio value Eb / 0 cloely paced in the range of interet (6 to 0 db). he I and Q ample are caled uch that the rm amplitude of that channel poeing the larger mean amplitude over the ample et 6

8 prior to normalization equal that of the reference ignal. he E of each channel i computed from I and. Correponding channel pecific noie denity et are computed: Q E 0 γ 0 = 0 { } (6) oie variance in the detection bandwidth i determined for each channel with the relation 0 { σ } h () t = R dt where hr ( t) i the impule repone of the detection filter. Each ample block contain K ymbo K per channel. Average BEP veru E b / 0 of the I channel i computed: (7) { P ( j) } K = erfc K k C ( k) ** Ri j = ( j) = σ,,..., J (8) where * denote ummation over all index et. he X contribution to performance lo in exce of the reference ignal lo are etimated at BEP benchmark value P b, Pb by earching P for the value cloet to each benchmark. he correponding value γ, P γ b P are compared to b thoe of the reference waveform at the benchmark. he larget difference (I or Q) i reported a X 6 0 lo. able lit practical lower bound for X lo for Pb = x0 and Pb = x0. Another parameter of interet i the amount of noie headroom or the noie margin available for 0 operation at P b = x0. hi value i ued becaue ome application trive for eentially error free operation without channel coding. he denominator of equation (4) i for practical purpoe, the U noie floor and σ aociated with γ Pb i the amount of noie added at detection filter output to create the irreducible BEP floor. Auming AWG, σ i referred back to external noie power: Added = σ P b h h R () t () t dt dt (9) X noie margin at P b in db i then etimated: M Pb 0log + Added (0) hi guarantee a wort cae analyi in term of the range of amplitude control method ued on commercial demodulator. 7

9 able 3 lit lower bound of M with thi detection filter. PHASE RAJECORY AD JIER Examination of carrier phae trajectory and it deviation from expected path can lend inight to ytematic and incidental X defect. Intra-ymbol carrier phae evolution (pre-d) of the U i compared to that of the reference ignal on a bit-by-bit bai with the angle function hown in table 5. hee function and their invere produce the 4 poible bit interval CE OQPSK trajectorie. able 4 lit lower bound for rm and maximum phae deviation. Exceive I and Q zero croing jitter can diturb carrier and ymbol timing recovery mechanim. he CE OQPSK modulation create ignificant ISI related jitter. ranmitter exhibiting jitter much beyond that inherent in the technique hould be ued with caution. Peak-to-peak and rm jitter i computed by projecting z outer contellation point ample onto the ymbol timing axe. Realitic lower bound are lited in table 6. EXAMPLE Figure 6-9 in the appendix are ample product taken from a commercial 5-Watt FQPSK-JR X with operating condition: carrier frequency = 70.5 MHz, and bit rate = 5 Mb/. Space doe not allow a detailed review of reult. However, comparion of the tabular data in figure 6 with correponding bound in table -4 and 6 hould lead the reader to the concluion that thi i a good X deign. V are marked with croe in figure 7 along with the radiu and angle of each. he ytematic variation of V radiu i due to LA interaction with modet modulation ymmetry defect preent in thi particular X. Four dahed curve in figure 8 preent ideal QPSKdeal reference waveform, projected I channe and projected Q channel performance repectively. he olid curve i the actual prediction of U AWG detection performance. hree circled data point were taken from a commercial SH benchmark demodulator connected to thi U. Figure 9 how the baeband power pectrum of each channel and the power pectral denity mak defined in reference []. COCLUSIO he off-line CE OQPSK ignal analyzer i applicable to all of the CE OQPSK variant addreed in reference [] and ha proven itelf to be a ueful upplement to conventional tranmitter teting procedure. Many lab already own high peed digitizing ocillocope. he only pecial requirement for thi particular tool i an appropriate licene for Matlab oftware and a reaonably high-peed peronal computer. An experienced uer who i alo familiar with the underlying modulation method will find that the data product can readily point to a number of defect ource not dicernable from conventional tet data. 8

10 REFERECES [] Jefferi R. P., FQPSK-B Baeband Filter Alternative, Proceeding of International elemetering Conference, San Diego, California, October -4, 00. [] Document 06-04, elemetry Standard, Secretariat, Range Commander Counci U.S. Army White Sand Miile Range, ew Mexico, May 004. [3] ou H., Darden S., and Yan.-Y, An Off-line Coherent FQPSK-B Reference Receiver, Proceeding of the International elemetering Conference, San Diego, California, October 3-6, 000. [4] Lee D., Simon M.K., and Yan.-Y, Enhanced Performance of FQPSK-B Receiver Baed on relli Coded Viterbi Demodulation, Appendix A, Proceeding of International elemetering Conference, San Diego, California, October 3-6, 000. [5] Proaki J.G., Digital Communication, 4 th edition, McGraw Hil ew York, ew York, 00. [6] Simon M.K., and Yan.-Y,, Performance Evaluation and Interpretation of Unfiltered Feher- Patented Quadrature Phae Shift Keying (FQPSK), JPL MO Progre Report 4-37, May 999. APPEDIX able Lower Bound of λ / SDR (db) FQPSK-B FQPSK-JR SOQPSK-G Linear 0. / / / 8 w/la 0. / / / 8 able X Lo at BEP=0-6 / 0-0 (db) Cae FQPSK-B FQPSK-JR SOQPSK-G Linear 0. / 0-0. / /. w/la 0. / / /. able 3 Upper Bound of oie Margin (db) FQPSK-B FQPSK-JR SOQPSK-G Linear 4 9 w/la able 4 rm/max. phae deviation (degree) FQPSK-B FQPSK-JR SOQPSK-G Linear.7/8.4.5/8 4.0/ w/la./ / 8 4. / tan able 5 Bit Interval Phae rajectorie of Reference Waveform 90 phae change 45 phae change o phae change in 0 < t τ b 0 < t τ bit interval b in β( t) ± =± β( t ) co () A β t tan A ± =± coβ( t) tan ± () A A =, t = Acoβ t β( ) πt in τ ( ) tan A β t ± Ain β( t) contant able 6 Baeline RMS/peak-peak Jitter (degree) Cae FQPSK-B FQPSK-JR SOQPSK-G Linear 3.5/7 3.3/6 4.4/6 w/la.8 / 8 4. / / 7 9

11 EXAMPLE PRODUCS FIGURE 6 FIGURE 8 FIGURE 7 FIGURE 9 0