MUOS KA DOWNLINK PERFORMANCE EVALUATION WITH TRANSMITTER DISTORTION

Liang C. ChuAdvanced Technology CenterLockheed Martin Corporation

Sunnyvale, CA 94089

and

Daisy ChengMUOS System Integration

Lockheed Martin CorporationSunnyvale, CA 94089

ABSTRACT

Mobile User Objective System (MUOS) employs a Ka-band feeder downlink from the satellite to the RadioAccess Facility (RAF). The feeder downlink transmits an

Octal Phase Shift Keying (8-PSK) modulated signal. AHigh Power Amplifier (HPA) is used for the amplificationof transmitted signals. The HPA produces distortions bycreating AM/AM and AM/PM modulations in thetransmitted signals. This non-linearity induces bandwidthexpansion and nonlinear distortion in the in-band signals.8-PSK is sensitive to HPA non-linear distortion. In thispaper, we analyze the sensitivity of the MUOS feederdownlink Bit Error Rate (BER) degradation to HPAOutput Back-Off (OBO). The analysis model consists ofthe non-linearity, Additive White Gaussian Noise (AWGN),and ideal carrier recovery and synchronization. MonteCarlo Bit Error Rate (BER) simulations are performedwith the analysis model to derive the distorted Energy-per-Bit to Noise Density Ratio (EbIN) at the average BER.Finally, we derive reduction in Eb/NO to achieve the targetBER and characterize EbIN0 degradation sensitivity toHPA OBO.

1. INTRODUCTION

Mobile User Objective System (MUOS) employs a Ka-band feeder downlink from the satellite to the RadioAccess Facility (RAF). 8-PSK is common for high datarate satellite links, providing bandwidth efficiency on theorder of 3 bits/sec/Hz. Each 8-PSK carrier contains up to11 user traffic WCDMA carriers to the Radio AccessFacility (RAF). However, 8-PSK is sensitive to non-lineardistortion of which the high power amplifier (HPA) is themain contributor. Given the large propagation losses atKa-band, the HPA operating point selection is a trade-offbetween the output power required to overcome the

propagation loss and waveform sensitivity to the non-linearity. Since Traveling Wave Tube Amplifiers(TWTAs) are individually tested and tuned tosimultaneously meet all specifications, the Output Back-Off (OBO) optimization for a specific TWTA is critical forcommunication performance. The OBO determines theoperating point on the TWTA gain and phase responsesversus input power. MUOS uses the Error VectorMagnitude (EVM) of the transmitted signal as a figure ofmerit. However, the performance of 8-PSK systems withcomplex magnitude and phase distortion has beeninvestigated [1]. In Ref [1], results show that equal valuesof EVM RMS may correspond to significantly differentSymbol Error Rate (SER) and Bit Error Rate (BER)performances. As expected, it also confirms that the phasedistortion is more critical than other types of distortion. InMUOS transmitted signals, there is a random distortionbetween phase and magnitude due to the signal passingthrough the TWTA and transmitted filters. Therefore,there are noticeably different SER with the sameEVMRMS specification because of the transmitteddistortion randomization. In addition, phase noise has asignificant effect on the 8-PSK satellite transmissionsignal. Mainly, it impacts the MUOS Ka feeder downlink,due to the high data rate and low Signal-to-Noise Ratio(SNR) operating point (from implementation of powerfulforward error correction coding). The discussion of thephase noise degradation to the Ka link is a complex topicand not the scope of this paper. In conclusion, EVM andSER (or BER) together are an accurate evaluation forcharacterizing the end-to-end Ka feeder downlink.

Transmitted 8-PSK with a targeted channel received BERof 10-5 is assumed. The Ka-band feeder downlinksimulation testbed consists of the non-linearly distortedtransmit signals, an AWGN channel, an ideal carrierrecovery, and ideal synchronization. In the receiver, ideal

phase-coherent demodulation of the carrier is performed.It is known that an explicit expression for the SER isdifficult to obtain for arbitrary decision regions, whenthere are more than two signals in a given region.Asymptotic error expressions assuming large SNR or somebounding techniques have been used to approximate theSER [2]. However, these cannot be applied to the MUOSnonlinearly-distorted transmit signals. The absence of asimple, traceable error probability evaluation techniquehas prevented a highly precise analytical determination ofthe performances of modulation schemes, including 8-PSK. We present a simple and general semi-analyticalmethod and simulation platform for calculating the exactbit error probability for the MUOS received signals withtransmitter non-linear distortion. This determines thereduction in Energy-per-bit to Noise-Density Ratio (Eb/N0)to achieve the desired target BER. The analysis isperformed as follows. Derive the averaged BER first forcoherent reception in the AWGN channel. Apply the non-linearity function, which changes the decision boundaries.Derive the average BER with distorted input signals.Finally, derive the distorted EJNO at the average BER andreduction in Eb/NO to achieve target BER. Determine thesensitivity of EJNO to HPA OBO.

2. KA-BAND FEEDER DOWNLINK SIMULATIONMODEL

Figure 1. depicts a high-level block diagram of the satellitepayload transmitter model. The first simulation module isthe source module that creates the 8-PSK modulatedsignal. This module first generates normally distributedrandom binary digits to create an 8PSK symbol vector. Itthen produces the In-phase (I) and Quadrature (Q) railswith random phase and amplitude imbalance. The I rail isdelayed by a specified amount to simulate I/Q symbolskew between the I and the Q rails. The two paths arefurther distorted by symbol jitter, modeled as phaseperturbation in the modulated signal. Then, the two signalvectors are modified so that a specific number of zeros areintroduced in between symbol values. This is necessary toemulate the period length of the simulated data. The I andQ vectors are then filtered by the Square Root RaisedCosine (SRRC) shaping filter. Together, the two vectorsform the complex modulated signal vector.

In the satellite payload, the output of the digital modulatoris processed by a digital-to-analog converter (DAC) beforeRadio Frequency (RF) transmission. In the simulation,the modulator output is filtered by the Analog Back End(ABE) and up-converter (U/C) filters in the payload path.The ABE is the reconstruction filter after the DAC, and the

U/C filter represents the frequency response of theIntermediate Frequency (IF) to RF frequency converter.(In MUOS, the IF is S-band, while the RF is Ka-band).This analysis is not focused on the filtering effects on thesignal. After filtering, the signal is distorted by worst-casespurs and incidental Amplitude Modulation (AM). Thedistorted modulated signal is further modified by themeasured response of the Linearized Traveling Wave TubeAmplifier (TWTA) module. Lastly, the signal istransmitted through a simulated AWGN channel to theideal matched receiver. The receiver is modeled as anideal matched filter to isolate the transmitter distortioneffects. The output multiplexer is not included because itsnon-linear amplitude and phase response versus frequencymay be compensated with equalization.

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Figure 1. Satellite Ka-band Transmitter SimulationModel

3. NONLINEARITY DISTORTION and FILTERS

A transmitted signal is amplified by the satellite TWTA toproduce high transmission power for Ka downlinksystems. The TWTA has a nonlinear property especiallyfor high power inputs and low OBO used in the Kadownlink. The non-linear characteristic of a TWTA isrepresented by its AM/AM and AMIPM modulationproperties. It can be characterized as [3].

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The AM/AM produces a different gain and AM/PM resultsa different phase shift. These effects can distorttransmitted signals and extend a signal bandwidth, causingirreducible detection errors.

In principle, the TWTA is a memoryless nonlinear device.In practice, it is usually preceded by a dynamic linear filterthat confines the signal spectral distribution [4]. Theoverall baseband equivalent system becomes a nonlinearsystem with memory. In addition to the spectralbandwidth spreading, when a transmitted 8-PSK signal

passes this memory device, it induces two impacts to thesignal: the symbol constellation warping (resulting inseveral SERs/BERs with a given target EVM) and theinter-symbol interference (ISI). Both of these arerandomized. Performance in these conditions can bespecified by both the transmitter/receiverEVMRms andBER/SER after the decoding. Furthermore, the primaryKa downlink performance requirement is to achieve thetargeted 105 BER.

3.1. TRANSMITTER DISTORTION MODELLING

The simulation generates mixer-related spuriouscomponents that are produced in the payload by the S-band to Ka-band upconversion after the filtering in Figure1, and prior to the TWTA. Worst-case spur interferencesare the two highest-level mixer products. This additivedistortion is modeled as sinusoidal signals at distinctspectral locations. The spurious interference is representedin the model as follows,

s(t)Spu,n, = SI cos(24ft)+ S2 cos(27W2t) (3)

where S1 and S2 are expressed in terms of the modulatedpower and the relative strength of each spur and where f1GHz and f2 GHz are the spur offsets from centerfrequency.

The simulation also generates an incidental amplitudemodulated waveform onto the 8-PSK modulated signal.The MUOS system is specified to constrain the modulationindex of the incidental AM. The simulated incidental AMwaveform is composed of the superposition of sinusoids atthe harmonic of the Electronic Power Conditioner (EPC)switching frequencies. Each of the sinusoids is offset byuniform distributed random phases. A typical fundamentalswitching frequency is given by 20 KHz, producingharmonics frequencies over two bands. The amplitude ofeach of the sinusoids in the lower band is specified to obeyout-of-band transmission regulations. The incidental AMis given by the following expression,

I(t)^ = [A, N N

(4)

where A1 and A2 are given in terms of dB below the carrier(dBc) described above, mn is the n-th modulation index, N,and N2 are the number of harmonics in the two EPCmodulation spurious bands, and (on are uniformly

distributed random phases. It follows that the 8-PSKmodulated waveform, s(t), distorted with incidental AM isgiven by

s (t) = s(t)[l + I(t)AM I (5)

The most significant contributor to transmit distortion isthe TWTA. The TWTA model uses measured data. Thedata is implemented as a look-up table that maps the inputsignal to the corresponding TWTA output power. Thesignal has to be normalized according to the specifiedOBO operating condition. This normalization scales theinput signal to operate at the corresponding Input Back-Off(IBO). Once the data is normalized, a subroutineinterpolates the input value to find the correspondingoutput power and output phase. These values are thenused to modify the value and phase of the input signal. Atypical linearized TWTA Amplitude Modulation toAmplitude Modulation transfer (AMIAM) curve at thisfrequency is linear to about 4.0 dB IBO. A typicalAmplitude Modulation to Phase Modulation transfer(AM/PM) response has approximately a + 1.8 deg phaseshift from linear at 4.0 dB IBO. These responses are oftentuned on a case-by-case basis, and each TWTA will have aunique resopnse.

3.2. MATCHED FILTER RECEIVER

The receiver model used in this simulation is an idealmatched receiver. The simulation first filters the receivedsignal with a square root raised cosine impulse filter withthe same excess bandwidth as the transmit filter. Thefiltered output is then sampled at the optimum point, anddecisioning is performed on the symbol at the optimumsample point to derive the received waveform phase value.The demodulated vector is then mapped and parceled intosets of three bits.

4. BIT ERROR RATE ESTIMATION

BER is an important transmission quality measure forsatellite communication systems. The targeted receiver10-5 BER is the assumed performance specification in theKa downlink. In general, an estimation of BER can beobtained by either adopting Gray approximation, oremploying a union bound method. However, theseapproximations in the low SNR region (the Ka receiver)are not accurate. Ref [5] has provided an ingenious andefficient method for the symbol error rate calculation,which is applicable to arbitrary 2-D constellations in anAWGN channel. Although it is a simplified analyticaltechnique, it is still complicated to apply to the Ka

downlink transmitter conditions. A simulation is typicallythe desired approach to model non-linear satellitecommunication systems. The simulation uses Monte CarloBER estimation. The demodulated vector is compared tothe reference modulator output. At a given EJNO, at least100 errors are collected before terminating the simulationand recording BER. The BER test has been performed forthe operational TWTA OBO point. BER results are

interpolated to derive the Eb/N. at 10-5.

5. DISTORTED TRANSMIT SIGNAL ANALYSIS

Figure 2 shows an example of the real component of theimpulse response of the transmitter without the LTWTAnon-linearity. The figure is only an example. Theimaginary component would look very similar.

Figure 3 shows an example of the real component of theimpulse response of the transmitter with the LTWTA non-

linearity. As can be seen, the non-linear distortion of theLTWTA has significant impact on the transfer functioncharacteristic of the payload transmitter. The figure isonly an example. The imaginary component would lookvery similar.

Figure 2. Ka-band Transmit Impulse Response withoutTWTA, Real or Imaginary Component

Figure 3. Ka-band Transmit Impulse Response withTWTA, Real or Imaginary Component

6. PERFORMANCE RESULTS AND DISCUSSIONS

Figure 4 shows the Eb/NO degradation with assumeddistortion parameters and the non-linearity for differentOBO values. The Eb/NO degradation is monotonicallydecreasing with TWTA OBO as expected. Thedegradation is more significant for OBO values less than2.5 dB. At this operating point, small amplitudemodulations in the signal constellation induce significantphase modulations. This is due to the steepness of theTWTA AM/PM response.

OBO is a trade-off between mitigation of AM/AM andAM/PM distortion impact and available output power.

Figure 4 data can be used for a preliminary OBO versus

E/NO degradation study. But this must be further verifiedby simulations with a receiver model. The disadvantage ofa higher OBO is that the TWTA operates at a lowerefficiency, and the transmit output power is reduced.Reduction in transmit power is a trade-off with the abilityof the forward error correcting coding to provide the targetBER at a lower Eb/N0. In other words,

(Eb/No)sat (Eb/No)th + (Eb/No)deg + OBO - Gcode, (6)

where(E/No)sat = the available Eb/No at the saturated TWTAoutput power(EJN4),h = theoretical Eb/NO for 8-PSK at BER of 10-5(Eb/No)deg = degradation due to transmitter distortion.OBO = TWTA Output Back-OffGcode = reduction in required Eb/NO to achieve BER of 10-5

Assuming the available Eb/No at the TWTA saturatedoutput is at least 13.0 dB,

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Figure 5. quantifies reduction in required Eb/NO versusTWTA OBO, using the data of Figure 4. The data can beused to estimate the FEC performance required, based onthe characteristics of the TWTA, namely saturated outputpower, OBO, and non-linear distortion. If demodulationand decoder performance is such that a higher Eb/NOdegradation may be tolerated, then it may be traded withamplifier efficiency and effective isotropic radiated power(EIRP).

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Figure 4. Eb/N0 Degradation Sensitivity to TWTAOutput Back-off

7. SUMMARY

In this paper, we present a simplified and accuratemethodology for predicting the MUOS Ka-band feederdownlink sensitivity to TWTA non-linearity. Thesimulated 8-PSK waveform is distorted by the measuredTWTA gain and phase responses versus input power inaddition to non-ideal transmit hardware. BER results arecollected at various OBO values to determine thesensitivity of Eb/NO to HPA OBO. The snap-shot of 8-PSKlink performance with an ideal receiver shows that 8-PSKis very sensitive to the non-linear profile of a specificTWTA, and it is critical to perform the OBO optimizationanalysis early in the system design. The TWTA operatingpoint selection is a trade-off between the required outputpower, payload operating power efficiency, and waveformsensitivity. The methodology of this paper may be used asa guideline for MUOS feeder downlink communicationsdesign trades. Furthermore, the methodology may beextended to performance evaluation and specification ofother communication links in the MUOS system

REFERENCE

[1] J. Pinto and I. Darwazeh," Phase Distortion and ErrorVector Magnitude for 8-PSK Systems", Electronics Letter37 (7), pp 437438, 29' March 2001.[2] G. J. Foschini, R. D. Gitlin, and S. B. Weinstein,"Optimization of two dimensional signal constellations inthe presence of Gaussian noise," EEE.E Trans. Commun.,vol. COM-22, pp. 28-37, Jan. 1974.[3] A. A. M. Saleh, "Frequency-independent andfrequency-dependent nonlinear models for TWTamplifiers," IEEE Trans. Commun., vol. 29, pp. 1715-1720, Nov. 1997.[4] S. Pupolin and L. J. Greenstein, " Digital radioperformance when the transmitter spectral shapingfollowing the power amplifier," EEE Trans. Commun.,vol. COM-35, No. 3, pp. 261-266, March 1987.[5] J. W. Craig, "A new simple and exact result forcalculating the probability of error for two-dimensionalsignal constellations," Proc. IEEE Milit. Commun. Conf.,pp. 571-575, 1991.

Figure 5. Reduction in EJNO vs. Output Back-Off

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