RFI modeling and prediction approach for SATOP

RFI1 Modeling and Prediction Approach for SATOP Applications: RFI Prediction Models Tien M. Nguyena, Hien T. Tranb, Zhonghai Wangc, Amanda Coonsb, Charles C. Nguyena, Steven A. Laned, Khanh D. Phamd, Genshe Chenc, Gang Wangc a The Catholic University of America, bNorth Carolina State University, c Intelligent Fusion Technology, Inc, dAFRL/RVSV, New Mexico Abstract This paper describes a technical approach for the development of RFI prediction models using carrier synchronization loop when calculating Bit or Carrier SNR degradation due to interferences for (i) detecting narrow-band and wideband RFI signals, and (ii) estimating and predicting the behavior of the RFI signals. The paper presents analytical and simulation models and provides both analytical and simulation results on the performance of USB (Unified S-Band) waveforms in the presence of narrow-band and wideband RFI signals. The models presented in this paper will allow the future USB command systems to detect the RFI presence, estimate the RFI characteristics and predict the RFI behavior in real-time for accurate assessment of the impacts of RFI on the command Bit Error Rate (BER) performance. The command BER degradation model presented in this paper also allows the ground system operator to estimate the optimum transmitted SNR to maintain a required command BER level in the presence of both friendly and un-friendly RFI sources. Key Words: RFI modeling and prediction, RFI prediction, Carrier synchronization loop, Signal-to-Noise Ratio (SNR), Unified S-Band, RFI estimating and predicting, Command, Bit Error Rate (BER)

1. Background and Introduction This paper is a follow-up to the initial effort on RFI modeling and prediction topic that our team presented at the 2015 SPIE conference [1]. The focus of this paper is to describe the analytical and simulation models for RFI prediction, and present the corresponding analytical and simulation results for various operating scenarios to illustrate the performance prediction of a typical USB SATOPS Command system. The paper is organized as follows:  Section 2 describes the analytical models to predict the USB waveforms acquisition performance in the presence of narrow band or CW RFI and wideband or WB RFI,  Section 3 presents the simulation and analytical models to predict the USB waveforms tracking performance in the presence of CW and WB RFI’s,  Section 4 provides the analytical models to predict the USB waveforms Bit Error Rate Performance in the presence of CW and WB RFI’s,  Section 5 presents analytical and simulation results obtained from the RFI prediction models presented in Sections 2, 3 and 5.  Section 6 discusses the integration of the RFI prediction models presented in the Sections 2, 3 and 5 into the IFT (Intelligence Fusion Technology, Inc.) SATCOM Tool  Section 7 presents the conclusion of the paper and describes the way-forward.  Section 8 provides the references.

2. RFI Analytical Models for Assessing USB Waveforms Acquisition Performance 2.1.

Standard Carrier Acquisition Approach

Most USB Command Detector Unit (CDU) performs carrier acquisition at the Satellite by going through four Carrier Modulation Mode (CMM) recommended by the Consultative Committee for Space Data System (CCSDS) [Ref. 2] as shown in Table 1. For CMM-2 the “acquisition sequence” is usually an alternating sequence (+1) with a predefined length L in terms of number of command bits N. The length L is usually selected using the following relationship: 1

RFI = Radio Frequency Interference Sensors and Systems for Space Applications IX, edited by Khanh D. Pham, Genshe Chen, Proc. of SPIE Vol. 9838, 98380I · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2223518

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𝑳 = 𝟐𝑵 Equation 1 The “idle sequence” is usually a nonalternating sequence. CCSDS also recommends two approaches for the carrier frequency. The approaches are described in Figure 1. The main difference between the two approaches is the approach for reacquiring the carrier when the subcarrier and/or data timing synchronizers drop lock. Approach 1 assumes the subcarrier and/or data timing synchronizers drop lock but the carrier synchronizer is still “in-lock”. Approach 2 assumes the subcarrier and/or data timing synchronizers drop-lock and the carrier synchronizer is also “drop-lock”. Carrier Acquisition Approach 1 Begin Command Session 1. CMM-1:

UNMODULATED CARRIER ONLY

CARRIER MODULATION MODE (CMM) CMM-1

UNMODULATED CARRIER ONLY

CMM-2

*

CARRIER MODULATED WITH "ACQUISITION SEQUENCE"

CMM-3

CARRIER MODULATED WITH COMMAND DATA

CMM-4

CARRIER MODULATED WITH "IDLE SEQUENCE"

* Note that the modulation index is set at 900 for this mode Table 1. Carrier Modulation Mode (CMM) for SATOPS USB Acquisition

Carrier Acquisition Approach 2 Begin Command Session 1. CMM-1:

DESCRIPTION

UNMODULATED CARRIER ONLY

The carrier acquisition mode includes carrier frequency acquisition and carrier phase acquisition modes. The subsections below describe these two modes.

2.2.

3. (CMM-4): (OPTIONAL: CARRIER MODULATED WITH IDLE SEQUENCE)

4. CMM-3: CARRIER MODULATED WITH DATA: TRANSMIT ONE FRAME

5. (CMM-4): (OPTIONAL: CARRIER MODULATED WITH IDLE SEQUENCE)

6.

REPEAT (4) AND (5) FOR EACH FRAME

7.

CMM-1: UNMODULATED CARRIER ONLY

End Command Session

Carrier Frequency Acquisition Mode

2. CMM-2: CARRIER MODULATED WITH ACQUISITION SEQUENCE

2. CMM-2: CARRIER MODULATED WITH ACQUISITION SEQUENCE

3. (CMM-4): (OPTIONAL: CARRIER MODULATED WITH IDLE SEQUENCE)

4. CMM-3: CARRIER MODULATED WITH DATA: TRANSMIT ONE FRAME

5. (CMM-4): (OPTIONAL: CARRIER MODULATED WITH IDLE SEQUENCE)

6.

REPEAT (4) AND (5) FOR EACH FRAME

7.

CMM-1: UNMODULATED CARRIER ONLY

End Command Session

Figure 1. Carrier Acquisition Approaches for USB SATOPS Systems

PLL will lock onto the carrier signal, Assuming that the selected sweep rate is not too large. In practice, the SATOPS USB receiver utilizes a hard limiter in front of the PLL to control the tracking loop. The second order PLL is typically employed by military, civil and commercial satellites for tracking the carrier signal component. The minimum Sweep rate and Probability of Lock for the loop are usually obtained by simulation using actual operating conditions. When the carrier is acquired, the PLL will track it with certainty, i.e., with Probability of Lock greater than 90%. For Frequency Sweep technique, the carrier frequency acquisition time, TFreq, which is developed using the minimum sweep rate specified in Figure 23 and simulation results using actual operational conditions from practical SATOPS missions, is given by:

The most commonly used technique for frequency acquisition mode is the Frequency Sweep Technique shown in Figure 2. The technique consists of the following steps: (i) Step 1: Select the frequency sweep rate based on the estimated received Carrier signal-to-Noise power Ratio or CNR or Carrier SNR. The frequency sweep rate as a function of received signal power is derived based on simulation and actual operational data; (ii) Step 2: Uplink command carrier frequency is swept during carrier acquisition using the selected sweep rate; Step 3: When the command signal carrier frequency and the receiver PLL VCO frequency coincide, the Frequency

DwUn  2fUn

wVCO

where f Un  Carrier frequency uncertainty due to

wF

platform dynamic and VCO drift, etc Search Region = DwUn

Signal Frequency, wC

w0

.

Dw = Sweep Rate

Lock In

Time

Figure 2. Carrier Frequency Acquisition Using Frequency Sweep Technique

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TFreq 

DwUn 

Dw



2fUn 

Dw

where fUn  Frequency uncertainty due to Doppler, VCO drift, etc

Equation 2

and 1/ 2     1   , for 3  Loop SNR Acq  4.75 D w  Sweep rate in Hz/sec  w 1    Loop SNR Acq - 2     1/ 2      2 w N2 1         D w     Loop SNR Acq - 4  , for 6  Loop SNR Acq  9.5  w N2 , for Loop SNR Acq  9.5   2 

2 N

2 BLAcq  1  1  2 ,   0.707      BLAcq  Acquisition loop bandwidth

Equation 3

Equation 4

w N2 

Equation 5

Note that during acquisition, the Loop SNR is defined as:

J 02 (m) PT N 0 BLAcq Carrier Phase Acquisition Mode

Loop SNR Acq  2.3.

For carrier phase acquisition mode, the most commonly used techniques in practice are carrier phase sweep and Synchronization (or sync) word. The carrier phase acquisition process is described in Figure 3, and is briefly described as: (i) T0 = Time required for the PLL to estimate the initial phase 0, (ii) Te = Time it takes the PLL to reach steady state phase errore, and (iii) The Carrier phase acquisition time, TPAcq, is calculated using the following relationship: TPAcq = T0 + Te Equation 7 The carrier phase acquisition time improves significantly with phase aided acquisition using the Sync Word or phase sweeping technique to estimate initial phase. The discussion of these techniques is provided below.

2.3.1.

Equation 6

Phase, Rad

Carrier Phase Acquisition Using Sync Word Technique

Initial Phase

Steady State Phase Error, O

Time, sec Lock In

Figure 3. Carrier Frequency Acquisition Using Typical carrier phase acquisition technique is to use Sync Frequency Sweep Technique Word (or alternating sequence or acquisition sequence) to estimate initial phase. This subsection assumes that the Doppler frequency and timing are known in advance and that the command data is formatted as an NRZ rectangular data pulse, and the sync word or acquisition sequence with length L is known, and the sync word is transmitted during CMM-2 (see Table 1), using direct modulation with word sequence. The performance of the ML Phase Estimator shown in Figure 25 is expressed in terms of the variance of the estimated carrier phase, which is given by [Ref. 3]:

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 2  var C   C   ^

^

C





 N0 1 1  1    .  2 2 L (2 J 1 (m) PT Tb )  2 L   Bit SNR Acq 

where

Equation 8

2 J 12 (m) PT Tb N0 The above equation as a function of Bit SNR is only for acquisition mode. For a given bit SNR and a specified variance of the estimated carrier phase, the length, L, of the sync word sequence is determined using Equation 8. Thus, the carrier phase acquisition time using sync word of length L, TPhase_Sync, is found to be: 1 Equation 9 TPhase _ Sync   LTb 2 BLAcq where L  Length or number of bits in the sync word Bit SNR Acq 

Tb  Sync word bit duration in second BLAcq  Acquisition loop bandwidth in Hz The length of sync word must be selected to ensure the variance of the carrier phase estimate error is small such that the time it takes the PLL to reach steady state phase error, e , is about 1/2BAcq-DL. The acquisition models presented here ensure the probability of synchronization failure at 10-8.

2.3.2.

Carrier Phase Acquisition Using Sync Word Technique

Based on the simulation results using the various sources, the carrier phase acquisition time using phase sweeping technique is found to be: TPhase _ Swp

12.2  1 , for Loop SNR Acq  10 dB   2 B 4 BLAcq   LAcq 1 8   , for Loop SNR Acq  14 dB  2 BLAcq 4 BLAcq

Equation 10

The total carrier Acquisition Time, Tacq, is calculated using the following relationship:

TAcq  TFreq  TPhase

Equation 11 Where TFreq is defined in Eqn. 2 and TPhase is defined as in Eqn. 9 or Eqn. 10, depending on the phase sync technique used by the SATOPS USB receiver.

2.3.3.

Carrier Phase Acquisition Performance in the Presence of RFI 2.3.3.1 Analytical Models of PLL Acquisition with CW RFI

The CW RFI signal model is defined as: I (t )  2 PI cos(2 ( f c  Df c )t   I )

where PI  RFI power Df c  RFI frequency offset from the desired carrier frequency f c

 I  RFI phase

Equation 12 For CW RFI, the effects of RFI depend on the RFI carrier frequency, namely, Case 1 for out-of-band interference, and Case 2 for in-band interference. The in-band interference occurs when the RFI carrier frequency is within the carrier acquisition loop bandwidth, BLAcq, and the out-of-band interference happens when RFI carrier frequency is outside the carrier tracking loop bandwidth.

Case 1 : Δf C  B LAcq For Case 1, the loop SNR in the presence of CW RFI is given by:

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LSNRCW 1 

LSNRAcq D Acq1

Equation 13

where

J 02 (m) PT Equation 14 , and D Acq1  1 N 0 BLAcq For case 1, the carrier Acquisition Time, Tacq, remains the same as the non-interference case presented in the previous section. LSNR Acq 

Case 2 : Δf C  B LAcq For Case 2, the loop SNR in the presence of CW RFI is given by: LSNRAcq LSNRCW  2  D Acq  2 where: D Acq  2  1  INR

Equation 16

where INR 

Equation 15

PI N0

INR is defined as the Interference power-to-Noise Ratio. For case 2, the carrier Acquisition Time, Tacq-CW-2, will be longer due to the Loop SNR degradation by a factor

D Acq 2 . The frequency sweep rate will be calculated using LSNRCW  2 , i.e.     1  Dw CW  2  w N2 1     Loop SNR CW - 2 - 2 

1/ 2



D wCW  2

 , for 3  Loop SNR CW - 2  4.75 

1/ 2      2 w N2 1            LSNR CW -2 - 4  , for 6  LSNR CW -2  9.5  w N2 , for LSNR CW -2  9.5   2

2 BLAcq  1  1 ,   0.707    2  BLAcq  Acquisition loop bandwidth

Equation 17

Equation 18

w N2 

Equation 19

The carrier frequency acquisition time becomes:

TFreqCW 2 

2fUn 

D wCW 2

Equation 20

Similarly, for case 2, the carrier phase acquisition time becomes 12.2  1  , for LSNR CW -2  10 dB  2B 4 BAcq DL  TPhase _ Swp CW  2   Acq DL 1 8   , for LSNR CW -2  14 dB 2 B 4 B Acq  DL  Acq DL TPhase _ SyncCW 2 

1  LCW 2Tb 2 BLAcq

LCW 2  Required length or number of bits in the sync word in the presence of CW RFI

Equation 21

Equation 22

Tb  Sync word bit duration in second

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For CW RFI case 2, the performance of the ML Phase Estimator becomes:

 1   1  INR   .     2 LCW 2   Bit SNR Acq 

2

^

 C CW  2

Equation 23

where bit SNR is defined for USB signal as: Bit SNR Acq 

2 J12 (m) PT Tb N0

Equation 24 To compensate for the CW RFI, one can increase the length of the sync word or the Bit SNR. For phase sweep technique, the carrier acquisition time in the presence of CW RFI becomes:

TAcq Sweep CW  2  TFreq CW  2  TPhase _ Swp CW  2

Equation 25

For sync word technique, the carrier acquisition time is given by:

TAcq Phase SyncCW  2  TFreq CW  2  TPhase _ Sync CW  2

Equation 26

2.3.3.2 Analytical Models of PLL Acquisition with WB RFI The WB RFI Signal is defined as: I (t )  2 PI d I (t ) cos(2 ( f c  Df c )t   I ) d I (t ) 

Equation 27



 I n . p(t  nTI   ),

n  

where PI  RFI power TI  RFI bit duration in seconds, where TI  Tb Df c  RFI frequency offset from the desired carrier frequency f c

 I  RFI phase

The loop SNR in the presence of WB RFI can be shown to have the following form: LSNRAcq LSNRWB  D AcqWB

Equation 28

where the loop SNR is given by:

LSNR Acq 

J 02 (m) PT N 0 BLAcq

Equation 29

é ù P P D Acq-WB = ê1+ I S RFI -WB (BDL , fUn ) ú , I = INR ë N0 û N0 1 S RFI -WB ( f , fUn ) = éë S I ( f - fUn ) + S I ( f + fUn ) ùû 2 BAcq- DL

S I ( f ) = TI

ò

- BAcq- DL

Equation 30

2

é sin(p fTI ) ù ê ú df , where TI = 1/ RI ë p fTI û

Again, fUn is defined as the frequency uncertainty due to Doppler and VCO drift, etc. For phase sweep technique, the carrier acquisition time in the presence of WB RFI becomes:

TAcq Sweep WB  TFreq WB  TPhase _ Swp WB

Equation 31

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For sync word technique, the carrier acquisition time is:

TAcq Phase Sync WB  TFreq WB  TPhase _ Sync WB where

Equation 32

2fUn

TFreqWB 



D wWB

Equation 33

where 

D wWB

1/ 2      2 wn2 1            LSNR WB - 4  , for 6  LSNR WB  9.5  wn2 , for LSNR WB  9.5   2

TPhase _ Swp WB

12.2  1  , for LSNR WB  10 dB  2 B 4 BLAcq LAcq  1 8   , for LSNR WB  14 dB  2 BLAcq 4 BLAcq

TPhase _ SyncWB 

1  LWB Tb 2 BLAcq

LWB  Required length or number of bits in the sync word in the presence of WB RFI

Equation 34 Equation 35

Equation 36

Tb  Sync word bit duration in second

For WB RFI, the performance of the ML Phase Estimator becomes:

2

^

 C WB

 1   D AcqWB  .     2 LWB   Bit SNR Acq 

Equation 37

D Acq-WB = éë1+ INR.S RFI -WB ( BAcq-DL , fUn ) ùû 1 S RFI -WB ( f , fUn ) = éë S I ( f - fUn ) + S I ( f + fUn ) ùû 2 2

BAcq- DL

S I ( f ) = TI

Equation 38

é sin(p fTI ) ù ê ú df , where TI = 1/ RI ò p fTI û - BAcq- DL ë

For the ML Phase Estimator, the acquisition loop bandwidth, BAcq-DL, is identical to LWB. To compensate for the WB RFI, one can increase the length of the sync word or the Bit SNR.

3. RFI Analytical/Simulation Models for Assessing USB Waveforms Tracking Performance The performance of the PLL is characterized by the variance of the tracking phase error,  2c , and in the absence of RFI, it is given by: D  2c  LSNR where LSNR = Loop SNR =

Equation 39

PC ,note that PC / N 0 is the carrier SNR N 0 BL

PC = J 02 (m)PT

Equation 40

é ù P D = ê1+ C SCD (1,0) ú N ë û 0 SCD (k, f ) =

¥

å

k=1,k=odd BL

J k2 (m) éë S d ( f - kf SC ) + S d ( f + kf SC ) ùû 2

é sin(p fTb ) ù S d ( f ) = Tb ò ê ú df , where Tb = 1/ Rb p fTb û - BL ë

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Note that when fSC > 4Rb,  2c becomes:

 2  c

1 LSNR

Equation 41

In practice, for reliable tracking, the Loop SNR is usually set at about 11 dB or more to ensure reliable tracking performance.

3.1

Analytical Models of PLL Tracking with CW RFI

The CW RFI signal model is defined as in Eqn. 12. There are two cases, namely, Case 1 for out-of-band interference, and Case 2 for in-band interference.

Case 1 : Δf C  B DL For Case 1, the variance of the tracking phase error,  2c , in the presence of CW RFI can be shown to have the following form: D  2c  LSNR Here D is defined as in Eqn. 74, and for fSC > 4Rb, D becomes 1.

Equation 42

Case 2 : Δf C  B L For Case 2, the variance of the tracking phase error,  2c , in the presence of CW RFI can be shown to have the following form: D  2  CW LSNR D CW  1  INR P INR  I  Interference - to - noise power ratio N0 c

Equation 43

Here one can assume that fSC > 4Rb. Note that when INR is greater than the carrier SNR, the PLL will drop lock on the command Signal and lock onto the CW RFI signal. Note that for this case, the effective loop SNR, LSNR Eff , is calculated from Eqn. 43, using: LSNREff  LSNR

DCW

.

3.2.

Analytical Models of PLL Tracking with WB RFI

The WB RFI Signal is defined as in Eqn. 27. The variance of the tracking phase error,  2c , in the presence of CW RFI can be shown to have the following form:

 2  c

DWB LSNR

Equation 44

Here one can assume that fSC > 4Rb, and the degradation factor DWB is found to be: DWB  1  INR.SWB ( BL , TI , Df C ) INR 

Equation 45

PI N0

SWB ( f , TI , Df C ) 

1 S RFI ( f  Df C )  S RFI ( f  Df C ) 2

where

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S RFI ( f )  TI

2

BL

 sin(fTI )   fT  df  I   BL 

Equation 46

here TI  1 / RI  Tb  1 / Rb

Note that for this case, the effective loop SNR, LSNR Eff , is calculated from Eqn. 81, using: LSNREff  LSNR

DWB

.

3.3.

Simulation Model of PLL Tracking with CW RFI

This section presents the simulation models for a second-order PLL using Type I imperfect integrator. Figure 4 depicts a block diagram of this PLL. The carrier Tracking Phase Error of a typical Second Order PLL in the Presence of RFI can be characterized by a differential equation shown below [5]:   0 1 d 1  e (t )   FA ( p) sin( e (t ))  ISR sin( e (t )  D 0t  D 0 )  n(t ) KJ 0 (m) PT dt KJ 0 (m) PT J ( m ) P 0 T  

Equation 47

where “p” is defined as the heavy side operator:

p

d (.) dt

Equation 48

For typical NASA, civil and commercial SATOPS receiver using Type I integrator, the loop gain and filters shown in Figure 4 are given below [5, 6]: Equation 49 Equation 50 Equation 51 Equation 52 Where Equation 53 Equation 54 The phase smoother filter V(s) is defined as:

I (t )

 e (t )

n(t )

e(t )

S (t )

r (t )  c (t )

FA ( s)  F ( s)

Imperfect Integrator loop filter Type I:

AK.F(s)

VCO (t ) KVCOK(s)

Figure 4. Simulation Model for Incorporating Carrier Tracking Error into Typical Type I Imperfect Integrator Second Order PLL

Equation 55 The VCO filter is: Equation 56 For Type I Imperfect Integrator loop filter with the worst case CW RFI, Eqn. 47 becomes: d2 K'é n (t) ù q (t) = ê - sin(q e (t)) - ISR sin(q e (t)) - 1 ú dt 2 e t1 ë A' û 1 d 1 d - éë1+ K 't 2 cos(q e (t)) + K 't 2 ISR cos(q e (t)) ùû q e (t) + n1 (t) t1 dt A't 1 dt

Equation 57

where we have defined the worst case scenario when  I (t )  0 , D 0  0 , and D 0  0 . The parameters A’, K’ and ISR are defined as: Equation 58 A'  J 0 (m) 2 PT

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K AK .KVCO  A' J 0 (m) 2 PT P ISR  I PT

Equation 59

K '

Equation 60

Note that n1(t) is the defined as:

n1 (t )  nc (t ) cos( e (t ))  nS (t ) sin( e (t ))

Equation 61

where nC(t) and nS(t) are the in-phase and quadrature components of the AWGN n(t). Viterbi [Ref. 36] has shown that n1(t) is essentially white Gaussian noise with spectral density N0/2 when the carrier loop bandwidth is smaller than the input noise bandwidth. Using Ref. 5, Eqn. 57 can be transformed into two first-order differential equations that are suitable for simulation using MATLAB program. If we define TS as the sampling interval and “n” as the number of sample points, the Eqn. 57 can be rewritten as: q e ((n +1)TS ) = q e (nTS ) + TSq e' (nTS )

Equation 62

T K'é n (nT ) ù q ((n +1)TS ) = S ê -sin(q e (nTS )) - ISR sin(q e (nTS )) - 1N S ú t1 ë SNR û ' e

-

TS T ' é1+ K 't 2 cos(q e (nTS )) + K 't 2 ISR cos(q e (nTS )) ùq e' (nTS ) + S n1N (nTS ) û t1 ë t 1SNR

where

 e' (t ) 

d  e (t ) dt

Equation 63

and

 e' (nTS ) 

 e ((n  1)TS )   e ((n)TS )

Equation 64

TS

n1N (nTS ) 

n1 (nTS ) n1 (nTS )

Equation 65

When  I (t )   I 0 , D 0  0 , and D 0   0 , Eqn. 62 becomes:

q e ((n +1)TS ) = q e (nTS ) + TSq e' (nTS ) q e' ((n +1)TS ) = -

TS K ' é n (nT ) ù -sin(q e (nTS ) + q 0 ) - ISR sin(q e (nTS ) + q I 0 ) - 1N S ú t 1 êë SNR û

Equation 66

TS T é1+ K 't 2 cos(q e (nTS ) + q 0 ) + K 't 2 ISR cos(q e (nTS ) + q I 0 )ùq e' (nTS ) + S n1N' (nTS ) û t1 ë t 1SNR

Lock Point and Definition of Loss of Lock: It is assumed that the PLL is initially in-lock with the phase of the desired signal, and the RFI signal is subsequently injected into the receiver. Difference of Tracking Phase Error as a Function of Time Since the Type I imperfect integrator is of a lag-lead type filter, the PLL is SNR - 18dB.ISR - -15dB.lnitial Phase Offset - p04 rads a second-order loop, and consequently only one stable point in the phase 1 error region of (-, +). In this  Tracking Phase Enor as e Function of Time rr same region, there also exists -SNR= I6dB,ISR= -15áB, Initial Phase Oiset ppl4 rads a single saddle point. Thus, using the same argument in Ref. 5, the selected threshold for determining the loss of lock of a PLL is /2. This 4 Time. seconds threshold will be used in Figure 6. Difference of Tracking Phase analyzing the loss of lock of a Error vs. Time PLL using Type I imperfect 1.5 integrator. 0 4 5 6 7 9 10 Tone, seconds Eqn. 66 is simulated in MATLAB, and the results are presented Figure 5. Tracking Phase Error vs. Time in Figures 5, 6, and 7. These figures show the simulation of the second3

2

1

0

1

miní.om Imavauumam_T y' 2

3

5

2

Proc. of SPIE Vol. 9838 98380I-10 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/24/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

6

7

9

10

order Type I imperfect Integrator PLL with SNR = 16 dB, ISR = -15 dB, and initial phase offset 0 between the desired signal and the reference VCO phase is set at /4 radians. Figure 5 shows the tracking jitter settled down to /4 as expected. Figure 6 shows the difference of tracking error fluctuates around 0 radian, and Figure 7 shows the PLL’s VCO phase starts at 0 degrees and it eventually locks on to the incoming phase at /4 Type I Imperfect Integrator PLL Phase Plan Plot

SNR = 16dB, ISR = -15dB. Initial Phase Offset = p1/4 rads

2

1

o -1

-2

- SNR= 18dB,ISR= 25dB,Desired Phase Offset =O Rad,RFI Phase Offset =p1/18 rads

0.5 {

IIAMM MMr1EIM Typa I Imperfect Integrator PLL Phase Plan Plot

3

IM\

MEItMMAN

-14

m

óy

i

-0 2

-0.5

e_ C N

-0 8 -0 6 -0 4 Tracking Phase Error In Radians

-1

Figure 7. Difference of Tracking Phase Error vs. Time

w

2 a

-12

1.5

-2

-0.22

-0 2 -0.18 -0.18 -0.14 -0.12 -0 1 -0.08 -0.06 -0.04 -0.02 Tracking Phase Error in Radians

Figure 8. Difference of Tracking Phase Error vs. Time

radians. When the initial phase offset 0 between the desired signal and the reference VCO phase is set at 0 rad, and the phase offset between the RFI signal and the reference VCO phase is set at /18 radians, Figure 8 shows that the PLL drops lock on the desired signal phase at 0 degree and it eventually locks on to the incoming RFI phase at /18 radians.

4. RFI Analytical Models for Assessing USB Waveforms BER Performance This paper assumes that the PLL tracking error follows the Tikhonov distribution and that the carrier tracking phase error is sufficiently small, such that by using Taylor series expansion on the average uncoded BER equation, one can approximate the uncoded BER as [Ref. 4]: BERRL 





1 1 1 erfc BSNR0  BSNR0  2e BSNR0  2 2 

Equation 67

where BSNR 0  2 J12 (m)

PT Tb N0

1 LSNR0

 2 

As defined earlier, the PLL tracking loop bandwidth is BL and the carrier tracking loop SNR, LSNR0, is defined as: P Equation 68 LSNR  J 2 (m) T 0

0

N 0 BL

The uncoded BER, in the absence of RFI with small carrier tracking error, can be rewritten as a function of the carrier tracking loop SNR, LSNR0: 1 = erfc 2

BERRL

{

a ( BLTb ) LSNR0

}

1 1 + 2

p

a ( BLTb ) LSNR0 LSNR0

- a ( B T ) LSNR0 } e{ Lb

Equation 69

where

 2

Equation 70

J12 (m) J 02 (m)

The first term of Eqn. 49 represents the ideal BER performance with perfect carrier tracking, and the second term is the BER degradation due to imperfect carrier tracking due to the presence of AWGN. The imperfect carrier

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tracking represents by the carrier tracking Jitter,  2 . This term is also defined as the “Radio Loss” (RL). From Eqn 49, the effective loop SNR is defined as:

Effective Loop SNR = LSNREff = a ( BLTb ) LSNR0

Equation 71

Substituting Eqn. 51 into Eqn. 49, the uncoded BER becomes: 1 a ( BLTb ) p LSNREff -{ LSNREff } 1 Equation 72 BERRL = erfc LSNREff + e 2 LSNREff 2 Note that the effective loop SNR must be chosen for the uncoded BER to meet the desired threshold BER value, e.g., BERThreshold = 10-9 or 10-6. The SATOPS BER performance in the presence of AWGN and RFI taking into account of imperfect carrier synchronization can be calculated using Eqn. 52 with the effective loop SNR models developed in the previous sections.

{

}

5. Simulation Results Verifying and Validating the RFI Analytical Models The analytical models for RFI detection and prediction, which were derived and discussed in previous section, were implemented in MATLAB (The MathWorks, Inc., Natick, MA) for verification and validation (V&V) purpose. These models were tested and verified for various operating scenarios to ensure the accuracy of the performance prediction of a typical USB SATOPS Command system. The MATLAB programs used to generate the results described in this section were implemented on an Apple MacBook Pro.

10 dB 1, =2075 MHz. rr=1.1 rad. e = 32 feo, Rb =2003 bps. ISR =-40 250

20 15

c ¢ir Z

5

{150

0

100

50

10

o

15 0

10

N.

00

5

10

15

20

25

20

25

LoopSNRAcq (dB)

SNR (dB) 140

06

120

06

100 :E.

0A

o -20

80

Jr 60 40

02

20

-_--10

0

10

LddpSNRA, (dB)

o

20

30

0

5

10

15

10

15

20

LoopSNRAbb (dB)

80

0

30

5

Figure 9. Plots of Total Carrier Acquisition Times Vs. Loop SNR Without RFI and With CW RFI at ISR = -10 dB.

O

20

10

20

50

20

-200

15

150

40 -10

10

LoopSNRAbb (dB)

H - 100

FB 60

o

5

200

100

¢zi

o

30

250

-N8 - no RFI

120

20

20

10

SNR

10.2075 MRL, db1.1 fad, o= a12 fad, Rb =2000 Ops,15R =-10 dB, R, =1 Ops 140

-roRFI

3

Figures 9-12 depict the impacts of CW and wideband RFI signals on the second order PLL acquisition performance, respectively. In particular, they compare the carrier acquisition times without RFI and in the presence of RFI as functions of loop SNR for the following cases:

30

-GSN

200

10

LddpSNRA,q (dB)

Figure 10. Plots of Total Carrier Acquisition Times vs. Loop SNR Without RFI and With WB RFI at ISR = -10 dB.

 Signal carrier frequency = fC = 2075 MHz  m = Command modulation index = 1.1 rad  The threshold carrier jitter  =/2 rad  Command Bit rate = Rb = 2 Kbps  Interference-to-Signal Power Ratio = ISR = -10 dB and -40 dB. Figure 9 shows the assessment of PLL Acquisition Performance in the Presence of CW RFI at ISR = -10 dB. The plots of loop SNR versus received SNR without RFI and with CW RFI are shown on the top left of Figure 9. The plots of carrier frequency acquisition times as functions of loop SNR without RFI and with CW RFI are shown on the top right of Figure 9. The plots of carrier phase acquisition times as functions of loop SNR without RFI and with CW RFI are shown on the bottom left of Figure 9. As expected, the acquisition time increases due to the presence of CW RFI. Figure 10 provides results for the assessment of the PLL acquisition performance in the

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presence of WB RFI at ISR = -10 dB. The plots of loop SNR versus SNR without RFI and with WB RFI are shown on the top left of Figure 10. The plots of carrier frequency acquisition times as functions of loop SNR without RFI and with WB RFI are shown on the top right of Figure 10. And, the plots of carrier phase acquisition times as functions of loop SNR without RFI and with WB RFI are shown on the bottom left of Figure 10. The results show that the acquisition time increases due to the presence of WB RFI. Figure 11 provides the assessment of PLL acquisition performance in the presence of CW RFI at ISR = - 40 dB. The plots of loop SNR versus SNR without RFI and with CW RFI are shown on the top left of Figure 11. The plots of carrier frequency acquisition times as functions of loop SNR without RFI and with CW RFI are shown on the top right of Figure 11. The plots of carrier phase acquisition times as functions of loop SNR without RFI and with CW RFI are shown on the bottom left of Figure 11. The results show that the total acquisition time 1 -2075MMz.m-l.l rad, e=,2 rad, Rb=2000 bps. I5R=i0 dB. R,=10pS 30

m

60

-NB -roR'I

50

20

40 10

¢

6 30 0

20

10

10

20 10

0

20

20 (dB)

30

10 20 Lo6pSNRAcq (dB)

30

10

30

SNR (dB)

LoopSNR

60

Ob

50 0.6

40 30

d 0.4

20

02 10

0

40

.10

0 10 20 L60pSNR (dB)

30

0 0

40Uri 1 =2075 MIR. m=1.1 rari, e: x2Iad, R6= 2000rrps, ISR =40 15

60

10

50

-CW

no R=1

40

HE

30 20

.10

10

45

0

20

10

0

30

4

8

10 12 8 LoopSNRAcq (dB)

4

8

10 12 8 LOBpSNR4G1 (dB)

SNR

-

14

60 50

40 J30

20 10

0

14

Figure 11. Plots of Total Carrier Acquisition Times as Functions of Loop SNR Without RFI and With CW RFI at ISR = -40 dB.

degradation is negligible when the CW RFI interference-to-signal power ratio, ISR, is at - 40 dB. Figure 12 presents the assessment of PLL acquisition performance in the presence of WB RFI at ISR = -40 dB. The plots of loop SNR versus SNR without RFI and with WB RFI are shown on the top left of Figure 12. The plots of carrier frequency acquisition times as functions of loop SNR without RFI and with WB RFI are shown on the top right of Figure 12. And, the plots of carrier phase acquisition times as functions of loop SNR without RFI and with WB RFI are shown on the bottom left of Figure 12. Similarly, for WB RFI, the numerical results show that the total acquisition time degradation is negligible when the ISR is at - 40 dB. Figures 13 shows plots of PLL tracking jitters v

l

S=

11

W L=

l'

W'DPJ

Z= '6eC = oDOZ aSl'Sdp DI.= Qa

='a'BD

01 'SdG

='8

Ol za

Figure 12. Plots of Total Carrier Acquisition Times as Functions of Loop SNR Without RFI and With WB RFI at ISR = -40 dB.

in the absence of RFI and with both CW and WB RFI signals as functions of loop SNR with DfRFI = 5 Hz, m = 1.1 rads, margin = 2 deg, Rb= 2Kbps, ISR = -10dB, RI= 10bps, BL= 10Hz. The plots show that the tracking performance of the PLL in the presence of CW RFI is worse than WB RFI under the specified operating conditions. Simulation results of PLL tracking jitters in the absence of RFI and with both CW and WB RFI signals as functions of loop SNR with DfRFI = 10 Hz, m = 1.1 rads, margin = 2 degs, Rb= 2Kbps, ISR = -10dB, RI= 10bps, BL= 10Hz are depicted in Figure 14. The plots show that the tracking performance of the PLL in the presence of CW RFI is still worse than WB RFI under the same operating conditions. But for this case, the

Figure 13. Plots of PLL Tracking Jitters in the Absence of RFI and Presence of CW/WB RFI Signals vs. SNR With DfRFI = 5 Hz

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plots show that the carrier tracking performance of the WB RFI is better than the previous case for DfRFI = 5 Hz. This is expected, since the RFI is moving away from the center carrier frequency. Figures 15-18 depict the BER performance due to AWGN and RFI signal as functions of loop SNR taking into account carrier synchronization loop. Figures 15 and 16 show plots of BER performance due to RFI for CW

c1ipFi-10HZ,m-1.lfâtl,om=2 deg, Rb=2000 bps, I5R -1008,R-10 bps, 8,-10Hz 35

25 . 2.

05-

-10

-5

0

LSNR (dB)

10

15

20

Figure 14. Plots of PLL Tracking Jitters in the Absence of RFI and Presence of CW/WB RFI Signals vs. LSNR With DfRFI = 10 Hz

and WB RFI signals and plots of BER performance in the absence of RFI and with both CW and WB RFI

Figure 18. Plots of BER due to RFI for Both CW RFI and WB RFI Signals vs. LSNR With DfRFI = 5 Hz. C 1,bn=5115 m=1.1

m4'=.a =2019.0p =200000& 0H=