具有處理能力的衛星轉頻器之架構與效能

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國立交通大學

電信工程學系碩士班

碩士論文

具有處理能力的衛星轉頻器之架構與效能

Architecture and Performance of a Satellite

Transponder with On-Board Processing Capability

研究生：廖明堃

指導教授：蘇育德博士

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具有處理能力的衛星轉頻器之架構與效能

Architecture and Performance of a Satellite

Transponder with On-Board Processing Capability

研究生 : 廖明堃 Student : Ming-Kun Liao

指導教授 : 蘇育德博士 Advisor : Dr. Yu T. Su

國立交通大學

電信工程學系碩士班

碩士論文

A Thesis

Submitted to Department of Communication Engineering

College of Electrical and Computer Engineering

National Chiao Tung University

in Partial Fulfillment of the Requirements

for the Degree of

Master of Science

in

Communication Engineering

July 2006

Hsinchu, Taiwan, Republic of China

中華民國九十五年七月

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具有處理能力的衛星轉頻器之架構與效能

研究生：廖明堃指導教授：蘇育德博士

國立交通大學電信工程學系碩士班

中文摘要

本論文探討具抗干擾(anti-jam, AJ)能力的衛星轉頻器之架構及效能。

我們所考慮的上傳鏈路(uplink)除有加成性的白高斯背景雜訊(AWGN)另有

惡意的干擾，即所謂的部份頻寬雜訊干擾(partial-band noise jamming)。我

們發現具有處理(processing)或再生(regenerative)功能之衛星轉頻器可以

提供強大的抗干擾能力。為強化抗干擾能力我們使用了慢跳頻式的差分相

位相移鍵信號並加上了渦輪編碼。

經過差分相位相移鍵調變的渦輪編碼信號可視為等同於一個串聯編碼

架構，其中內部碼(inner code)為碼率為一的特殊迴旋碼而外部碼(outer code)

則為渦輪碼。基於此種等效模式，我們提出一種迭代的解碼結構並且藉由

數值的模擬檢驗此種不同於以往的解碼排程的效率。我們更進一步使用塊

間重排(IBP)的渦輪碼使得在解碼時可藉由迭代交換不同區塊之間的解碼

訊息以有效的更正錯誤。實驗數值證實這種改錯碼能夠在跳頻速率很低時

仍維持相當良好的性能。另一方面，傳統的渦輪碼需有較高的跳頻速率方

能滿足系統的抗干擾能力性能要求。

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Architecture and Performance of a Satellite Transponder with

On-Board Processing Capability

Student : Ming-Kun Liao Advisor : Yu T. Su Department of Communications Engineering

National Chiao Tung University

Abstract

We consider a secure satellite link in which a slow frequency-hopped (FH), turbo-coded DPSK signal is used in the uplink. Several detector structures are proposed and both processing and bent-pipe transponders are considered although our emphasis is on the former class. Regarding the turbo-coded DPSK signal as an equivalent seri-ally concatenated coding scheme with the inner code being the rate-1 DPSK encoder, we propose an iterative decoder architecture and examine the effectiveness of different decoding schedules. We also consider two interleaver structures for the corresponding turbo codes. The first one is a conventional block oriented interleaver while the second one is the so-called inter-block permutation (IBP) interleaver. Numerical results indicate that sufficient AJ margin is achievable with the proposed signal waveform and decoding scheme. Furthermore, the IBP-interleaved turbo coded system offer additional tradeoff between hopping rate and performance. It offers sufficient AJ capability even the FH rate is relatively low.

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List of Figures

2.1 Block diagram of a turbo coded slow FH/DPSK system. . . 4 2.2 AJ performance of a turbo coded BPSK system with interleaver size 400,

100 bits/hop and (Eb/N0)t = 15 dB. . . 9

2.3 AJ performance of a turbo coded BPSK system with interleaver size 400, 1 bits/hop and (Eb/N0)t= 15 dB. . . 9

3.1 SNR sensitivity of a turbo coded DPSK system; code rate 1/3, interleaver size 400, {15,13} component codes, 10 decoding iterations; AWGN channel. 12 3.2 SNR sensitivity of a IBP-turbo coded DPSK system; code rate 1/3,

inter-leaver size 400, {15,13} component codes, 10 decoding iterations; AWGN channel. . . 13 3.3 Mean and standard deviation performance of Estimator A. . . 15 3.4 BER performance of a turbo coded DPSK system using perfect SNR and

Estimator A with interleaver size 400 AWGN channel. . . 16 3.5 BER performance of an IBPTC-DPSK system using perfect SNR and

Estimator A with interleaver size 400, AWGN channel. . . 16 3.6 Mean and the standard deviation of Estimator B for coherent BPSK. . . 18 3.7 Mean and the standard deviation performance of Estimator C for DPSK

modulation. . . 20 3.8 Mean and SD performance of decision-aided SNR estimator (Estimator D). 21 3.9 Mean of Estimator A and Estimator D. . . 22

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3.10 Standard deviation performance of the decision-aided estimator and

Es-timator A. . . 22

3.11 A multiple-hop SNR estimate scheme. . . 24

3.12 AJ performance of a turbo coded FH/DPSK system; interleaver size 400, perfect SNR estimate. . . 25

3.13 AJ performance of a turbo coded FH/DPSK system; interleaver size 400, Estimator C. . . 26

3.14 AJ performance of a turbo coded FH/DPSK system; interleaver size 400, multihop SNR Estimator C. . . 26

4.1 The turbo code encoder defined by the 3GPP standard. . . 28

4.2 A turbo decoder structure (with zero internal delay). . . 28

4.3 A modular pipelined turbo decoder. . . 29

4.4 Decoding module for one decoding iteration. . . 29

4.5 An IBP turbo decoder module. . . 33

4.6 Block diagram of DDIIR scheme . . . 35

4.7 Structure of the phase compensated DDIIR filter. . . 37

4.8 Block diagram of the IIR-filtered turbo DPSK system. . . 38

4.9 State diagram of differential encoder. . . 39

4.10 A pipeline IIR filtered turbo DPSK receiver structure. . . 41

5.1 BER performance of a turbo coded DPSK system. . . 44

5.2 BER performance of an IBPTC coded DPSK system. . . 44

5.3 BER performance of an IIR filtered turbo coded DPSK system. . . 45

5.4 BER performance of an IIR filtered IBPTC DPSK system. . . 45

5.5 AJ performance of a turbo coded DPSK system; interleaver size 400, Eb/N0 = 15 dB. . . 48

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5.9 AJ performance of an IIR-filtered turbo coded DPSK system; interleaver size 400, Eb/N0 = 15 dB. . . 50

5.13 AJ performance of an IBPTC coded DPSK system; interleaver size 400, Eb/N0 = 15 dB. . . 52

5.16 AJ performance of an IIR-filtered IBPTC coded DPSK system; interleaver size 400, Eb/N0 = 15 dB. . . 53

5.17 AJ performance of an IIR filtered IBP turbo coded DPSK system; inter-leaver size 800, Eb/N0 = 15 dB. . . 54

5.18 AJ performance of an IIR filtered IBP turbo coded DPSK system; inter-leaver size 1600, Eb/N0 = 15 dB. . . 54

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6.2 A bent-pipe satellite link. . . 57 6.3 Block diagram of a TWTA subsystem. . . 59 6.4 BPL CNR suppression ratio . . . 60 6.5 Typical TWTA AM/AM and AM/PM distortion characteristic

(normal-ized). . . 62 7.1 AJ performance of a turbo coded DPSK nonlinear satellite system;

inter-leaver size 3200, (Eb/N0)t= 10 dB and multihop SNR Estimator C. . . . 66

7.2 AJ performance of a turbo coded DPSK nonlinear satellite system; inter-leaver size 3200, (Eb/N0)t= 15 dB and multihop SNR Estimator C. . . . 66

7.3 AJ performance of an IIR-filtered turbo coded DPSK nonlinear satellite system with interleaver size 3200, (Eb/N0)t = 10 dB and multihop SNR

Estimator C. . . 67 7.4 AJ performance of an IIR-filtered turbo coded DPSK nonlinear satellite

system with interleaver size 3200, (Eb/N0)t = 15 dB and multihop SNR

Estimator C. . . 67 7.5 AJ performance of an IBPTC coded DPSK nonlinear satellite system with

interleaver size 1600, (Eb/N0)t= 10 dB and multihop SNR Estimator C. 68

7.6 AJ performance of an IBPTC coded DPSK nonlinear satellite system with interleaver size 1600, (Eb/N0)t= 15 dB and multihop SNR Estimator C. 68

7.7 AJ performance an IIR-filtered IBPTC coded DPSK nonlinear satellite system with interleaver size 1600, (Eb/N0)t = 10 dB and multihop SNR

Estimator C. . . 69 7.8 AJ performance an IIR-filtered IBPTC coded DPSK nonlinear satellite

system with interleaver size 1600, (Eb/N0)t = 10 dB and multihop SNR

Estimator C. . . 69 7.9 BER performance of the rate 1/2, {554,744} convolutional code in an

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7.10 Uplink AJ performance of a turbo coded DPSK system; interleaver size 3200, (Eb/N0)u = 13 dB, multihop SNR Estimator C. . . 72

7.11 Uplink AJ performance of a turbo coded DPSK system; interleaver size 3200, (Eb/N0)u = 18 dB, multihop SNR Estimator C. . . 72

7.12 Uplink AJ performance of an IIR-filtered turbo coded DPSK system; interleaver size 3200, (Eb/N0)u = 13 dB, multihop SNR Estimator C. . . 73

7.13 Uplink AJ performance of an IIR-filtered turbo coded DPSK system; interleaver size 3200, (Eb/N0)u = 18 dB, multihop SNR Estimator C. . . 73

7.14 Uplink AJ performance of an IBPTC coded DPSK system; interleaver size 1600, (Eb/N0)u = 13 dB, multihop SNR Estimator C. . . 74

7.15 Uplink AJ performance of an IBPTC coded DPSK system; interleaver size 1600, (Eb/N0)u = 18 dB, multihop SNR Estimator C. . . 74

7.16 Uplink AJ performance of an IIR-filtered IBPTC coded DPSK system; interleaver size 1600, (Eb/N0)u = 13 dB, multihop SNR Estimator C. . . 75

7.17 Uplink AJ performance of an IIR-filtered IBPTC coded DPSK system; interleaver size 1600, (Eb/N0)u = 18 dB, multihop SNR Estimator C. . . 75

7.18 AJ performance of a turbo coded DPSK nonlinear satellite system; 1000 bits/hop, interleaver size 3200, (Eb/N0)t= 10 dB, multihop SNR

Estima-tor C. . . 77 7.19 AJ performance of a turbo coded DPSK nonlinear satellite system; 1000

bits/hop, interleaver size 3200, (Eb/N0)t= 15 dB, multihop SNR

Estima-tor C. . . 77 7.20 AJ performance of an IBPTC coded DPSK nonlinear satellite system;

1000 bits/hop, interleaver size 1600, (Eb/N0)t = 10 dB, multihop SNR

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7.21 AJ performance of an IBPTC coded DPSK nonlinear satellite system; 1000 bits/hop, interleaver size 1600, (Eb/N0)t = 15 dB, multihop SNR

Estimator C. . . 78 7.22 Uplink AJ performance of a turbo coded DPSK system; 1000 bits/hop,

interleaver size 3200, (Eb/N0)u = 13 dB, multihop SNR Estimator C. . . 79

7.23 Uplink AJ performance of a turbo coded DPSK system; 1000 bits/hop, interleaver size 3200, (Eb/N0)u = 18 dB, multihop SNR Estimator C. . . 79

7.24 Uplink AJ performance of an IBPTC coded DPSK system; 1000 bits/hop, interleaver size 1600, (Eb/N0)u = 13 dB, multihop SNR Estimator C. . . 80

7.25 Uplink AJ performance of an IBPTC coded DPSK system; 1000 bits/hop, interleaver size 1600, (Eb/N0)u = 18 dB, multihop SNR Estimator C. . . 80

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Chapter 1 Introduction

Anti-jamming (AJ) capability is the most critical measure and requirement of a military communication system. In general, AJ strategies are built upon the following technologies: 1) wideband transmission, 2) multiple antennas (i.e. antenna array), 3) robust modulation, and 4) forward error-correcting (FEC) codes. Spread spectrum (SS) techniques belong to the first category and frequency-hopping (FH) is generally considered as a more robust and efficient electronic counter counter-measure (ECCM) scheme than the direct sequence spread spectrum (DSSS) waveform. In conjunction with FHSS waveform, one can use either differential phase shift keying (DPSK) [1] or M -ary phase shift keying (MFSK) to enhance the system’s AJ robustness, as these two modulation schemes can be incoherently detected and is thus immune to phase noise.

To further improve a ECCM system’s AJ capability, one can invoke a powerful FEC coding scheme. In particular, turbo codes, which form a class of very powerful FEC codes [2], have been shown to be effective in meeting the AJ requirement [3, 4]. It has been shown in [11] that a turbo coded system is not sensitive to the mismatch of SNR if the BPSK modulation is used. However, whether this conclusion is valid when the DPSK or MFSK modulation is used remains unanswered. Hence, the robustness of DPSK and MFSK in the presence of phase error should assessed against their SNR sensitivity. In light of such a concern, we need to find a reliable SNR estimation scheme to avoid performance degradation.

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The purpose of this thesis is to propose and validate solutions to some critical sys-tem issues concerning the design of a turbo-coded FHSS DPSK satellite link. Several new techniques are incorporated into the physical layer design. We use a inter-block permutation (IBP) turbo code, an improved DPSK detector, a very efficient signal to noise ratio (SNR) estimator, and an efficient iterative joint demodulation and decoding structure. As will be shown by numerical examples, the proposed system design makes possible for the overall satellite link to render a large enough AJ margin. The reasons for invoking these new techniques are given in the following paragraphs.

Although a differential coherent DPSK receiver is more robust it suffers from per-formance degradation with respect to a coherent detector. In [6], an infinite impulse response (IIR) filter with decision feedback equipped with a conventional differential de-tection circuit is proposed to improve the reference SNR. It was shown that the resulting DPSK performance comes very close to that of the coherent DPSK detector.

For turbo-coded DPSK system, we modify the structure of [6] to compensate for the received phase offset φ0. We also replace the conventional DPSK demodulator by

a soft-input soft-output (SISO) MAP DPSK detector whose output, after proper de-interleaving, is forwarded to a turbo decoder. We thus have a turbo coded DPSK receiver structure that is equivalent to that of an iterative decoder for a serial concatenated code first conceived by Forney [5]. This receiver structure will be referred to as IIR filtered (or IBP-) turbo DPSK detector.

It has been shown that the IBP turbo code (IBPTC) is an efficient high speed turbo code. However, the use of an IBP turbo code in a military communication system is motivated by another attractive feature of IBPTCs, i.e., an IBPTC decoder continuously expands its message-passing range as the number of decoding iterations increases. Note that in a channel that suffers from partial band jamming, the received samples consist of jammed (unreliable) and unjammed (reliable) samples. Increasing the iteration number thus enable the decoder to collect more reliable samples to help decoding unreliable bits.

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The rest of this thesis is organized as follows. Chapter 2 presents the system and channel (jammer) model of a Ka-band satellite link. Various SNR estimation algorithms are discussed in Chapter 3 and the two key performance-enhancing technologies, i.e., IBP interleaving and IIR filter-aided DPSK detection are presented in the ensuing chapter. Chapter 5 gives numerical uplink performance for a regenerative link with various on-board receiving structures. We discuss the satellite nonlinear effect in Chapter 6 and provide end-to-end (overall link) performance in the following chapter. The last chapter summarizes our major results and compares the worst case performance of the proposed architectures.

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Chapter 2 System and Channel Models

2.1 Turbo coded FH/DPSK systems

turbo encoder i b ci xi _DPSK modulator channel interleaver channel i s i r SISO turbo decoder ' i b _{deinterleaver}channel frequency hopper frequency dehopper M ake decision modulatorDPSK

Figure 2.1: Block diagram of a turbo coded slow FH/DPSK system.

Shown in Fig. 2.1 is a block diagram of the turbo-coded DPSK digital satellite communication system. In the (ground) transmitter site, we have three main building blocks representing the turbo encoder, channel interleaver and DPSK modulator. A sequence of Nb information bits b = (b1, b2, · · · , bNb) is encoded by a rate

1

3 turbo

encoder without puncturing into a sequence of N coded bits c = (c1, c2, · · · , cN). Coded

bit stream is then interleaved by the channel interleaver, denoted by π, through which c is written by columns and the interleaved sequence is read by rows. We represent the interleaving operation by xi = π(ci). The DPSK modulator differentially encode the

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interleaved sequence into the sequence d = (d1, d2, · · · , dN) and produce the bi-phase

sequence, {si = e(jφi)}, where φi ∈ {0, π}.

2.2 Frequency-hopped systems

In a frequency hopping (FH) system, the modulated carrier is hopped in a pseudo-random fashion. An FH system with a hopping rate larger than one hop per channel symbol is called a fast FH system; otherwise it is referred to as a slow FH system. Be-cause the phase coherency among different hops is very difficult to maintain, coherent FH/DPSK systems remain only a theoretical interest. Our study considers a DPSK modulated slow hopping FHSS system. The phase continuity among adjacent samples of a slow FH system makes the DPSK modulated signals detectable. When we observe an FH/DPSK waveform over a number of hop periods, the its frequency content might span the entire spread spectrum bandwidth Wss. Let Rb be the DPSK rate so that

the SS band consists of Wss/Rb = Nss subbands. In the absence of jamming and radio

frequency interference (RFI) a satellite channel is often modelled as an additive white Gaussian noise (AWGN) channel. One can then express the baseband matched filter output at the ith subband as

ri =

p

Esej(φi+φ0)+ ni. (2.1)

where φ0 is a random phase rotation with uniform distribution U [0; 2π) and ni is a zero

mean complex Gaussian random variable.

It is reasonable to assume that the jammer does not have the knowledge of the hop-ping pattern but it does know the frequency band in which the signal was transmitted. A common approach for a jammer is to concentrate its limited power resource over a fraction of Wss in the form of random noise or random tones. The former strategy is

called a partial band noise jammer (PBNJ) while the later strategy is referred to as a multitone jammer (MTJ). Because the communicator in an FH system can in principle

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avoid using certain frequency bands that it has detected as being jammed and changing its hopping pattern, the jammer should also varies its targeted band. For a worst case consideration, we assume that the jammer can modify its power distribution strategy, alter the jammed band over Wss. But the rate of changes is slow relative to the FH dwell

time 1/Rh = Th and yet fast enough to deny the opportunity of the FH communicators

to detect the location of jammed bands and to take necessary remedial action. We also assume that shifts in the jammed band are synchronous with the hop clock so that the communication channel is stationary during a hop period. Finally, we assume that dur-ing a given hop period, the band used by the modulated signals lies entirely inside or outside the jammed band.

2.3 Partial-band noise jammer

A PBNJ emits a fixed amount radiated power over a portion of the frequency hopping band WSS, it distributes its total available power PJ over a band of WJ Hz band. The

jammed band occupies a fraction u = WJ/WSS (0 < u ≤ 1) of the full spread spectrum

(SS) bandwidth. For a perfect FHSS system, the probability that a transmitting band is jammed can be determined by an independent Bernoulli distribution with jamming probability u, i.e. a jammed subsequence on a given band is irrelevant to other sub-sequences. The equivalent power spectrum density (PSD) within the jammed band is

N_J0 = PJ WJ = PJ/WSS u = NJ u (W/Hz). (2.2)

If a DPSK encoded sub-sequence is not jammed, the total noise PSD density level, Nt,

is identical to that of AWGN N0, i.e.,

SN R = Es Nt

= Es N0

(2.3) where Esis symbol energy. In case of a band is jammed, the total noise power corrupting

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i.e., the equivalent signal to noise plus jamming power ratio is given by SN R = Es Nt = Es N0+ N 0 J = Es N0+N_uJ . (2.4)

When the channel state is known, the receiver can classify the channel condition as the jammed and the un-jammed states. The previous independent Bernoulli distribution assumption shows that the probability of the jammed state is u while the probability of the unjammed state is 1 − u. Note that knowing the channel state helps the receiver a lot in boosting its AJ performance and our simulation results show the fact.

2.4 Multitone jammer

Another jammer model which is more effective against FH waveforms is the multitone jammer (MTJ). This kind of jammer divide its total jamming power evenly among Q independent random tones that are uniformly distributed over all the candidate FH bands (Qt = Wss/Rh) within the whole SS band. We assume that the jammer know

how the communicator partition the total hopping band into disjoint subbands and each jamming tone coincide with one of the Qt available carrier frequencies. Thus a

signal jammed at most one jamming tone per hopping period. We also assume that the multitone jammer can randomly rearrange the jamming tones locations to thwart any FH avoidance measures. And the time of the jammer to relocate the jamming tones is also assumed to be synchronous with the communicator’s hopping clock. With these above assumptions the probability a signal is jammed by a MTJ is given by

ρ ≡ Q Qt

(2.5) Let SJR be the signal-to-jammer power ratio and the power of each jamming tone is denoted as Jt,

SJR = S

J =

signal power

total jamming power, (2.6)

Jt =

J

Q =

total jamming power

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The signal-to-jamming tone power ratio SJRt is given SJRt= S Jt = S J/Q = S J(Qtρ) (2.8) Qt= Wss/Rh def

= G is known as the processing gain.

2.5 AJ capability of an FH system

Figs. 2.3 and 2.2 show the AJ performance of a BPSK system when a conventional rate 1/3 convolutional turbo code (CTC) with two identical {15, 13} component codes is used. We will use the same CTC component codes throughout our discussion. It is found that the AJ effectiveness improves as the hopping rate increases. If a fast hopping rate of 1 bit/hop is employed, the jammer is forced to distribute its power over the entire spread spectrum bandwidth while Fig. 2.2 indicates that if a much slower hopping rate 100 bits/hop is used full band jamming is optimal only if the jammer has enough power, i.e., Eb/N0 < 0.8 dB. For a slow FH system with hopping rate = 100 hops/sec and date

rate = 1 Gbits/sec, we have 100 bits/hop which will be used as the default hopping block size in all subsequent discussion unless otherwise specified.

The ultimate goal of an FH AJ system is to force the jammer to jam the entire SS band regardless of how much power it can emit. In other words, we hope to eliminate the jammer’s degree of freedom in choosing which portion of Wss for jamming.

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 1E-5 1E-4 1E-3 0.01 0.1 u=1.0 u=0.7 u=0.4 Eb/NJ (dB)

Bit error rate

Figure 2.2: AJ performance of a turbo coded BPSK system with interleaver size 400, 100 bits/hop and (Eb/N0)t= 15 dB. -4 -3 -2 -1 0 1 2 3 1E-6 1E-5 1E-4 1E-3 0.01 0.1 u=1.0 u=0.7

Bit error rate

E_b/N_J (dB)

Figure 2.3: AJ performance of a turbo coded BPSK system with interleaver size 400, 1 bits/hop and (Eb/N0)t= 15 dB.

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Chapter 3 Channel Estimation Schemes

3.1 Gaussian approximation and extrinsic

informa-tion

It is well known that a turbo decoder needs to have good SNR estimate, as it represents the channel information in computing the reliability of an information bit. For a BPSK signal transmitted over an AWGN channel, the corresponding received matched filter output is given by

ri = p Esxi+ ni (3.1) where xi = +1 if bi = 0, xi = −1 if bi = 1 and ni ∼ N ¡ 0,N0 2 ¢ . Then L (bi|ri) = ln p(ri|bi = 0) · P (bi = 0) p(ri|bi = 1) · P (bi = 1) = lnexp ³ −Es N0(ri− 1) 2´ exp³−Es N0(ri+ 1) 2´ + ln P (bi = 0) P (bi = 1) = 4 · Es N0 · ri+ L(bi) = Lc· ri+ L(bi) (3.2)

We have assumed that a PBNJ effectively increases the noise power level of the AWGN channel over which signal is transmitted. It is also assumed that the received waveform during a given hopping period is either jammed or jam-free. Therefore what we have to

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estimate is Es/Nt, the symbol signal energy to total noise power spectral density ratio

in each hopping block.

We first notice that the DPSK demodulator output is given by ui = rir∗i−1= Esxi+

p

Es(ni+ n∗i−1) + nin∗i−1

= Esxi+ wi (3.3)

where xi ∈ {+1, −1}. Here we have invoked the assumption of [12] that the combination

of three noise terms is an equivalent Gaussian random variable wi ∼ N(µw, σw2). Such

an approximation simplifies the decoding metric computation at the cost of negligible performance degradation. Since the first and the second moments of this Gaussian random variable are given by

E{wi} = µw = E{

p

Es(ni+ n∗_i−1) + nin∗_i−1}

= E{pEsni} + E{

p

Esn∗_i−1} + E{ni}E{n∗_i−1} = 0 (3.4)

var{wi} = σw2 = var{

p

Es(ni+ n∗i−1) + nin∗i−1}

= var{pEsni} + var{

p

Esn∗_i−1} + var{ni}var{n∗_i−1}

= EsN0+ N2 0 4 (3.5) , W02 2 (3.6)

the probability of ui conditioned on xi becomes

p(ui|xi = ±1) = 1 p πW2 0 exp · −E 2 s W2 0 (ui± 1)2 ¸ (3.7) and then L (bi|ui) = ln p(ui|bi = 0) · P (bi = 0) p(ui|bi = 1) · P (bi = 1) = ln exph−E2s W2 0(ui− 1) 2i exp³−Es2 W2 0(ui+ 1) 2´ + ln P (bi = 0) P (bi = 1) = 4 · E 2 s W2 0 · ui+ L(bi) = Lc· ui+ L(bi) (3.8)

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Unlike the BPSK case, the required channel side information (CSI) for DPSK is E2 s/W02.

3.2 Performance loss due to SNR mismatch

Summers and Wilson [11] studied the sensitivity to SNR mismatch for turbo coded BPSK systems in an AWGN channel. They found that turbo coded systems are rela-tively robust to SNR mismatch. At low SNRs the decoder performance degradation is negligible as long as the SNR estimation error is between +1 dB and -2 dB. If SNR is high one can have an even larger estimation error tolerance (between +6 dB and -2 dB).

-6 -4 -2 0 2 4 6 1E-5 1E-4 1E-3 0.01 0.1 1 E_b/N₀ 5.0dB E_b/N₀ 5.4dB

Bit error rate

E_s2 /W₀2

estimate error (dB)

Figure 3.1: SNR sensitivity of a turbo coded DPSK system; code rate 1/3, interleaver size 400, {15,13} component codes, 10 decoding iterations; AWGN channel.

As we are more interested in DPSK waveform, we would like know the SNR sen-sitivities of turbo coded DPSK and IBPTC-coded DPSK systems. IBPTC is a turbo code that uses an IBP interleaver which performs intra-block interleaving and an extra inter-block interleaving. Fig. 3.1 and Fig. 3.2 depict the BER performance as a func-tion of SNR estimafunc-tion error. IBP turbo coded DPSK systems are more sensitive to SNR mismatch than its conventional turbo coded counterpart. As SNR estimation error

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-6 -4 -2 0 2 4 6 1E-5 1E-4 1E-3 0.01 0.1 1 E_b/N₀=4.7dB E_b/N₀=4.5dB

Bit error rate

Es 2

/W0 2

estimate error (dB)

Figure 3.2: SNR sensitivity of a IBP-turbo coded DPSK system; code rate 1/3, inter-leaver size 400, {15,13} component codes, 10 decoding iterations; AWGN channel.

results in significant BER performance degradation in IBPTC-coded DPSK systems, it is important for an IBPTC decoder to have a reliable SNR estimator.

3.3 SNR estimation schemes

Several SNR estimators are presented in this section. Some are obtained using the so-called moment methods while others operate in a decision feedback manner, assuming perfect decisions.

3.3.1 Estimator A

In [11], an online SNR estimation method based on moments and second ordered polynomial curve fitting is proposed. For a BPSK system, the received matched filter output ri has the following statistical properties:

E{r_i2} = Es+ σn2 (3.9) E{|ri|} = σn r 2 πe −(Es/2σn2) +pEs " erf Ãs Es 2σ2 n !# (3.10)

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where erf(x) is the error function. Then the new variable z z = E{r 2 i} [E{|ri|}]2 = 1 + Es σn2 nq 2 πe−(E s/2σ2n)+ q Es σ2 n h erf³qEs 2σ2 n ´io2 = f µ Es σ2 n ¶ (3.11) is a function of Es/σn2. Estimating the moments and z by time-averaging and curve

fitting the inverse function f−1_{(·), we then obtain the estimate c}Es

σ2

n = f

−1_(ˆ_z).

This approach does not have a closed form expression for the inverse function and it is not suitable for a DPSK system needs an estimate of Es2

W2

0 in stead. We present

three SNR estimators that are also based on the moment method but do not need the nonlinear curve fitting coefficients.

Using the approximation erf Ãs Es 2σ2 n ! ≤ 1 −q1 πEs 2σ2 n , Es/2σn2 À 1 (3.12)

we obtain an SNR estimate for BPSK signals

z = E{r 2 i} [E{|ri|}]2 = 1 + Es σ2 n Es σ2 n = 1 + µ Es σ2 n ¶−1 (3.13) ⇒ Es σ2 n = 1 z − 1, Es N0 = 1 2(z − 1) (3.14)

For DPSK modulation, we have

z = E{u 2 i} (E{|ui|})2 = 1 + E 2 s/σw2 E2 s/σw2

from which we obtain the MM-based SNR estimator of the first kind E_s2/σ2_w = 1 z − 1 or, equivalently d_E2 s W2 0 = 1 2(z − 1) (3.15)

For convenience, we refer to the above SNR estimator as Estimator A. Fig. 3.3 shows the performance of the mean and standard deviation performance of this estimator for three different SNRs. This estimator results in a positive bias due to the approximation

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(3.11). Figs. 3.4 and 3.5 shows simulated BER performance when the receiver uses Estimator A and when perfect SNR is available. The code rate is 1/3, interleaver size is 400 and the decoder performs ten decoding iterations. The simulation results indicate that the performance loss due to imperfect SNR estimation is less than 0.1 dB for BER = 10−5_. 0 200 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 satndard deviation mean

Mean and standard deviation of

estimated E s /N0 Number of symbols Es/N0 = 1dB (1.26) mean SD Es/N0 = 2dB (2.59) mean SD Es/N0 = 3dB (2.0) mean SD

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3.0 3.5 4.0 4.5 5.0 5.5 1E-6 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

E_b/N₀ (dB)

zero estimation error Estimator A

Figure 3.4: BER performance of a turbo coded DPSK system using perfect SNR and Estimator A with interleaver size 400 AWGN channel.

3.0 3.5 4.0 4.5 5.0 5.5 1E-6 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

E_b/N₀ (dB)

zero estimation error Estimator A

Figure 3.5: BER performance of an IBPTC-DPSK system using perfect SNR and Esti-mator A with interleaver size 400, AWGN channel.

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3.3.2 Estimator B

Estimator A is a biased estimator with the bias depends on the true SNR. When SNR is low the bias becomes relatively large while the bias is negligible if SNR is high. We now present an SNR estimator which is almost unbiased no matter what the true SNR is.

For a coherent BPSK detector, the first four moments of its matched filter output are

E{ni} = E{n3i} = 0, E{n2i} = σ2n, E{n4i} = 3σ4n

These moments imply

E{r_i2} = E{Es+ 2 p Esxini+ n2i} = Es+ σ2n (3.16) E{r4_i} = E{E_s2+ 4(pEs)3xini+ 6Esn2i + 4 p Esxin3i + n4i} = E_s2+ 6Esσ2n+ 3σ4n (3.17)

and the relationships

3¡E{r_i2}¢2 − E{r_i4} = 2E_s2 Es = s 3 (E{r2 i}) 2 − E{r4 i} 2 (3.18) σ2_n= N0/2 = E{ri2} − s 3 (E{r2 i}) 2 − E{r4 i} 2 (3.19)

which lead to Estimator B c Es N0 = q 3[E(r2 i)] 2 −E(r4 i) 2 2 · E(r2 i) − q 3[E(r2 i)] 2 −E(r4 i) 2 ¸ (3.20)

where the expectations are replaced by time-averages.

Fig. 3.6 depicts the performance of Estimator B. It is obvious that the bias of this estimator is negligible regardless of the true SNR value as long as the number of symbols used for estimating is large enough, say > 300. Unfortunately, Estimator B does not work for DPSK systems.

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200 400 600 800 1000 1200 0.0 0.5 1.0 1.5 2.0 2.5 standard deviation mean

estimated E s /N0 Number of symbols E_s/N₀ = 1dB (1.26) mean SD E_s/N₀ = 2dB (1.59) mean SD E_s/N₀ = 3dB (2.0) mean SD

Figure 3.6: Mean and the standard deviation of Estimator B for coherent BPSK.

3.3.3 Estimator C

Consider the output of a DPSK demodulator. ui = rir∗i−1= Esxi+

p

Es(ni+ n∗i−1) + nin∗i−1 (3.21)

One can establish that

E¡u2_i¢ = E_s2+ 2Esσn2+ σn4 (3.22)

E¡u4i

¢

= Es4+ 12Es3σn2 + 18Es2σn4 + 36Esσn6 + 9σn8 (3.23)

Since W₀2 = 2σ_w2 = 2(2Esσ2n+ σ4n) = 2 £ E¡u2_i¢− E_s2¤ (3.24) and ¡ E_s2+ 6Esσn2 + 3σn4 ¢2

= E_s4+ 12E_s3σ_n2+ 42E_s2σ3_n+ 36Esσn6 + 9σn8

= E¡u4_i¢+ 24E_s2σ_n4 (3.25)

⇒ Es2+ 6Esσ2n+ 3σ4n =

q E (u4

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we obtain Es2 = 3E (u2 i) − (Es2+ 6Esσn2 + 3σn4) 2 = 3 2E ¡ u2 i ¢ − r E (u4 i) 4 + 6E 2 sσn4 (3.27) Therefore, E2 s W2 0 = 1.5E (u 2 i) − q E(u4 i) 4 + 6Es2σ4n 2E (u2 i) − 2 · 1.5E(u2 i) − q E(u4 i) 4 + 6Es2σ4n ¸ = 1.5E(u 2 i) − q E(u4 i) 4 + 6Es2σn4 −E(u2 i) + 2 q E(u4 i) 4 + 6Es2σn4 = −1.5 + 2 q E(u4 i) 4 + 6Es2σ4n −E(u2 i) + 2 q E(u4 i) 4 + 6Es2σn4 = −0.5 + E(u 2 i) −E(u2 i) + 2 q E(u4 i) 4 + 6Es2σn4 = −0.5 + 1 −1 + 2 s E(u4 i) 4[E(u2 i)] 2 + 6 · Esσ2n E(u2 i) ¸2 (3.28) For Es/σn2 À 1 · Esσn2 E (u2 i) ¸2 = µ Esσ2n E2 s + 2Esσ2n+ σ4n ¶2 =   ³ 1 Es σ2 n ´ + 2 +³Es σ2 n ´−1    2 ≈ 0 (3.29) When ·³Es σ2 n ´ + 2 +³Es σ2 n ´−1¸2 À 1, we obtain Estimator C dE2 s W2 0 = −1/2 + 1 −1 + 2 r E(u4 i) 4[E(u2 i)] 2 = q 1 E(u4 i) E(u2 i) − 1 − 1 2 (3.30)

where the expectations are to be replaced by time averages. The resulting performance of this estimator is presented in Fig. 3.7. These performance curves demonstrate that it is an almost-unbiased estimator.

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0 200 400 600 800 1000 1200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 standard deviation mean

estimated E s 2/ W 0 2 Number of symbols Es 2 / W0 2 = 1.14 (Es/N0=4dB) mean SD Es 2 / W0 2 = 1.47 (Es/N0=5dB) mean SD Es 2_{/ W} 0 2_{= 1.87 (E} s/N0=6dB) mean SD

Figure 3.7: Mean and the standard deviation performance of Estimator C for DPSK modulation.

3.3.4 Decision-aided SNR estimator

An alternate candidate estimator is to use decisions for SNR estimation. Note that decisions are made based on the detector output ui.

½ ˆ

xi = 1 if <{ui} ≥ 0

ˆ

xi = −1 if <{ui} < 0 (3.31)

Using the approximation ˆxi = xi and the i.i.d. assumption of ni in the product

<{ui}ˆxi = <{rir_i−1∗ }ˆxi = Esxixˆi+

p

Es<{ni+ n∗_i−1}ˆxi+ <{nin∗_i−1}ˆxi (3.32)

we obtain the estimate

PNe

i=1<{ui}ˆxi

Ne

≈ Es= ˆEs (3.33)

where Ne is the number of samples used in the estimate.

To estimate N0, we use the relation

var{ui} = Es2+ Es µ N0 2 + N0 2 ¶ + µ N0 2 ¶2 = µ Es+ N0 2 ¶2 (3.34)

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which leads to ˆ N0 = p var{ui} − ˆEs (3.35) c Es N0 = Ebs b N0 (3.36) Fig. 3.8 shows the mean and standard deviation of the above decision-aided estimator, which we refer to as Estimator D. Figs. 3.9 and 3.10 compare the mean and standard deviation performance of two biased estimators– Estimator A and Estimator D.

0 200 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

estimated E s /N0 Number of symbols E_s/N₀ = 1dB (1.26) mean SD E_s/N₀ = 2dB (1.59) mean SD E_s/N₀ = 3dB (2.0) mean SD

Figure 3.8: Mean and SD performance of decision-aided SNR estimator (Estimator D).

We find that the mean of Estimator A is closer to the exact value than Estimator D when Es/N0 = Eb/(3N0) is less than 1.59. The standard deviation performance of

Estimator A is also smaller than that of Estimator D. For the turbo coded system under consideration, the SNR region we are interested in is Eb/N0 < 6 dB. Since the code

rate R = 1/3, the Es/N0 region of interest is less than 1.3 dB. Estimator A seems to

be a better candidate in this region. However, this conclusion is based on the uncoded assumption, i.e., the decision is made right at the detector output which tends to give a high BER at low SNRs. If one uses the decoder decision which has much lower error rate, the performance of Estimator D would be much improved.

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0 200 400 600 800 1000 1200 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Mean of estimated E s /N0 Number of symbols Es/N0 = 1dB (1.26) Estimator A Estimator D E_s/N₀ = 2dB (1.59) Estimator A Estimator D E_s/N₀ = 3dB (2.0) Estimator A Estimator D

Figure 3.9: Mean of Estimator A and Estimator D.

0 200 400 600 800 1000 1200 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 _E s/N0 = 1dB (1.26) Estimator A Estimator D E_s/N₀ = 2dB (1.59) Estimator A Estimator D E_s/N₀ = 3dB (2.0) Estimator A Estimator D

Standard deviation of estimated E

s

/N0

number of symbols

Figure 3.10: Standard deviation performance of the decision-aided estimator and Esti-mator A.

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3.4 SNR estimator based on multiple hops

Numerical results presented in the above section indicate that Estimator C is the best choice for incoherent DPSK systems while Estimator B is best SNR estimate for coherent DPSK systems in terms of bias. In the subsequent discourse we will use these two estimators for incoherent and coherent DPSK systems, respectively.

Figs. 3.6 and 3.7 tell us that the performance of a SNR estimator improves as the number of symbols used increases. On the other hand, the AJ capability improves as the hopping rate increases or equivalently, as the number of bits per hop decreases. A higher hopping rate forces the jammer to distribute its total power over a wider bandwidth; see Fig. 2.3. But if the the number of bits per hop decreases the number of bits so is the number of samples used for estimating SNR. To solve this dilemma we propose the multiple-hop SNR estimation scheme shown in Fig. 3.11.

As bits in a hop are either jammed or unjammed, we need to determine whether a received block (hop) is jammed. Assuming the jamming strategy remain unchanged over a period of several hops, we associate each hop with either SNR1 (jammed) and SNR2

(jamming-free). Let C1and C2be the number of hops that belong to the jammed (SNR1)

and unjammed (SNR2) categories, respectively. Every time a new block is received and

the corresponding SNR estimate [SNR is obtained, we classify this block according to the estimated SNR, checking whether it is closer to SNR1 or SNR2. Hence, after the

SNR estimate [SNR for the kth received hop is obtained, we update both representative SNR and the number of each class via

ˆ t = arg min(|[SNR − SNR1|, |[SNR − SNR2|) (3.37) SNRˆt = µ Cˆt Cˆt+ 1 ¶ · SNRˆt+ µ 1 Cˆt+ 1 ¶ · [SNR (3.38) Cˆt = Cˆt+ 1 (3.39)

SNRt is then used to normalize the received bit’s reliability. However it is necessary to

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SNR estimator new received signal in

a hopping block Initial SNR1=0, SNR2=0 Close to SNR1 ? weighted average with SNR1 weighted average with SNR2 True False set to be SNR1 and scale receive

reliablity set to be SNR2

and scale receive reliablity

Figure 3.11: A multiple-hop SNR estimate scheme.

and SNRt are likely to be far apart. By having an upper limit for Ci, the averaged SNRt

be able to track the true SNR closely. In our simulation we let the upper limit be 100 in this multiple-hop SNR estimator. One important assumption is that the jammer can change its jamming occupancy but the rate of the jammer changing jamming occupancy is very slow comparing to the speed that the averaged SNRt adapt to the SNR of the

new jamming occupancy.

Fig. 3.13 shows the simulation result of an IBP turbo coded FH/DPSK system with Estimator C. Since the hopping block size is 100, the number of symbols used to estimate SNR in every block is 100. It results in a performance degradation of 0.7 dB when compared with the perfect known SNR case shown in Fig. 3.12. For a full band

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jammer an error floor around BER = 10−5 _{does exist. When the multiple-hop SNR}

estimate is used Fig. 3.14 shows that the performance degradation is reduced to 0.3dB and the performance in the presence of full band jammer, like that of a conventional turbo code, has a water-fall region around BER = 10−5_.

0 1 2 3 4 5 6 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

E_b/N_J (dB)

u=1.0 u=0.7 u=0.4

Figure 3.12: AJ performance of a turbo coded FH/DPSK system; interleaver size 400, perfect SNR estimate.

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0 1 2 3 4 5 6 7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 3.13: AJ performance of a turbo coded FH/DPSK system; interleaver size 400, Estimator C. 0 1 2 3 4 5 6 7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

E_b/N_J (dB)

u=1.0 u=0.7 u=0.4

Figure 3.14: AJ performance of a turbo coded FH/DPSK system; interleaver size 400, multihop SNR Estimator C.

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Chapter 4 IBP Turbo Codes and

Decision-aided DPSK Detection

4.1 Turbo coded systems

A turbo code is composed of two parallel recursive systematic convolutional codes separated by an interleaver. It promises a BER performance close to the well known theoretical Shannon limit and was invented by Berrou et al. Berrou [2]. The key to the near Shannon-limit performance lies in the interleaver design and the iterative (turbo) decoding algorithm. Fig. 4.1 shows an exemplary turbo code defined by the 3GPP standard [7] while Fig. 4.2 presents a typical turbo decoder structure. For convenience of reference and comparison, we will use the corresponding convolutional codes and interleaver in our turbo coded systems. The input to the encoder is the data sequence {bn : bn = ±1} and the output consists of three bit streams: the information bits

{c0,i} = {bi}, the parity bit stream {c1,i} out of the first convolutional encoder and

the parity bits {c2,i} out of the second convolutional encoder with the interleaved data

stream {π(bi)} as the input. The soft-in soft-out decoder notated as SISOois composed

of two a posteriori probability (APP) decoders and an interleaver-deinterleaver pair. The APP decoders are responsible for computing the log-likelihood ratio and the so-called extrinsic information associated with each bit bn based on the noise-corrupted versions

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D D D D D D Interleaver b _C 0 C2 C1

Figure 4.1: The turbo code encoder defined by the 3GPP standard.

1st SISO APP Decoder 2nd SISO APP Decoder Interleaver Interleaver r0 r1 r2

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The log-likelihood ratio of a given bit is a probabilistic reliability measure which is related to the corresponding a prior information and the extrinsic information. The first and the second APP decoders provides the reliability and extrinsic information about the data sequence {bn} and its interleaved version while the interleaver and the

de-interleaver make sure that the extrinsic information is in right order. As shown in Fig. 4.2, the APP decoding process is carried out for several times until the decoder output meets some stopping criterion or a maximum number of iterations has been reached. For our turbo coded systems, the maximum number of decoding iteration is set to be 10 and no early-stopping mechanism is in place.

Decoding

M odule DecodingM odule DecodingM odule

Figure 4.3: A modular pipelined turbo decoder.

1st SISO decoder (N) Interleaver (N) Delay N 2nd SISO decoder (N) De-Interleaver (SN) Ex[i] r0[i] r1[i] r2[i] to the next decoding module Delay N De-Interleaver (SN) intermediate decoder output to the next decoding module

Figure 4.4: Decoding module for one decoding iteration.

The iteratively (turbo) decoding algorithm can be implemented as P pipelined iden-tical elementary SISO decoders SISOeo [2]; see Figs. 4.3 and 4.4.

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4.1.1 MAP decoding algorithm

The MAP decoding algorithm computes the conditional a posteriori probabilities of a bit given the observed sequence r. It ensures the minimum symbol error probability performance. The corresponding log-likelihood ratio is given by

Li(bi) = log

P {bi = 1|rN1 }

P {bi = 0|rN1 }

(4.1) where 1 ≤ i ≤ Nb, Nb is the length of the information sequence and rN1 is the vector

representation of the received sequence of duration N samples. The decision about bi is

made based on ½ 1 Li(bi) ≥ 0 0 otherwise (4.2) Since Li(bi) = log P {bi = 1|rN1 } P {bi = 0|rN1 } = log P m P m0P {bi = 1, Si = m, Si+1= m0|r N 1 } P m P m0P {bi = 0, Si = m, Si+1= m0|rN₁ } = log P m P

m0P {bi = 1, Si = m, Si−1= m0ri−11 , ri, rNi+1}

P

m

P

m0P {bi = 0, Si = m, Si−1= m0ri−11 , ri, rNi+1}

= log P m P m0P {bi = 1, Si = m, ri, r N

i+1|Si−1 = m0ri−11 } · P {Si−1= m0, ri−11 }

P

m

P

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= log P

m

P

m0P {bi = 1, Si = m, ri, r_i+1N |Si−1= m0} · αi−1(m0)

P

m

P

m0P {bi = 0, Si = m, ri, r_i+1N |Si−1= m0} · αi−1(m0)

= log P m P m0P {bi = 1, Si = m, ri, r N

i+1, Si−1= m0} · αi−1(m0)

P

m

P

m0P {bi = 0, Si = m, ri, r_i+1N , Si−1= m0} · αi−1(m0)

= log P

m

P

m0P {rN_i+1|bi = 1, ri, Si = m, Si−1= m0} · αi−1(m0)

P

m

P

m0P {rN_i+1|bi = 0, ri, Si = m, Si−1= m0} · αi−1(m0)

= log P

m

P

m0P {rN_i+1|Si = m} · P {bi = 1, ri, Si = m, Si−1= m0} · αi−1(m0)

P

m

P

m0P {rN_i+1|Si = m} · P {bi = 0, ri, Si = m, Si−1= m0} · αi−1(m0)

= log P m P m0βi(m) · P {bi = 1, ri, Si = m, Si−1= m0} · αi−1(m0) P m P m0βi(m) · P {bi = 0, ri, Si = m, Si−1= m0} · αi−1(m0) = log P m P m0αi−1(m) · P {bi = 1, ri, Si = m|Si−1 = m0} · βi(m) P m P m0αi−1(m) · P {bi = 0, ri, Si = m|Si−1 = m0} · βi(m)

We have the BCJR form of the log-likelihood ratio Li(bi) = log P m P m0αi−1(m0) · γ_i1(m, m0) · βi(m) P m P m0αi−1(m0) · γ_i0(m, m0) · βi(m) (4.3) where the auxiliary parameters are defined by

αi(m) = P {Si = m, ri1} (4.4)

βi(m) = P {rN1+1|Si = m} (4.5)

γi(m, m0) = P {Si = m0, ri|Si−1= m} (4.6)

These parameters (decoding metrics) have probabilistic interpretations:

• αi(m) is the forward state metric which can be seen as the probability of being at

state m at time i given the observation of the received sequence from the beginning to time instant i.

• βi(m) is the backward state metric which is the probability of the received sequence

form time instant i + 1 to the end given that the encoder state is m at time instant i.

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• γi(m)(m0) is the branch metric which is the probability of receiving ri and being

at state Si = m0 given the previous state Si−1= m.

Moreover, the forward and backward state metrics can be recursively computed via αi(m0) = M −1_X m=0 αi−1(m) · γi(m, m0) (4.7) βi(m) = M −1_X m0₌₀ βi+1(m0) · γi(m, m0). (4.8)

Proper boundary conditions for αi(0) and βi(N ) should be given, depending on how

{bn} and {π(bn)} are encoded. In case of RSC encoders, the received values ri are split

into two component vectors, representing the systematic and parity parts. ri = (yis, y

p

i) (4.9)

and the branch metric can be separated into the following two terms according to whether 1 or 0 is transmitted.

γ1

i = p(ysi|bi = 1) · p(ypi|bi = 1, Si = m, Si−1= m0) · π(Si = m|Si−1= m0) (4.10)

γ_i0 = p(ys_i|bi = 0) · p(ypi|bi = 0, Si = m, Si−1= m0) · π(Si = m|Si−1= m0) (4.11)

where π(Si = m|Si−1 = m0) is the state transition probability and is a function of the

encoder structure and input statistic. For an AWGN channel, log [p(y_is|bi = l)] = 2 Es N0 xs_i(l)y_is (4.12) log [p(y_ip|bi = l)] = 2 Es N0 xp_i(l)yp_i (4.13) where xs i(l) and x p

i(l) are the systematic and parity bits when the ith information bit is

l(= 1 or −1). Es/N0 has to estimated by a proper algorithm given in the last chapter.

4.2 Inter-block permutation (IBP)

Inter-block permutation (IBP) has been shown to be a effective interleaving rule in enhancing the performance of a turbo code regardless of what component codes are

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used [8, 9]. IBP is actually a two-step permutation procedure that consists of an intra-block permutation and an intra-intra-block permutation which further permutes the contents of intra-block permuted blocks. With an IBP interleaver, unbounded interleaving depth with bounded decoding delay is achievable and parallel real-time decoding is made easy. The BER performance curve of an inter-block permutation turbo code (IBPTC) usually has a very sharp waterfall and a low error floor even with a small latency constraint.

1st SISO decoder (N) Interleaver (SN) Interleaver (SN) Delay N 2nd SISO decoder (N) De-Interleaver (SN) De-Interleaver (SN) Delay N Delay (S+1)N (S+1)NDelay Delay 2(S+1)N Ex[i] r0[i] r1[i] r2[i]

Decoding Module (1iteration)

Figure 4.5: An IBP turbo decoder module.

Two IBP algorithms are proposed in [9] and we will use the one given in Table 4.1 as our inter-block permutation rule.

4.3 IIR filtered turbo DPSK structure

In the previous work, we have presented a turbo coded FH/DPSK system and introduced IBP turbo codes for AJ purpose. We expect the additional inter-block per-mutation performed amongst adjacent blocks within which more hops exist will force the jammer to distribute its power in larger band and reduce its jamming effectiveness.

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Table 4.1: An IBP Algorithm [9]. Variables

I[S] - block index

N - interleaver block size K - block number index

D(i,k) - data on the k-th block i-th position Initialization

K=0 Recursion for i=o to S-1

if (K mod (2·(i+1)) < i+1) I[i]=0 else I[i]=1 for i=0 to S-1 m=I[i]+2·i+1 for k=m k+=2S+1 k < N D(k,K)←→D(k,K-i-1) K++

On the other hand, it is known that a turbo coded incoherent DPSK system suffers a 3.5 dB performance degradation against a BPSK system [13]. This degradation can be minimized by applying methods such as multiple-symbol differential detection (MSDD), which detects a transmitted symbol based on the observation over a sequence of received symbols, or the differential detection with IIR filter (DDIIR) approach, which enhances the DPSK performance to the extent that the performance loss is almost negligible [6]. The latter approach will used in our system.

In the following subsections, we will discuss how to modify the DDIIR structure and apply it to our either turbo coded FH/DPSK or IBP turbo coded FH/DPSK systems.

4.3.1 Decision-aided DPSK differential detection

DPSK modulation is often used for terrestrial and satellite mobile communication systems because it does not a carrier recovery circuit and has fast acquisition perfor-mance. A DPSK demodulator recovers the information bit by comparing the phase

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difference of two consecutive symbols. Since the decision involves samples from two symbol periods, more noise is introduced. Thus the energy per bit to noise power den-sity ratio (Eb/N0) required for DPSK incoherent detection is higher than that required

for coherent DPSK detection to attain the same BER under the same channel condition. To improve the performance of a differential coherent DPSK receiver, several remedies have been proposed.

T * Hard Decision complex conjugate 1 symbol delay

_d

_k k

r

IIR filter

exp

k k

A

S

=

Figure 4.6: Block diagram of DDIIR scheme

Fig. 4.6 is the DDIIR structure proposed in [6]. This DDIIR scheme has a desirable characteristic that a wide range of performance between coherent and differential detec-tion is achievable by simply changing the real valued weighting parameter α. When α is chosen to be close to 1 (see Fig. 4.6), the resulting BER performance becomes very close to that of differentially encoded coherently detected PSK (DEPSK) while if α is chosen to be 0, the performance is just that of an incoherent DPSK detector.

4.3.2 Phase compensated DDIIR

It had been showed that the DDIIR structure for increasing the reference bit SNR can improve DPSK detection performance [6]. With this detection structure, the BER performance in AWGN channels comes very close to that of a coherent DPSK detector. Since the detection BER performance is close to that of coherent detection, we can treat

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the output of the hard decision signals as coherent DPSK decision output signals and further use them to estimate the phase offset φ0. We will name the modified structure

as the phase compensated DDIIR filter; see Fig. 4.7. The filter is basically composed of two parts, one is the DDIIR part whose responsibility is to increase the reference bit SNR and the other part is responsible for phase estimation and compensation.

In the second part, the decision ej4φi is sent to an accumulative multiplier whose

output value is conjugated, giving e−j ¯φi. Phase offset estimation φ

0 is obtained by (i)

multiplying the the received sample by e−j ¯φi and (ii) averaging the accumulated product.

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T * Hard Decision complex conjugate 1 symbol delay d_k k r T * T accumulate loop atan(.) ( ) j e-· phase compensate phase compensated signal IIR filter phase estimate & compensate

exp

k k

A

S

=

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4.3.3 Turbo DPSK receiver with phase estimation

Suppose the phase offset has been compensated for, we can compute the soft values of phase compensated channel information. The original DPSK demodulator can then be replaced with a soft in soft out (SISO) decoder, we denote the inner SISO decoder as SISOi and the outer SISO decoder as SISOo. The receiver that iteratively decodes

the serial concatenated coded waveform is henceforth called the turbo DPSK detector. The turbo coded DPSK system with the proposed receiver structure is referred to as the IIR-filtered turbo DPSK receiver as shown in Fig. 4.8.

turbo encoder i b ci xi _DPSK modulator channel interleaver channel i s i r SISO turbo decoder ' i b _{deinterleaver}channel frequency hopper frequency dehopper M ake decision modulatorDPSK channel interleaver { } APP yi APP{ }xi

Figure 4.8: Block diagram of the IIR-filtered turbo DPSK system.

The iterative decoding procedure between inner DPSK SISO decoder and the outer turbo code decoder is summarized in the following.

1. Scale the real part values of the received phase compensated signal to provide channel information for the codeword bits of the inner code. For the first iteration, set the a priori probability equal-likely.

2. Calculate γi(m, m0), αi(m0), and βi(m) with the recursive computation equations

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the extrinsic information λj.

3. Deinterleave the stream of λj to λi as be the log-likelihood ratio (LLR) input for

the code word bits of the outer code.

4. Run the turbo decoding procedure as mentioned before and compute the extrinsic information of the information bits.

5. Encode the extrinsic information of the information bits to get extrinsic informa-tion of the code word bits and interleave them to be a priori informainforma-tion for the next iteration inner decoding.

6. Go back to step.2 and begin the next decoding iteration. Or stop the procedure in step.5 and make decision if the maximum number of iterations is reached.

1 1 0 0 0/1 0/0 1/0 1/1 i i+1

Figure 4.9: State diagram of differential encoder.

Note that because the inner encoder is a two-state differential encoder, Step 2 can be simplified without recursively computing the backward state metrics. Consider the state diagram of differential encoder in Fig. 4.9. When computing the backward state metric for each state in instant i, it has a metric path of bit 0 from the state 0 in instant i + 1 and a metric path of bit 1 from the state 1 in instant i + 1. Thus the backward state

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metrics will all be equal after recursive computation. Therefore it has no contribution to the inner decoding.

We know that using an IIR filter to estimate the phase offset the estimated phase will be more accurate as the symbol index i increase. In other words, the phase compensation for the beginning symbols in each code word may not be good enough. Therefore we should have some special design for the IIR filtered turbo DPSK pipeline structure as Fig. 4.10. Since the turbo decoded systems have to implement in pipelined structure, the received signals should be delayed for the next decoding module. And the IIR filter estimated phase in the last last symbol index is always the most accurate one. We can use the estimated phase in the last last symbol index to do phase compensation of the pipeline delayed signals for the decoding iterations other than one. This action has to be done only once as illustrated in Fig. 4.10.

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T * Hard Decision complex conjugate 1 symbol delay dk k r T * T accumulate loop atan(.) ( ) j e-· phase compensate for 1st iteration inner decoder Delay Line ( ) j e-· for 2nd iteration inner decoder Delay Line for 3rd iteration_{inner decoder}

. · · · . · · · IIR filter phase estimate & compensate exp k k A S =

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Chapter 5 Uplink Performance: Numerical

Results and Discussion

In this chapter we report the simulated performance of the four system structures we have presented, namely, turbo coded DPSK, IBPTC coded DPSK, IIR filtered turbo coded DPSK and IIR filtered IBPTC coded DPSK systems. The interleaver size is assumed to be 400. Furthermore, each system structure with different turbo encoder interleaver size are simulated in the communication environment of PBNJ interference with AWGN background noise. Error correcting ability of turbo codes can be enhanced by increasing the encoder interleaver size. We will see how large the interleaver size is enough for each receiver structure to force the PBNJ jammer distribute his jamming power over the full spreading spectrum. It means that we want the intersections of the full band jamming BER performance curve and the other jamming occupancy BER per-formance curve lie in very low BER, such as 10−5_{. Then the four system structures with}

suitable turbo encoder interleaver size will be simulated more practically by introducing the nonlinearity effect of the TWTA subsystem.

5.1 Performances in AWGN channels

To begin with, we consider the case where the only channel perturbation is AWGN and no FH is employed. The system parameters for all receiver structures are identical: code rate = 1/3, interleaver size = 400 and {15,13} component codes are used. Our

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simulation run stops whenever 50 (or 100) frame errors are detected.

From Figs. 5.1-5.3, we conclude that to reach a BER = 10−5_{, the required E}

b/N0 for

turbo coded, IBP turbo coded, IIR filtered turbo and IIR filtered IBPTC DPSK systems are 5.4 dB, 4.7 dB, 4.6 dB and 4.1 dB, respectively. It means that by using an IBPTC, 0.7 dB is gained. The IIR filtered mechanism provides a 0.8 dB gain to the turbo coded DPSK system and a 0.6 dB gain to the IBPTC coded DPSK system.

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3.0 3.5 4.0 4.5 5.0 5.5 6.0 1E-6 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

E_b/N₀ (dB) 1 iteration

3 iterations 5 iterations 10 iterations

Figure 5.1: BER performance of a turbo coded DPSK system.

3.0 3.5 4.0 4.5 5.0 1E-6 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

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0 1 2 3 4 5 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

Figure 5.3: BER performance of an IIR filtered turbo coded DPSK system.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

E_b/N0 (dB) 1 iteration

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5.2 Performances in PBNJ interference and AWGN

Numerical results reported in this section assume the presence of PBNJ in addition to AWGN. All the system parameter values are the same as before except for the interleaver size. We consider interleaver with sizes 400, 800 ,1600 and 3200. It is known that the larger the size of interleaver is the more powerful the error correcting ability of the associated turbo code becomes and thus the more coding gain and better AJ capability we obtain. To have a fair comparison between IBP turbo coded and conventional turbo coded systems, the interleaver size of the latter should be twice as large as that of the former system since the IBP span is only 1.

Figs. 5.5-5.12 show the performance of various DPSK systems for different inter-leaving sizes. The optimal interinter-leaving sizes for them are 3200, 3200, 1600 and 1600, respectively. The jammer will be forced to be jam the full band. The worst case for each system with a proper interleaver size is summarized in Table 5.1.

Table 5.1: System performance comparison (known Eb/N0 = 15 dB but without

nonlin-earity effect).

system structure proper interleaver size SJR for BER 10−5

turbo coded FH/DPSK 3200 5.1 dB

IIR filtered turbo coded FH/DPSK 3200 3.7 dB

IBP turbo coded FH/DPSK 800 (1600) 5 dB (4.8 dB)

IIR filtered IBP turbo coded FH/DPSK 1600 4.05 dB

We compare the AJ performance of the IBPTC coded FH/DPSK system using an interleaving size of 1600 with that of the turbo coded FH/DPSK system using an in-terleaving size of 3200, as both systems have the same encoding and average decoding delays. The IBPTC provides a 0.3 dB gain against conventional turbo coded system at BER = 10−5_{. With the same delays, to have BER = 10}−5 _{at SJR = 5 dB, the IBPTC}

system need an interleaver size of 800 while the conventional turbo coded system needs 3200–that is four-fold increase in the interleaver size and two-fold increase in decoding

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5.2.1 Turbo coded FH/DPSK systems

0 1 2 3 4 5 6 7 8 9 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 5.5: AJ performance of a turbo coded DPSK system; interleaver size 400, Eb/N0 =

15 dB. 0 1 2 3 4 5 6 7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 5.6: AJ performance of a turbo coded DPSK system; interleaver size 800, Eb/N0 =

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0 1 2 3 4 5 6 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 5.7: AJ performance of a turbo coded DPSK system; interleaver size 1600, Eb/N0 = 15 dB. 0 1 2 3 4 5 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

E_b/N_J (dB)

u=1.0 u=0.7

Figure 5.8: AJ performance of a turbo coded DPSK system; interleaver size 3200, Eb/N0 = 15 dB.

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5.2.2 IIR-filtered turbo coded FH/DPSK systems

0 1 2 3 4 5 6 7 8 1E-6 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 5.9: AJ performance of an IIR-filtered turbo coded DPSK system; interleaver size 400, Eb/N0 = 15 dB. 0 1 2 3 4 5 6 1E-6 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 5.10: AJ performance of an IIR-filtered turbo coded DPSK system; interleaver size 800, Eb/N0 = 15 dB.

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0 1 2 3 4 5 1E-6 1E-5 1E-4 1E-3 0.01 0.1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 5.11: AJ performance of an IIR-filtered turbo coded DPSK system; interleaver size 1600, Eb/N0 = 15 dB. 0 1 2 3 4 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

E_b/N_J (dB)

u=1.0 u=0.7

Figure 5.12: AJ performance of an IIR-filtered turbo coded DPSK system; interleaver size 3200, Eb/N0 = 15 dB.

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5.2.3 IBPTC coded FH/DPSK systems

0 1 2 3 4 5 6 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

Eb/NJ (dB)

u=1.0 u=0.7 u=0.4

Figure 5.13: AJ performance of an IBPTC coded DPSK system; interleaver size 400, Eb/N0 = 15 dB. 0 1 2 3 4 5 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Bit error rate

Eb/NJ (dB) u=1.0

u=.7 u=0.4

Figure 5.14: AJ performance of an IBPTC coded DPSK system; interleaver size 800, Eb/N0 = 15 dB.

具有處理能力的衛星轉頻器之架構與效能

國 立 交 通 大 學

電信工程學系碩士班

碩 士 論 文

具有處理能力的衛星轉頻器之架構與效能

Architecture and Performance of a Satellite

Transponder with On-Board Processing Capability

研 究 生：廖明堃

指導教授：蘇育德 博士

具有處理能力的衛星轉頻器之架構與效能

Architecture and Performance of a Satellite

Transponder with On-Board Processing Capability

研 究 生 : 廖明堃 Student : Ming-Kun Liao

指導教授 : 蘇育德 博士 Advisor : Dr. Yu T. Su

國 立 交 通 大 學

電 信 工 程 學 系 碩 士 班

碩 士 論 文

A Thesis

Submitted to Department of Communication Engineering

College of Electrical and Computer Engineering

National Chiao Tung University

in Partial Fulfillment of the Requirements

for the Degree of

Master of Science

in

Communication Engineering

July 2006

Hsinchu, Taiwan, Republic of China

中華民國九十五年七月

具有處理能力的衛星轉頻器之架構與效能

研究生：廖明堃 指導教授：蘇育德 博士

國立交通大學電信工程學系碩士班

中文摘要

本論文探討具抗干擾(anti-jam, AJ)能力的衛星轉頻器之架構及效能。

我們所考慮的上傳鏈路(uplink)除有加成性的白高斯背景雜訊(AWGN)另有

惡意的干擾，即所謂的部份頻寬雜訊干擾(partial-band noise jamming)。我

們發現具有處理(processing)或再生(regenerative)功能之衛星轉頻器可以

提供強大的抗干擾能力。為強化抗干擾能力我們使用了慢跳頻式的差分相

位相移鍵信號並加上了渦輪編碼。

經過差分相位相移鍵調變的渦輪編碼信號可視為等同於一個串聯編碼

架構，其中內部碼(inner code)為碼率為一的特殊迴旋碼而外部碼(outer code)

則為渦輪碼。基於此種等效模式，我們提出一種迭代的解碼結構並且藉由

數值的模擬檢驗此種不同於以往的解碼排程的效率。我們更進一步使用塊

間重排(IBP)的渦輪碼使得在解碼時可藉由迭代交換不同區塊之間的解碼

訊息以有效的更正錯誤。實驗數值證實這種改錯碼能夠在跳頻速率很低時

仍維持相當良好的性能。另一方面，傳統的渦輪碼需有較高的跳頻速率方

能滿足系統的抗干擾能力性能要求。

Architecture and Performance of a Satellite Transponder with

On-Board Processing Capability

Contents

List of Figures

Chapter 1

Introduction

Chapter 2

System and Channel Models

2.1

Turbo coded FH/DPSK systems

2.2

Frequency-hopped systems

2.3

Partial-band noise jammer

2.4

Multitone jammer

2.5

AJ capability of an FH system

Chapter 3

Channel Estimation Schemes

3.1

Gaussian approximation and extrinsic

informa-tion

3.2

Performance loss due to SNR mismatch

3.3

SNR estimation schemes

3.3.1

Estimator A

3.3.2

Estimator B

3.3.3

Estimator C

國立交通大學

碩士論文

研究生：廖明堃

指導教授：蘇育德博士

研究生 : 廖明堃 Student : Ming-Kun Liao

指導教授 : 蘇育德博士 Advisor : Dr. Yu T. Su

國立交通大學

電信工程學系碩士班

碩士論文

研究生：廖明堃指導教授：蘇育德博士

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