Enhancement of the phase and frequency recovery for E-SSA protocol.

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UNIVERSITA’ DI PISA

Scuola di Ingegneria

Corso di Laurea in Ingegneria delle Telecomunicazioni

Laurea Magistrale

Enhancement of the phase and frequency recovery for the E-SSA

protocol.

Candidato: Relatore:

Chesi Ivan Prof. Filippo Giannetti

Tutors aziendali:

Ing. Marco Andrenacci Ing. Claudio Cicconetti

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Ad Alessia, ai momenti che ci aspettano, ai preziosi momenti trascorsi

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1 The Phase Noise Project

1.1 Background

This document contains the report of the activity of the Phase Noise Project carried out by the University of Pisa (UNIPI) in collaboration with MBI SrL. (MBI), the European Space Agency (ESA) and Eutelsat SA (EUT). The objective was to enhance the phase and frequency recovery algorithms created by MBI to build its E-SSA Demodulator.

The E-SSA protocol was originally proposed by ESA in 2008 to implement the air-interface of the messaging system adopted by terminals in a Mobile Satellite Services (MSS) platform based on L/S-band geostationary satellites [30]. E-SSA protocol establishes that E-SSA terminals can access the channel in a very asynchronous manner since the same spreading sequence and bandwidth are reused for a large number of terminals. This can occur provided the terminals are locked to the FWD link signal and also the congestion control information distributed by the hub enables transmission. The collisions caused by this asynchronous system are resolved by the hub using a Successive Interference Cancellation (SIC) algorithm. It exploits the inherent power unbalance due to fading provoked by the Land Mobile Satellite (LMS) channel and by G/T variation within the beam. In addition, in order to mitigate the effect of the MAI (Multi-Access Interference) the hub can introduce power unbalancing by means of the signaling channel. The original channelization of E-SSA for S-band Mobile Interactive Multimedia (S-MIM) [32][33] has been standardized by ETSI [31]. It includes modes with chiprates of 240 Kchip/s, 1920 Kchip/s and 3840 Kchip/s together with an information payload of 300, 600 and 1200 bits, bitrate of 15 and 30 Kbps and spreading factor 16, 64, 128 and 256.

At later stage, EUT involved the E-SSA protocol into F-SIM (Fixed Satellite Interactive Multimedia) in order to introduce a messaging return link to the commercial VSAT terminal via the innovative LNB, called Smart LNB1_{. This protocol can be operated on C, Ku and Ka bands.}

The air-interfaces of F-SIM were adapted to higher channelizations. The key characteristics are:

• Channelization: 1920 Kchip/s (2,5 MHz), 3840 Kchip/s (5 MHz) and 7680 Kchip/s (10 MHz)

• Info payload: from 304 bits to 12104 bits

• Spreading factor: 16, 32, 64, 128 and 256

• Bitrate: up to 160 Kbps

• F-SIM burst duration: 2 msec to 300 msec

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12 Finally, the ESA funded project FREQUENCY FLEXIBLE M2M TERMINAL MODEM DEVELOPMENT2_{introduced S-M2M (Satellite Machine-to-Machine), a new protocol}

specification with 4 modes (WF#1 to WF#4) for low data rates on C, Ku and Ka bands. S-M2M has the following key figures:

WF#1 WF#2 WF#3 WF#4

Channelization (Kchip/s) 240 240 240 240

Info payload (bits) 1200 1200 1200 640

Spreading factor 16 64 256 64

Bitrate (Kbps) 5 1,25 0,3125 1,25

burst duration (sec) 240 960 3480 512

Fig. 1 Key figures of S-M2M

MBI has been involved in the project since the start. At the current time MBI provides EUT with a commercial solution for F-SIM (named STARFISH, [18]) as well as many European companies with E-SSA and S-M2M TESTBEDs for laboratory and on-field R&D and test activities (i.e. using W2A and ARTEMIS satellites).

Recent test sessions with S-M2M and F-SIM showed performance degradations due to the effects of the phase noise (PN) of the communication channel as well as of the Local Oscillator of terminals. In particular, the performances of the S-M2M terminals were dramatically worsened by PN, while losses with F-SIM terminals were much lower.

Due to this an enhancement of the algorithms for phase and frequency recovery must be done. The algorithms implemented in E-SSA Demodulator and described in this document must be analyzed in presence of phase noise. The scope is to understand why the phase noise worsens the performances and how we can restore the performances obtained with only AWGN.

The E-SSA protocols addressed by this project are S-M2M [1] and F-SIM [9].

1.2 Executive Summary

The aim of the Phase Noise Project was to improve the performances of the E-SSA Demodulator for S-M2M and F-SIM by introducing enhanced phase and frequency recovery algorithms able to cope with such phase noise.

User requirements gathering were carried out in collaboration with ESA, MBI and EUT.

A trade-off analysis of the new algorithms which can be used to increase the performances of the E-SSA demodulator was carried out using a MATLAB simulator developed by the University of

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13 Pisa. It focused both on the performance improvements and the increased computational load resulting from the software implementation of the new algorithms on the E-SSA Demodulator, in order to allow for industrial development of the new proposed algorithms.

Given that the MBI E-SSA Demodulator is based on an SDR fully software architecture [34], the selected algorithms have been implemented in C++ by MBI.

At the time of writing, the feasibility analysis of the C++ development of all the new algorithms proposed by the current activities has been successfully completed. The selected ML DA algorithms selected in this document as optimum were implemented in the MBI E-SSA Demodulator.

Primarily, this document presents the performance results obtained by the V&V NDA (Viterbi and Viterbi No Data Aided) algorithm. V&V NDA is the original phase recovery algorithm3_used

by MBI. These performance results have been obtained using the C++ S-M2M Testbed developed by MBI, where the ability to introduce phase noise has been added by MBI. Finally, these results have been used to validate the V&V NDA MATLAB simulator developed by UNIPI.

In addition to the V&V algorithm, a study of the following 3 selected4_{candidate data-aided}

algorithms has been carried out:

• [algorithm#1] ML DA (Data Aided) using the pilot symbol within the control channel

of E-SSA with Sliding Window (SW) M=K: ML DA with Sliding Window (SW) [see 2.2 for definition] (M is the size of the sliding window in symbols while K is the moving step of the sliding window)

• [algorithm#2] ML DA with sliding window M and K=1

• [algorithm#3] Hybrid V&V: Hybrid V&V is based on two stages of phase recovery: the first is ML DA with M, K=1 that uses pilot symbols; the second is V&V NDA that uses only PDCH previously corrected by ML DA. These two blocks are preceded by frequency recovery for both PCCH and PDCH.

Furthermore, the satellite Doppler effects have been modelled and added to the MATLAB channel emulator while at the reception side, all the new 3 algorithms have been coupled with an initial frequency recovery algorithm.

3_{In fact, the pilot symbols present within the control channel of E-SSA is not used by the current}

implementation of the MBI E-SSA to improve the demodulation.

4_{The trade-off analysis of algorithms publicly available as well as the definition of the innovative Hybrid}

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14 Simulations (with and without Doppler effects) have been carried out with the aim of optimizing the large number of parameters associated with these estimators.

1.3 Conclusion Summary

The preliminary observations and conclusions are as follows:

• For windows greater than 10 ms, the V&V NDA algorithm is validated after the correction of the algorithm for phase noise generation in MBI E-SSA Demodulator. For windows smaller than 10 ms, the MBI E-SSA Demodulator cannot generate the window, thus validation is not possible.

• The current algorithm (V&V NDA) for phase and frequency recovery fails because of Phase Noise when low bit rate modes are used (i.e. S-M2M or F-SIM with high spreading factor). The PNIL (Phase Noise Induced Loss, see 2.2 for definition) for S-M2M is higher than 10 dB, meaning that the current implementation cannot be used in a real scenario.

• [algorithm#1] Good results for S-M2M can be obtained with ML DA with Sliding Window with K=M symbols. A simulation for parameters optimization with F-SIM is carried out in ‘Appendix 5: F-SIM optimization’. For this system the impact of phase noise is less relevant, however the parameters optimization is still required. For S-M2M, the PNIL obtained are approximately:

ML DA M,K=M WF PNIL (dB) @ BER=10-2 PNIL (dB) @ BER=10-3 DPNIL( ) (dB) @ BER=10-2 DPNIL( ) (dB) @ BER=10-3 Optimum M Optimum gain factor 1 0.6 0.6 0.6 0.6 160 88.89 % 2 1.6 1.7 1.6 1.7 90 88.89 % 3 2.6 2.9 2.7 2.9 40 71.56 % 4 0.8 1 0.9 1 60 78.22 %

(1) DPNIL is calculated using the frequency estimation based on preamble of PDCH and PCCH

• [algorithm#2] The reduction in the step size of the Sliding Window leads to a further improvement in the results. In particular, for WF#3 ML DA, a Sliding Window with length of M symbols and K=1 symbol is required in order to lower the implementation loss, due to the much lower bit rate. With this configuration, the PNIL for the S-M2M modes are:

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15 ML DA M,K=1 WF PNIL (dB) @ BER=10-2 PNIL (dB) @ BER=10-3 DPNIL( ) (dB) @ BER=10-2 DPNIL( ) (dB) @ BER=10-3 Optimum M Optimum gain factor 1 0.5 0.5 0.4 0.4 190 88.89 % 2 0.9 1.1 0.9 1 140 88.89 % 3 1.6 1.7 1.7 1.7 40 71.56 % 4 0.6 0.6 0.6 0.6 110 78.22 %

Again, the WF#3 is the least robust waveform.

• [algorithm#3] The best performance is obtained using algorithm [#2]. In order to further improve these performances, the Hybrid V&V was implemented. This algorithm could have had even better performances thank to using two stages for phase estimation and recovery. Enhancement on the performances are obtained for WF#1 and partially for WF#2 and WF#4 but, however, the decrease in BER is small.

WF DPNIL( ) (dB) @ BER=10-2 DPNIL( ) (dB) @ BER=10-3

Optimum Optimum Optimum gain factor 1 0.3 0.3 190 240 88.89 % 2 0.8 0.9 140 360 88.89 % 3 The same for ML DA M,K=1 The same for ML DA M,K=1 40 DISABLED 71.56 % 4 0.6 0.5 110 600 78.22 %

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16 Fig. 2 DPNIL [dB] vs SF at BER=10-3

As the SF increases, the symbol rate decreases, thus the waveform with higher SF is more sensitive to phase noise [see Section 5.4.4 and 8]. Note that the different performance for WF#2 and WF#4 is due to the different length of the interleaver and the different Gain Factor used [see Eq. 6 for definition].

Considering the above results, it is evident that the ML DA K=1 is the candidate algorithm for the upgrade of the current version of the MBI S-M2M Demodulator. The Hybrid V&V has the best performances, but the gain with ML DA K=1 is small and the computational cost increases.

1.4 Organization of the document

This document is divided into eight sections. Section 2 lists the acronyms and references used.

Section 3 shows the system architecture with the description of the E-SSA transmitter stages and of the channel emulator model used in this work. It includes the study of the different phase masks collected by MBI, ESA and EUT as well as a brief discussion of the Doppler effect.

Section 3.5 contains the description of the V&V NDA receiver implemented by MBI to demodulate F-SIM and S-M2M messages, as well as the architecture of the MATLAB simulator developed by UNIPI.

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17 Section 0 shows the validation of the MATLAB simulator which implements the V&V NDA algorithm with and without phase noise, and compares the MATLAB results with those obtained by the MBI receiver.

Section 5 reports the simulation results obtained with the MATLAB simulator running tests with three different phase recovery algorithms: V&V NDA (currently implemented on the MBI receiver), [#1] ML DA with Sliding Window with M=K symbols and [#2] ML DA with Sliding Window with length M symbols and K=1 symbol.

Section 6 provides the preliminary feedback on the frequency recovery and Doppler effect in ARTEMIS in addition to the simulation results on this topic.

Section 7 presents the simulation results obtained with the MATLAB simulator for Hybrid V&V. Finally, Section 8 describes the conclusions resulting from the comparison between a BER for V&V NDA, ML DA with Sliding Window with K=M symbols, ML DA with Sliding Window with length of M symbols and K=1 symbol and the Hybrid V&V.

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2 References

2.1 Acronyms

PN: Phase Noise

NDA: No-data aided

DA: Data Aided

PSD: Power Spectral Density

CDMA: Code Division Multiple Access

WF1-WF2-WF3-WF4: Waveform planned in S-M2M

BER: Bit Error Rate

S-M2M: Satellite Machine-to-Machine

F-SIM: Fixed Satellite Interactive Multimedia

V&V: Viterbi & Viterbi phase estimator

PCCH: Control channel in S-M2M and F-SIM

PDCH: Data channel in S-M2M and F-SIM

β: Identify the gain factor [see Eq. 6 for definition] on PDCH and PCCH.

SIC: Successive Interference Cancellation

SDR: Software Defines Radio

OVSF: Orthogonal Variable Spreading Factor is an implementation of CDMA

CDMA: Code Division Multiple Access

DSSS: Direct Sequence Spread Spectrum

MAI: Multiple Access Interference

BPSK: Binary Phase Shift Keying

MATLAB: Programming language uses for simulations

SF: Spreading Factor of CDMA

Tb: Time of bit

Ts: Time of symbol

Tc: Time of chip

PSD: Power Spectral Density

I/Q branch: In-phase and Quadrature branch on transmitter and receiver

SW: Sliding Window

Hybrid V&V: Hybrid Viterbi and Viterbi

2.2 Definitions

PNIL: Phase Noise Induced Loss. Indicates the loss between a system with only AWGN and a system with AWGN and phase noise impairments.

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20 | !" #$ %" ( ) & '$() !" ( ) #$ * +,(,- , ./'0 12. (1)

DPNIL: Doppler and Phase Noise Induced Loss. Indicates the loss between a system with only AWGN and a system with AWGN, phase noise and Doppler impairments.

4 |56 7

0 9:;< =>? , AB5 4CDDEFG(56)

& 7

0 9:;< CBEH =>? (56) AB5 IFEFJ;F5 KGCL M.11

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M, K and Sliding Window:

Using a Sliding Window (SW) on the received symbols is a way to slice a sequence of symbols received. There are two indices that characterize a Sliding Window:

1. M: is the length 2. K: is the step

For example the behavior of the Sliding Window with length M and step M (Sliding Window with K=M) is explained in Fig. 3:

M samples M samples M samples M samples

window window window window

Fig. 3 Sliding Window with length M and step M

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21 Parameter M defines the number of bits on which the phase estimation is performed.

-V&V NDA/DA with SLIDING WINDOW [5]

The Sliding Window is identified by a window with a length of M symbols that runs on the entire sequence of symbols received by the steps of K symbols.

The first block of simulations is made with the Sliding Window with K=M symbols [see Section 5.4].

The second block is made with the Sliding Window with a length of M symbols and K=1 symbol. These techniques are considered for the resolution of the problem affecting WF#3 [see Section 5.4.4].

M and K must be optimized.

Eb/N0: Eb is the overall energy (PDCH+PCCH) during simulations

Gain factor: It is a percentage of power on PDCH in relation to a power on PCCH. It is calculated as: ?A:B KAJ;CG O1 & _C9FGC9FG%PPQ %RPQS ∗ 100 (3) With: C9FG%PPQ U V1 + X (4) C9FG%RPQ U 1 V1 + X (5) Thus, ?A:B KAJ;CG (1 & ) ∗ 100 (6) For example, a Gain factor = 100% means all the power on PDCH ( 0).

DA: Data-aided (DA) means an algorithm of phase recovery that uses a pilot symbol for the phase estimation (PCCH).

NDA: An algorithm of phase recovery that uses only PDCH for the phase estimation.

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2.3 Notations

Index ‘i’: Index ‘i’ indicates the symbols at bitrate. For BPSK the symbol rate after mapper is equal to the bitrate. Thus, it indicates the symbols coming out the mapper.

Index ‘k’: Index ‘k’ indicates the symbols coming out the Turbo Encoder, therefore the rate of ‘k’ is three times the bitrate.

Index ‘m’: Index ‘m’ indicates the chip resulting from the spreading.

2.4 Reference documents

[1] "Air interface for Satellite Machine-to Machine (S-M2M) Physical Layer Specification, Return Link," 2015.

[2] N. Noels, H. Steendam and M. Moeneclaey, "Pilot-symbol assisted iterative carrier synchronization for burst transmission," IEEE, 2004.

[3] R. Harris and M. Yarwood, "A simulation study of the Viterbi and Viterbi carrier phase estimation algorithm," IEEE.

[4] S. Dris, P. Bakopoulos, I. Lazarou, C. Spatharakis and H. Avramopoulos, "M-QAM carrier phase recovery using the Viterbi-Viterbi monomial-based and maximum likelihood estimators," Optical Society of America, 2012.

[5] G. Corazza and R. D. Gaudenzi, "Pilot-Aided coherent uplink for mobile satellite CDMA networks," IEEE, 1999.

[6] N. Malek, "Optimization of the Viterbi and Viterbi carrier phase error detection algorithm," Islamic Azad University.

[7] A. Viterbi and A. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE, 1983.

[8] K. Cartwright and E. Kaminsky, "A simple improvement to the Viterbi and VIterbi monomial-based phase estimators," IEEE, 2006.

[9] Eutelsat, "Satellite earth stations and systems; Air interface for fixed satellite interactive multimedia (F-SIM); Part 3: physical layer specification, return link, asynchronous access".

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23 [10] M. Luise and R. Reggiannini, "Carrier frequency recovery in all-digital modems for

burst-mode transmissions," IEEE, 1995.

[11] M.Morelli and U.Mengali, "Feedforward frequency estimation for PSK: A tutorial review," IEEE, 1998.

[12] F.Giannetti, M.Luise and R.Reggiannini, "Simple carrier frequency rate-of-change estimators," IEEE, 1999.

[13] W.Gappmair, "Analysis of non-data-aided carrier frequency recovery with Luise-Reggiannini estimators pplied to M-PSK schemes," IEEE, 2005.

[14] S.Kay, "A fast and accurate single frequency estimator," IEEE, 1989.

[15] U.Mengali and M.Morelli, "Data-Aided frequency estimation for burst digital transmission," IEEE, 1997.

[16] M.Morelli and U.Mengali, "Feedforward carrier frequency estimation with MSK-type signals," IEEE, 1998.

[17] M.Morelli and U.Mengali, "Carrier-frequency estimation for transmissions over selective channels," IEEE, 2000.

[18] R. D. Gaudenzi, S.Cioni, N.Alagha, M. Andrenacci, A.Arcidiacono, S.Scalise, D. Finocchiaro, F. Collard and F. Blasco, "From S-MIM to F-SIM: making satellite interactivity affordable at Ku and Ka-band".

[19] "Local oscillator phase noise effects," InsideGNSS, 2010.

[20] E.Cianca and C. Sacchi, "EHF for satellite communications: the new broadband frontier," IEEE.

[21] D.Ham, W.Andress and D.Ricketts, "Phase noise in oscillators," IEEE.

[22] G.Gallinaro and R. Gaudenzi, "ME-SSA: an advanced random access for the satellite return channel," IEEE, 2015.

[23] R. D. Gaudenzi, "High efficiency satellite multiple access scheme for machine to machine communications," IEEE, 2012.

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24 [24] M. Andrenacci, G.Mendola, F.Collard, D.Finocchiaro and A.Recchia, "Enhanced spread

spectrum aloha demodulator implementation, laboratory tests and satellite validation," International journal of satellite communications and networking, 2014.

[25] ESA, "Live Validation of S-MIM Protocol using L-Band Payload of ARTEMIS," 2015. [26] Eutelsat, "Ka-UPC," 2011.

[27] ETTUS, "USRP n200/n210," 2012.

[28] MBI, "E-SSA DEMODULATOR_algorithm description," 2015.

[29] G. L. De gaudenzi, "Signal Synchronization for Direct-Sequence Code-Division Multiple Access Radio Modems," ETT, 1998.

[30] D. G. R. Oscar del R'ıo Herrero, "A High Efficiency Scheme for Quasi-Real-Time Satellite Mobile Messaging Systems".

[31] "TSI TS 102 721-3 V1.2.1," 2013-8.

[32] "Satellite Earth Stations and Systems (SES)".

[33] "Air Interface for S-band Mobile Interactive Multimedia (S-MIM) PART3".

[34] "From S-band mobile interactive multimedia to fixed satellite interactive multimedia: making satellite interactivity affordable at Ku-band and Ka-band".

[35] J. W. Lambrechts, "Phase Noise reduction," Pretoria, 2010.

[36] F. G. L. L. R. R. A. Cavallini, "Chip-Level Differential Encoding/Detection of Spread-Spectrum Signals for CDMA Radio Transmission over Fading Channels," IEEE, 1997.

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3 System description

3.1 Introduction

The entire communication system is composed of three main subparts:

1. The F-SIM / S-M2M Transmitter that generates and transmits the E-SSA bursts (composed of a preamble, a BPSK data PDCH channel and an orthogonal BPSK control channel PCCH with a gain factor [see Eq. 6 for definition]) from the info payload, 1/3 turbo code, spreading and channelization and scrambling and finally SRRC filtering [1][9].

2. The Channel Emulator that emulates the Doppler effect, phase noise and AWGN. 3. The E-SSA receiver is composed of the following main stages: SRRC filtering, preamble

searching, chip timing recovery and tracking, phase and frequency recovery algorithm, dispreading, demodulation, channel estimation and MAI cancellation (SIC).

E-SSA Transmitter

Channel Emulator

E-SSA Receiver

A

B

Fig. 5 E-SSA system description

The architecture of the MATLAB simulator developed in the framework of this project is presented in the following.

The main assumptions considered for the development of the MATLAB simulator are:

• Simulations are made at symbol level (spreading-despreading are not used). See Section 3.3 for the justification.

• Preamble searching is considered ideal (thus, it was not used) • Chip timing recovery is considered ideal (thus, it was not used)

• The SIC is not implemented, thus a single burst is transmitted at a time (please Note that

the analysis of the effect of the phase noise on the SIC is not part of this activity).

• Eb represents the overall energy (PDCH + PCCH)

• In order to define clearly the power of the data channel (PDCH) compared to that of the control channel (PCCH), the Beta factor value was replaced with a percentage value defined below. In S-M2M and F-SIM the Beta Factor defines the energy of bit on PDCH and a power of pilot symbol on PCCH Eq. 8. :

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26 ?A:B KAJ;CG O1 & _C9FGC9FG%PPQ %RPQS ∗ 100 (7) with: C9FG%PPQ U V1 + X C9FG%RPQ U 1 V1 + X (8) Thus, ?A:B KAJ;CG (1 & ) ∗ 100 (9) For example, a Gain factor = 100% means all the power resides on the data channel PDCH ( 0).

The assumptions listed above are justified by the fact that the phase correction algorithm of the current implementation of the E-SSA Demodulator is the component most sensitive to the effect of the phase noise. This assumption is validated in Section 0 where the results obtained with a real receiver are in line with those obtained with the MATLAB simulator.

It is worth underlining that as a result of the above assumption, the MATLAB implementation of the receiver only contains:

• The V&V NDA. This receiver not uses the pilot symbol transmitted by the control channel. This receiver is the version currently implemented in MBI [28]. We added the use of the preamble and the initial phase estimation based on the preamble. We also added the algorithm for phase ambiguity solving which uses the preamble. Details are shown in Section 5.2.

• The ML DA SW receiver with two types of Sliding Windows (M=K and M, K=1) [29]. For the second, we added the preamble for the correction of the first symbols. Details are shown in Section 5.5. Both types of Sliding Window use a pilot symbol for phase and frequency recovery. We added the Doppler impairment and the initial frequency estimation and recovery. To do this, we simulated two algorithms, (see Section 6 for details). As mentioned, using this receiver the performances of S-M2M were dramatically improves.

• The Hybrid V&V receiver uses two stages for phase recovery. The first is the ML DA M, K=1 and the second is the V&V. The Doppler impairment and the initial frequency

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27 estimation and recovery were also added for this algorithm, (see Section 7 for details). The preamble is used as the ML DA for correcting the first symbols.

3.2 E-SSA Transmitter

The transmitter is described in [1] for S-M2M and in [9] for F-SIM and has the same DSP architecture for both systems.

Fig. 6 Transmitter for S-M2M and F-SIM The specifications for the four S-M2M waveforms [1] are:

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28 The values for Beta are chosen from:

Signalling values for β

Quantized amplitude ratio (β)

Gain Factor % [see Eq. 6 for

definition] 15 1,0000 0 14 0.9333 12.8951 13 0.8666 24.9004 12 0.8000 36.0000 11 0.7333 46.2271 10 0.6667 55.5511 9 0.6000 64.0000 8 0.5333 71.5591 7 0.4667 78.2191 6 0.4000 84.0000 5 0.3333 88.8911 4 0.2667 92.8871 3 0.2000 96.0000 2 0.1333 98.2231 1 0.0667 99.5551 0 Switch off 100.0000

Fig. 8 values and gain factor for S-M2M system [1]. With reference to Fig. 6, the transmitted signal is:

YZ,[ 1

V1 + Y[ (10)

where Y_[ are a Turbo Encoded BPSK data symbol.

The optimum values of have been defined by the project S-M2M SCADA as follows: • WF1: 0.3333, ?A:B KAJ;CG 88.89 %

• WF2: 0.3333, ?A:B KAJ;CG 88.89 %

• WF3: 0.3333, ?A:B KAJ;CG 88.89 % (11)

• WF4: 0.4667, ?A:B KAJ;CG 78.21 % The values of will be further optimized in the following.

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3.3 MATLAB E-SSA Transmitter

Given that the V&V NDA does not use the pilot symbol within the control channel, the MATLAB implementation of the transmitter can be:

BPSK

β

2 1 1 +

R

s

b

i

z

p,k

Turbo

Encoder

z

k

Fig. 9 MATLAB Transmitter for simulations with V&V NDA

At the receiver side, the OVSF code on PDCH branch extracts the PDCH channel from the entire signal transmitted (PDCH+PCCH). For this reason, if the pilot symbols are not used for phase recovery, they cannot be transmitted.

In the equivalent transmitter implemented in MATLAB [Fig. 9] the spreading of the signal is not considered. In fact, if the phase noise and its impact on BER are considered, the two systems shown are the same [Fig. 6 and Fig. 9]. The reason is that in order to focus on PN, the spreading, despreading, scrambling and descrambling can be ignored. This does not mean that the performances of the system are the same in the case of CDMA and no CDMA. Obviously there are many advantages in implementing a CDMA system, but applying PN to a chip, symbol or bit is the same if the autocorrelation of PN of SF consecutive chips or symbols is still close to one. This is clear from analyzing the autocorrelation function of phase noise in the case where WF#1 is transmitted (without loss of generality):

For S-M2M WF#1:

• d- 4.1667 x 10ef sec • d 2 x 10eg IFJ After d_- seconds from one chip, the autocorrelation is still close to one.

In addition, the autocorrelation is still close to one even when d seconds are considered. Consequently, the PN may be Fig. 10 Autocorrelation function for WF1 S-M2M system.

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30 considered constant even on two consecutive bits.

Another supposition is that the times for spreading and despreading chips are perfectly synchronized. For details see Section 5.4.4.

3.4 Channel Emulator

The Channel Emulator is used for simulation with AWGN, phase noise and the Doppler effect:

AWGN

A

B

Doppler

Effect

Phase noise

effect

Fig. 11 Channel emulator for simulations with AWGN and PN

3.4.1 Doppler effect

Due to the ARTEMIS inclination, the Doppler shift (Hz vs time) and its variation (Hz/s vs time) rate obtained with this satellite [25] can be considered as the worst reference scenario for S-M2M and F-SIM applications.

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31 Fig. 13 ARTEMIS Doppler rate

The Doppler shift can be modelled by:

K (;) ∆K0#i∗ sin (2mK ;) (12)

where

∆K0#i 4000 [oY] (13)

K _24 [<CqGI]1 _{24 ∗ 60 ∗ 60 [I] [oY]}1

The maximum Doppler rate is 0.25 sQt₊u [25].

A comparison must then be made between the Doppler rate and the duration of the chip, symbol, bit and the length of window of M symbols in S-M2M to verify if it can be ignored. WF#3, in particular, was analysed because it has the lowest bit-rate and therefore it is the most sensitive to the Doppler effect.

W F Rb [Kbit/s] Tb (s∗ 10eg) Ts (s∗ 10eg) Tc (s∗ 10ev) Doppl er rate MAX (Hz/s) Doppler rate for chip (Hz/chip ∗ 10ev) Doppler rate for symbol (Hz/symbo l∗ 10ev) Doppler rate for bit

(Hz/bit) Constellation rotation for symbol [deg/symbol] M Opt ML DA with SW with K=M Phase shift for window (M symbols) [deg*M] 1 5 2 0.667 4.17 0.25 1.04 1.67 5 ∗ 10ev 9.56 ∗ 10eg 160 0.1531 2 1.25 8 2.67 4.17 0.25 1.04 6.67 2 ∗ 10eg 0.0038 90 0.3439 3 0.3125 32 11 4.17 0.25 1.04 2.67 8 ∗ 10eg 0.0153 40 0.6112 4 1.25 Like WF#2 Like WF#2 Like WF#2 0.25 Like WF#2 Like WF#2 Like WF#2 Like WF#2 60 Like WF#2

Table 1 Doppler effect for all waveforms (with optimum M for ML DA with Sliding Window with K=M) The modulation is BPSK, thus the Doppler rate can be considered as a constant shift for all waveforms. Clearly, the larger the length of window, the larger the resulting phase shift. For the optimum M for each waveform, the Doppler rate can be ignored, so only a constant Doppler shift is estimated. This means that: in transmission a Doppler effect was generated using Eq.12 (Doppler shift is included). On the receiver we can estimate the Doppler effect as if it were constant at one packet. The frequency estimation was used to correct all the symbols inside the

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32 frequency estimation window. As a result, an error was made, although due to its limited size, it is not necessary to take it into consideration (see Table 1).

W F Rb [Kbit/s] Tb (s∗ 10eg₎ Ts (s∗ 10eg₎ Tc (s∗ 10ev₎ Doppl er rate MAX (Hz/s) Doppler rate for chip (Hz/chip ∗ 10ev₎ Doppler rate for symbol (Hz/symbo l∗ 10ev) Doppler rate for bit

(Hz/bit) Constellation rotation for symbol [deg/symbol] M Opt ML DA with SW with K=M Phase shift for window (M symbols) [deg*M] 1 5 2 0.667 4.17 0.25 1.04 1.67 5 ∗ 10ev 9.56 ∗ 10eg 2400 2.29 2 1.25 8 2.67 4.17 0.25 1.04 6.67 2 ∗ 10eg 0.0038 600 3.42 3 0.3125 32 11 4.17 0.25 1.04 2.67 8 ∗ 10eg 0.0153 150 2.37 4 1.25 Like WF#2 Like WF#2 Like WF#2 0.25 Like WF#2 Like WF#2 Like WF#2 Like WF#2 1200 4.46

Table 2 Doppler effect for all waveforms with default M

3.4.2 Phase Noise effect

The phase noise affects every local oscillator in the system on the transmitter, satellite or receiver.

If the local oscillator is ideal (without phase noise), the output signal from the oscillator is:

I('(;) Fw( x. yz{) (14)

With:

f= nominal frequency

| = the initial phase of the oscillator In the presence of phase noise instead [19]:

I('(;) Fw( x. y z{y z( )) (15)

|(;) characterizes a phase noise and is described in the frequency domain by the PSD [dBc/Hz] [35].

In these simulations, the effect of these non-ideal local oscillators is summarized in a single block. In fact, the only element of the whole system which is affect by phase noise is the channel emulator.

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33 Fig. 14 Masks of PN collected

The mask of F-SIM and S-M2M terminals is used for the simulations because it can be considered as the worst case. The ARTEMIS test is not considered in simulations because the particular condition of this satellite could worsen the results [25].

Fig. 15 PSD of phase noise used in simulations In Fig. 15 the phase noise masks are :

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34

• calculated from the output of the ESA function • theoretical

3.5 E-SSA Receiver

This section describes:

• The current MBI receiver that implements the V&V NDA [7][28] • The MATLAB implementation of the MBI receiver

• The new real receiver that will implement ML DA to enhance the phase correction [29] • The MATLAB implementation of the real ML DA receiver

3.5.1 MBI’s current E-SSA Demodulator (based on V&V NDA)

The non-data-aided (NDA) feed-forward carrier phase estimation algorithm for MPSK is described in [7].

In addition, the receiver used in MBI is a non-data-aided receiver [28]:

Fig. 16 MBI’s current E-SSA Demodulator In Figure 16 the following features are evident:

• Despreading

• Frequency recovery and phase recovery • Chip timing recovery

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35 • Preamble searching

• Regeneration and cancellation (SIC)

Work on the enhancement of the phase and frequency estimation was carried out on the block denoted ‘Frequency recovery & correction phase recovery & Tracking’. As can be seen in Fig. 16, the current receiver does not use pilot symbols. Inside the b ‘Phase Error Recovery’, ‘Slicing’ and ‘phase correction’ blocks there are the V&V NDA techniques described in Section 5.2. For other details of the MBI phase recovery see [28].

As seen in Section 3.1 and Section 3.2, many parts of the MBI receiver are not implemented in MATLAB. This is because they are considered ideal or they are not considered on first approximation.

3.5.2 MATLAB implementation of the V&V NDA receiver

For the reasons explained in Section 3.2, the equivalent receiver implemented in MATLAB simulations is:

Phase

Correction

Turbo

Decoder

r

p,k

Decision

B

Fig. 17 MATLAB implementation of NDA receiver

Using the transmitter in Fig. 6 and the channel emulator in Fig. 11 without Doppler effect, at point B:

GZ,[ YZ,[Fwz}+ 9[ (16)

Where 9_[∈ • Ν(0, • ) is a Gaussian noise and |_[ |(;)|_‚}

ƒ [Section 3.4.2].

3.5.3 ML DA algorithm

To improve the performances of the NDA receiver, a phase recovery that uses a pilot symbols [29] is considered. The DA algorithm proposed in this document uses a PCCH for phase estimation. This technique has the advantage of avoiding the ambiguity on received symbols (similar to a V&V NDA).

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36 For this purpose, the OVSF code used in transmission could be exploited [29]. The signal obtained after spreading at the transmitter is a DS/SS BPSK signal. A peculiar feature of this type of signal comes from the use of orthogonal spreading signatures on the I/Q signal component [Fig. 6]. At point A on the transmitter there are two orthogonal BPSK signals that correspond to a BPSK DATA branch and a BPSK SIGNAL branch. Consequently, the In-Phase component of PCCH is null and the In-Quadrature component of PDCH is null.

Due to the effect of Phase Noise, both constellations are rotated at point B. Consequently, neither the In-Phase component of PCCH nor the In-Quadrature component of PDCH is null.

The Data-Aided system shown below is able to resolve this problem using the OVSF code [29]. Thus, using a transmitter in Fig. 6 the signal at point A is:

I0 1 V1 + Y„0…†‡J0' (0,…†),Z+ jV1 + D„0…†‡J0' (0,…†),2 (17) Where: Y AGF A IHL7CEI AK;FG dqG7C BJC5FG KCG 4•o D AGF A D:EC; IHL7CEI KCG ••o

J0,Z AB5 J0,2 AGF J<:DD:B‰ JC5FI CK 4•o AB5 ••o

Š‹ :I A IDGFA5:B‰ KAJ;CG KCG 4•o AB5 ••o

Using the channel emulator in Fig. 11, at point B: ‰0 I0FwzŒ+ 90 1 V1 + Y„0…†‡J0' (0,…†),ZF wzŒ+ j V1 + D„0…†‡J0' (0,…†),2F wzŒ+ 9₀ (18)

As a result of previous considerations [Section 3.2]: 1 V1 + Y„0…†‡F wz_„Œ •Ž‡J_{0' (0,…†),Z}+ j V1 + D„0…†‡F wz_{„ Œ} •Ž‡J_{0' (0,…†),2}+ 9₀ (19)

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37 Turbo Decoder Decision

∑

SF_m₌−₀1

∑

SF_m₌−₀1

∑

SF_m₌−₀1

∑

SF_m₌−₀1 Cm,p Cm,q Cm,p Cm,q Phase/Frequency estimator + recovery Phase/Frequency recovery

For system control

B Quadrature branch In-phase branch Re{} Im{} j j Out2,k Out1,k Fig. 18 DA receiver On an In-phase branch: •F•‰0‘ 1 ’_{1 +} 2Y„Š‹L‡cos (|„Š‹L‡)JLC5(L,Š‹),D+V1 + D„Š‹L‡sin (|„Š‹L‡)JLC5(L,Š‹),M + 9L,G (20) On a Quadrature branch: L•‰0‘ 1 V1 + Y„_Š‹L‡sin (|„_Š‹L‡)JLC5(L,Š‹),D+_{V1 +} D„_Š‹L‡cos (|„_Š‹L‡)JLC5(L,Š‹),M + 9L,: (21)

Where 9₀ 9_0,/+ j 9_0,. After despreading, at receiver, multiplying [29]: • In-Phase signal for:

o (J_0,Z) we obtain the part of PDCH (In-Phase branch at transmitter) that was not

rotated by phase noise. • •F•‰0‘ ∗ J0,Z …†e 0‚ 1 V1 + Y[cos (|[) + 9[,/ (22)

o (J_0,2) we obtain the part of PCCH (Quadrature branch at transmitter) that was rotated

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38 • •F•‰0‘ ∗ J0,2

…†e

0‚ V1 +

D[sin (|[) + 9[,/ (23)

• Quadrature signal for:

o (J_0,Z) we obtain the part of PDCH (In-phase branch at transmitter) that was rotated

to the Quadrature branch due to the effect of phase noise. • L•‰0‘ ∗ J0,Z …†e 0‚ 1 V1 + Y[sin (|[) + 9[, (24)

o (J_0,2) we obtain the part of PCCH (Quadrature branch at transmitter) that was not

rotated by phase noise. • L•‰0‘ ∗ J0,2 …†e 0‚ V1 + D[cos(|[) + 9[, (25) Now, recombining: –q; ,[ 1 V1 + Y[cos(|[) + j 1 V1 + Y[sin(|[) + 9[,/+ 9[, 1 V1 + Y[Fwz}+ 9[ (26) –q; ,[ V1 + D[cos (|[) + jV1 + D[sin (|[) + 9[,/+ 9[, V1 + D[Fwz}+ +9[ (27)

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39

3.5.4 MATLAB implementation of the ML DA algorithm

This time it is necessary to generate also the control channel at the transmitter side as follows:

BPSK

β

β 2 1+

β

2 1 1 +

R

b-data PDCH PCCH

R

b-pilots

=R

s

R

s

p

k

b

i

z

p,k

z

q,k

Turbo

Encoder

A

z

k

Fig. 19 MATLAB equivalent implementation of DA transmitter

The following diagram shows the MATLAB implementation of the receiver based on the ML DA: Doppler effect AWGN Decision Phase/Frequency Estimator Doppler effect AWGN zp,k zq,k Out2,k Out1,k Phase/Frequency correction Turbo Encoder Phase noise effect Phase noise effect B A Out’1,k

Fig. 20 MATLAB equivalent implementation of DA receiver and channel emulator

If the timing of chips in spreading and despreading is perfectly synchronized, the transmitter and the receiver described in Fig. 6-Fig. 18 and its MATLAB implementation in Fig. 19 Fig. 20 are the same.

Note on Fig. 20: The two blocks denoted ‘Phase noise effect’ produce the same realizations of phase noise on the k-th symbol of PDCH branch and PCCH branch. The same applies to AWGN realizations.

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40

D[ 1 ∀˜ (28)

Where D(˜) are the pilot symbols.

Y2,[ j V1 + D[ (29) –q; ,[ IZ,[Fwz[+ 9[ 1 V1 + Y[Fw[+ 9˜ (30) –q; ,[ I2,[Fwz[+ 9[ V1 + D[Fwz}+ 9˜ (31)

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41

4 Validation of the MATLAB V&V NDA simulator

In this section, the V&V NDA MATLAB simulator is validated by comparing its results with those obtained with MBI’s E-SSA demodulator in the presence of only AWGN and with PN+AWGN.

From the real demodulator, the PER vs P_" was obtained. The •/ of the real demodulator is defined as (considered BPSK):

• - _{& 10 ∗ EC‰ (š)}

+ _{& 10 ∗ EC‰ (š) & 10 ∗ EC‰ (Š‹)}

& 10 ∗ EC‰ (š ∗ Š‹ ∗ G)

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With:

š as the roll-off factor

SF as the spreading factor

r as the rate of Turbo Code

4.1 AWGN only

To validate the MATLAB simulator in the presence of only AWGN, a real demodulator implemented at MBI’s premises is used. The result obtained is:

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42 Fig. 21 S-M2M PER with real demodulator of MBI

These performances are converted in function of 1_"›

{œ and compared with those obtained with the

MATLAB simulator. Due to the conversion from _"Pœ to 1_"›

{œ there is no difference between

WF#1, WF#2 and WF#3. In contrast, WF#4 produced a slightly shifted BER curve [Fig. 22], which is due to the different . This behavior is justified because when increases, the power on PDCH decreases [Fig. 8].

In these simulations we took the M used in MBI:

• 5FKAqE; †# 160 LI ∗ •I †# 2400 IALDEFI

• 5FKAqE; †# 160 LI ∗ •I †# 600 IALDEFI

• 5FKAqE; †#ž 160 LI ∗ •I †#ž 150 IALDEFI

• 5FKAqE; †#g 320 LI ∗ •I †#g 1200 IALDEFI

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For ML DA M=K and ML DA M, K=1 these values will be optimized in the following part of the document.

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43 Fig. 22 PER curves for WF#1-#2-#3-#4 obtained with MATLAB simulator and MBI E-SSA Demodulator Note: the PERs obtained with MBI’s real demodulator and shown in Fig. 22 are interpolated from a few points of PERs in Fig. 21, after which they are converted in function of Eb/N0 (dB). These simulations show that without phase noise for all waveforms, the PERs are the same as those made with MBI’s demodulator.

In order to verify the correct implementation of Gain Factor in MATLAB simulator, another simulation was carried out. The same graph was used to simulate:

1. the BER with 0 (100% of power associated to PDCH denoted in this document: gain factor [see Eq. 6 for definition])

2. the BER with 0.5 (75% of power associated to PDCH denoted in this document: gain factor)

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44 Fig. 23 Comparison to validate the implementation of Gain Factor in the simulator

The translation between the two BER is:

&10 ∗ EC‰₁₀(?= CB 4•o) &10 ∗ EC‰₁₀U 1 V1 + 2X

2

&20 ∗ EC‰₁₀(0.8) 0.9691 (56)

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This test shows that the implementation of Gain Factor in Matlab simulator is correct. In fact, the translation between red and blue curves in Fig. 23 is the same as calculated in Eq.34.

4.2 AWGN + phase noise

The MBI E-SSA demodulator is able to emulate the PNB mask. When tested in the presence of phase noise, results indicated the demodulator is not able to demodulate the received signal for all waveforms. For all simulations, represents the overall energy (PDCH + PCCH).

The MBI E-SSA Demodulator cannot simulate windows smaller than 10 ms, thus, the demodulator is validated for windows greater than 10 ms. For these windows, we obtained a floor in the same way as in a Matlab simulator (PER>0.1 for WF#1).

For smaller windows, Matlab simulations are made in Section 5.2 and the floor disappears for WF#1#2#4. For WF#3 the floor is still present.

On the basis of these results the assumptions listed in Section 3.1 can be assumed to be correct (at least at the time of writing). In other words, the phase recovery algorithm seems to be confirmed as the algorithm most sensitive to phase noise. For this reason, the following simulations have been carried out with this in mind.

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45

5 Phase Recovery Simulation Results

5.1 Simulated algorithm for phase recovery

Here is a summary of the studied algorithms:

Algorith ms simulated

Why we

simulated it Advantages Disadvantages

Characteristic s Simulated and described in: V&V NDA To validate the MATLAB simulator with and without phase noise Low complexity Very low performances with phase noise and AWGN impairments 1) It is the current phase estimator algorithm of MBI 2) It does not use pilot symbols Described and simulated in: Section 5.2 ML DA with Sliding Window with K=M symbols To improve phase recovery using pilot symbols Improves the performance compared to V&V NDA Increases the complexity compared to V&V NDA

Uses the pilot symbols Described in Section 5.3 and simulated in Section 5.4 ML DA with Sliding Window with length of M symbols and K=1 symbols To improve phase recovery using pilot symbols Best performance compared to V&V NDA and ML DA with Sliding Window with length and steps of M symbols Increases the complexity compared to V&V NDA

Uses the pilot symbols Described in Section 5.3 and simulated in Section 5.5 Hybrid V&V To further improve phase recovery Improves performances further The most complex Uses two stages for phase estimation: ML DA and V&V NDA Described in Section 7 and simulated in Section 7.3

5.2 V&V NDA estimator implemented by the MBI E-SSA Demodulator

This is the phase estimator implemented by MBI [28]. The MATLAB simulations are performed to verify the behavior of the phase estimator in the presence of phase noise.

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46 From Section 3.5.1 with reference to Fig. 17, the fine phase estimation and correction of V&V NDA splits received symbols G_Z,[ into windows of M symbols with steps of M symbols, from one window to another [see Section 3.5.1]. For each window, the calculation of V&V NDA implemented in MBI is:

|Ÿ 1_{2 AB‰EF • G}Z, ¡

¢ (35)

Using Eq.16 in Eq.34:

|Ÿ 1_{2 AB‰EF •£Y}Z,[Fwz} + 9[¤ ¡

¢ (36)

Firstly, the V&V NDA algorithm removes data dependency by raising it to the 2-th power. In other words, the 2-th power is used to remove the ambiguity on the phase of PDCH due to BPSK data. Then, the sum over M symbols removes the effect of AWGN (if M is sufficiently large). V&V NDA, in classic form, are [7]:

|Ÿ 1AB‰EF •¥GZ,¥1 ¡

Fw %∗#$¦(,(/§,¨)¢ (37)

thus, comparing Eq.35 with Eq.37, the V&V NDA algorithm implemented in MBI is V&V NDA with E=P=2.

Using Eq.35, the phase corrected symbols in one window of M symbols are:

Consequently, the same |Ÿ is used for phase correction for all M symbols.

Now we applied the algorithm already implemented in the MBI ESSA-Demodulator for ambiguity correction. This algorithm was not studied and was implemented as is.

|Ÿ is considered in the range [-pi,pi].

In order to correct the ambiguity of the phase estimation of V&V NDA, we used the follow algorithm:

:K œ¥2m + |ª & |Ÿ« e ¥ _x& mœ <m_{2 → |}ª |« ª + m «

|ª &LC5£3 ∗ D: & |« ª,2 ∗ D:¤ + D: «

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47 with:

|®| ;A˜FI ® 9:;<Cq; I:‰B. ®ALDEF: |&5| 5 |®| x ;A˜F ® LC5qEF 2m. ®ALDEF: |3m| x m

|¯ is the phase estimation carried out on preamble using:

|¯ AB‰EF( IqL( DGFAL7CEC%RPQ)) (40)

Using this algorithm for phase ambiguity solving and for high value of Eb/N0, we obtained this evolution of phase estimation for one packet compared to the phase noise introduced from channel emulator:

Fig. 24 Phase estimation with ambiguity solving and phase noise realization Instead, without any algorithm for phase ambiguity solving:

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48 Fig. 25 Phase estimation without ambiguity solving and phase noise realization

In order to verify the absence of the floor for smaller window sizes, the performances for V&V NDA are simulated with the MATLAB simulator for all waveforms with: AWGN, PN:

For the simulations with AWGN plus PN M is set as equal to: • †# 75 IALDEFI → d 5 LI

• †# 5 IALDEFI → d 1.33 LI

• †#ž 20 IALDEFI → d 21.3 LI

• †#g 5 IALDEFI → d 1.33 LI

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49 These values are not the result of an optimization process. In order to verify the behaviour of V&V NDA with smaller window sizes, we tested those M.

For the simulations with only AWGN, M is set as equal to default values [Eq.33].

Fig. 26 Matlab result for BER for WF#1 with M=75 symbols

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50 Fig. 28 Matlab result for BER for WF#3 with M=20 symbols

Fig. 29 Matlab result for BER for WF#4 with M=5 symbols

With phase noise, the V&V NDA used by MBI is not sufficient. For the study on the output signal of V&V NDA see Appendix 1: Statistical description for output signal of V&V NDA

5.3 ML DA phase estimator

ML DA is considered for the phase estimator because it is frequently referred to in the literature [2][3][4][5][6][7][8].

This phase estimator uses the pilot symbols to estimate the phase rotation which afflicted the signal.

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51 The difference from V&V NDA [Section 5.2] is that in this case there is no increase in power 2 of the received symbols. In fact, it is possible to eliminate the BPSK modulation from PCCH simply by multiplying the received signal: –q; _,[ by the pilot symbol transmitted D_[ [Eq.42-43]. From Eq. 30 and Eq. 31 [7][3], the received pilot symbols are split into windows of M symbols. This value will be optimized. The following formulas are calculated for each window:

–q; ,[ V1 + D[Fwz} + 9˜ (42) |¯ AB‰EF °• D ∗ –q;[ , ±e ‚ ² (43)

Eq.43 is the ML DA phase estimation. From Eq.43 and using D ∗ D 1 ∀: :

|¯ AB‰EF °• D ∗ –q;[ , ±e ‚ ² AB‰EF °• UD ∗ V1 + D Fwz¨+ 9:X ±e ‚ ² (44) AB‰EF °• U V1 + Fwz¨+ 9 X ±e ‚ ² GFAE ³∑ U V1 + Fwz¨+ 9 X ±e ‚ µ :LA‰ ³∑ U V1 + Fwz¨+ 9 X ±e ‚ µ (45)

The phase corrected bits, that compose one window, are:

Consequently, the same |Ÿ is used for phase correction for all M symbols. In other words, the estimate of the phase is considered valid for M consecutive symbols that constitute the window. To identify the window, two algorithms were used:

• Sliding Window with K=M symbols

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52

5.4 ML DA estimator with Sliding Window with K=M symbols (ML DA SW

K=M)

The following diagram shows the behaviour of Sliding Window with K=M symbols. The received pilot symbols are split into windows of M symbols. A phase estimation is calculated for each window.

M samples M samples M samples M samples

window window window window

Fig. 30 Behaviour of Sliding Window with K=M symbols

This method has a lower computational cost compared to a Sliding Window with length of M symbols and K=1 symbol, however, it is necessary for the autocorrelation function not to reach 0 after M symbols.

5.4.1 M optimization

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53 Fig. 31 M optimization for WF#1

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55 Consequently, the optimum values appear to be:

• >‹#1: ≅ 160 IALDEFI • >‹#2: ≅ 90 IALDEFI • >‹#3: ≅ 40 IALDEFI • >‹#4: ≅ 60 IALDEFI (47) 5.4.2 optimization

By changing , it was possible to study the behaviour of the estimator for all waveforms. The optimum value for M was used for each waveform.

5.4.2.1 WF#1

As seen in Fig. 35, the BER gets worse when the Gain factor [see Eq. 6 for definition] is greater or smaller than the default value (88.89 0.3333) for WF#1.

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56

5.4.2.2 WF#2

As seen in Fig. 36, the BER gets worse when the Gain factor is greater or smaller than the default value (88.89 0.3333) for WF#2.

Fig. 36 Gain factor optimization for WF#2

5.4.2.3 WF#3

As seen in Fig. 37, the BER gets worse when the Gain factor is greater or smaller than 71.56% for WF#3.This gain factor corresponds to 0.5333. The default value is 88.89 0.3333.

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57 Fig. 37 Gain factor optimization for WF#3

5.4.2.4 WF#4

As seen in Fig. 38, the BER gets worse when the Gain factor is greater or smaller than the default value (78.22 0.4667) for WF#4.

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58 Fig. 38 Gain factor optimization for WF#4

Thus, the optimum values for β for V&V NDA are:

• >‹#1: 'Z ≈ ,.#¸( • >‹#2: _'Z ≈ _,.#¸(

• >‹#3: _'Z ≈ 0.5333 → ?A:B ‹AJ;CG 71.5591 % • >‹#4: 'Z ≈ ,.#¸(

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5.4.3 ML DA Sliding Window K=M with optimum M and β

The simulations of ML DA estimations are made for all waveforms for M and β equal to the optimum values previously calculated, (for a comparison see Chapter 7). Thus, there are the following for each waveform in the same graph:

• ML DA simulation with:

o_{M = optimum value for that waveform} • V&V NDA without phase noise and with:

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59

o M = default value for that waveform

• Theoretical AWGN curve made with Beta=0

Fig. 39 Performance of ML DA with Sliding Window with K=M compared to V&V NDA for WF1

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60 Fig. 41 Performance of ML DA with Sliding Window with K=M compared to V&V NDA for WF3

Fig. 42 Performance of ML DA with Sliding Window with K=M compared to V&V NDA for WF3 with gain factor optimized

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61 Fig. 43 Performance of ML DA with Sliding Window with K=M compared to V&V NDA for WF4

WF#1 V&V NDA, no PN V&V NDA with PN ML DA with SW

with K=M symbols

M (symbols) 2400 2400 160 (optimum)

Gain Factor

[see Eq. 6 for definition]

88.89 % 88.89 % 88.89 % (optimum)

PNIL @ º»e¼ / > 5.3 0.6

PNIL @ º»e½ _/ _{> 5} _0.6

Table 3 Performance of WF#1 with ML DA K=M

WF#2 V&V NDA, no PN V&V NDA with PN ML DA with SW with

K=M symbols

Gain Factor

88.89 % 88.89 % 88.89 % (optimum)

PNIL @ º»e¼ / > 5.3 1.6

PNIL @ º»e½ / > 5 1.7

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62

WF#3 V&V NDA, no PN V&V NDA with

PN

ML DA with SW with K=M symbols

Gain Factor

88.89% 88.89 % 88.89 % 71.56 %

(optimum)

PNIL @ º»e¼ / > 5.1 3.6 2.6

PNIL @ º»e½ / > 4.9 4.2 2.9

WF#4 V&V NDA, no PN V&V NDA with PN ML DA with SW

with K=M symbols

Gain Factor

78.22 % 78.22 % 78.22 % (optimum)

PNIL @ º»e¼ / > 4.65 0.8

PNIL @ º»e½ / > 4.4 1

5.4.4 WF#3, origin of problem

In the case of PN, a V&V NDA estimate is not sufficient for phase recovery. The implementation of DA estimators with Sliding Window with K=M symbols improves the BER compared to V&V NDA. This is true as long as the signal is not excessively corrupted by PN. An example is WF#3, where a spectrum of the signal is covered by a strong PN, due to the low bitrate. For this waveform, the phase recovery is more difficult than in the others.

The problem of WF#3 is explained by analyzing an autocorrelation function of PN. Since a symbol-rate in WF#3 is •_{+, †ž} 937.5 IALDEFI/I, time of symbol is d₊ 1.1 LI, thus one symbol arrives each 1.1 LI. For ML DA we found the optimum M is 40, for WF#3. Thus the autocorrelation function should still be equal to 1 after ∗ dI seconds, which means the autocorrelation function is constant for the duration of one window. The autocorrelation function of PN, time of bit in WF#3 and duration of one window are shown in Fig. 44.

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63 Fig. 44 Autocorrelation function of PN in WF#3, Ts and duration of window for phase recovery

The correlation between symbols within a window is not constant. At the end of the window, one symbol is almost totally uncorrelated with the first. This produces the incorrect behaviour of WF#3.

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In WF#2, due M opt is 90, the correlation is not exactly 1 for the entire window.

Thus, for WF#3 it is necessary to use a Sliding Window with a length of M symbols and K=1 symbol; WF#2 may need it; for other waveforms a simple ML DA is sufficient.

To analyze more clearly the effect of phase noise on the waveforms tested, it is possible to simulate this system:

Pilots generator

PN rotation

PDF { angle( . ) }

Fig. 48 System for the test

The pilot symbols generated are affected by only phase noise impairment. On the receiver side, the PDF of the angle of the received symbols is calculated.

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66 Fig. 49 Comparison for the PDFs of the angle of received pilot symbols

In Fig. 49 a slight deterioration between WF#2-#3-#4 and WF#1 can be observed. This is because the PDF is slightly narrower for WF#1 than for the others. Thus, as in Section 5.4.4, it can be assumed that by increasing the symbol rate, the PDF becomes narrower, and conversely, by decreasing the symbol rate, the PDF becomes wider.

If the PDF of the phase noise becomes narrower, the phase estimation is facilitated. In fact, without phase noise, the PDF of the phase of the received symbols is a delta. This therefore explains the better performances obtained for WF#1.

To verify this assumption, a hypothetical waveform with Rs=1 Msps was tested. For this waveform a marked narrowing of the PDF was expected [Fig. 50].

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67 Fig. 50 PDF of the phase of received pilot symbols for a hypothetical waveform with Rs= 10f

5.5 ML DA estimator with Sliding Window with length of M symbols and K=1

symbol

ML DA with Sliding Window technique is implemented. In this case a window of M symbols continuously runs on the received pilot symbols. The phase correction for G_Z(˜) is still calculated on windows of M symbols, but they are now considered M/2 symbols before and M/2-1 symbols after a k-th symbol G_Z(˜).

Fig. 51 Behavior of Sliding Window with length M and K=1

In Fig. 51 the behaviour of Sliding Window with length M symbols and K=1 symbol is shown. In this figure M is equals to 10. For the correction of the phase of sixth symbol are used the previous five symbols and the next four in addition to the same symbol. At the next step, the same thing is done for the seventh symbol.

In this case, it is necessary to provide an algorithm for the correction of the first symbols of PDCH. In order to correct the first ¡& 1 symbols, we used the phase estimation calculated on the

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68 preamble. This behaviour is explained in Fig. 52. In that case the length of the window is 10 and the preamble size is 6 symbols.

1 2 3 4 5 6 7 8 9 10 1 12 ... 1 2 3 4 5 6 7 8 9 10 11 12 ... Size M PDCH data PCCH 1 2 3 4 5 6 PDCH Preamble Preamble phase estimation

Phase corrections

Fig. 52 Behaviour of phase correction using preamble for the initial symbols of PDCH

5.5.1 M optimization

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Consequently, the optimum values appear to be:

• >‹#1: ≅ 190 IALDEFI • >‹#2: ≅ 120 IALDEFI • >‹#3: ≅ 40 IALDEFI • >‹#4: ≅ 110 IALDEFI (49) 5.5.2 optimization

It is assumed that the optimum values for are equal to the case of ML DA with Sliding Window with K=M symbols, because changing the length of steps of window does not change the statistical characteristics of the signal.

5.5.3 ML DA Sliding Window M, K=1 with optimum M and β

The simulations of ML DA estimation with Sliding Window are made for all waveforms. For M equal to the optimum value calculated before, β is set to default value for each waveform. Consequently, there are the following for each waveform in the same graph:

• ML DA simulation with Sliding Window with length of M and K=1: o_{M = optimum value for that waveform}

• V&V NDA without phase noise and with:

o M = default value for that waveform

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71 Fig. 57 Performance of ML DA with Sliding Window with length of M symbols and K=1 symbol compared to V&V

NDA for WF1

Fig. 58 Performance of ML DA with Sliding Window with length of M symbols and K=1 symbol compared to V&V NDA for WF2

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72 Fig. 59 Performance of ML DA with Sliding Window with length of M symbols and K=1 symbol compared to V&V

NDA for WF3

Fig. 60 Performance of ML DA with Sliding Window with length of M symbols and K=1 symbol with gain factor optimized compared to V&V NDA for WF3

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73 Fig. 61 Performance of ML DA with Sliding Window with length of M symbols and K=1 symbol and V&V NDA for

WF4

For the study on the output signal of ML DA M,K=1 see ‘Appendix 2: Statistical description for output signal of ML DA M,K=1’.

WF#1 V&V NDA, no PN V&V NDA with PN

ML DA with SW with length of M symbols and K=1 symbol M (symbols) 2400 2400 190 (optimum) Gain Factor

88.89 % 88.89 % 88.89 % (optimum)

PNIL @ º»e¼ / > 5.3 0.5

PNIL @ º»e½ _/ _{> 5} _0.5

Enhancement of the phase and frequency recovery for E-SSA protocol.

UNIVERSITA’ DI PISA

Scuola di Ingegneria

Corso di Laurea in Ingegneria delle Telecomunicazioni

Laurea Magistrale

Enhancement of the phase and frequency recovery for the E-SSA

protocol.

Contents

1 The Phase Noise Project

1.1 Background

1.2 Executive Summary

1.3 Conclusion Summary

1.4 Organization of the document

2 References

2.1 Acronyms

2.2 Definitions

2.3 Notations

2.4 Reference documents

3 System description

3.1 Introduction

E-SSA Transmitter

Channel Emulator

E-SSA Receiver

A

B

3.2 E-SSA Transmitter

3.3 MATLAB E-SSA Transmitter

BPSK

β

R

b

i

z

Turbo

Encoder

z

k

3.4 Channel Emulator

AWGN

A

B

Doppler

Effect

Phase noise

effect

3.5 E-SSA Receiver

3.5.1 MBI’s current E-SSA Demodulator (based on V&V NDA)

3.5.2 MATLAB implementation of the V&V NDA receiver

Phase

Correction

Turbo

Decoder

r

Decision

B

3.5.3 ML DA algorithm

∑

∑

∑

∑

3.5.4 MATLAB implementation of the ML DA algorithm

BPSK

β

β

R

R

=R

R

p

b

i

z

z

Turbo

Encoder

A

z

k

4 Validation of the MATLAB V&V NDA simulator

4.1 AWGN only