Application of LDPC codes for Deep Space Communication under Solar Scintillation Condition

Transcription

1 Application of DPC codes for Deep Space Communication under Solar Scintillation Condition Qi i Department of Electronic Engineering Haidian District, Beijing, 84 qi-li9@mails.tsinghua.edu.cn iuguo Yin School of Aerospace Haidian District, Beijing, 84 yinlg@tsinghua.edu.cn Jianhua u Department of Electronic Engineering Haidian District, Beijing, 84 lujh@mails.tsinghua.edu.cn Abstract: Solar scintillation effects can be significant for deep-space telecommunication links during superior solar conjunction. In this paper, we propose to apply low-density parity-check (DPC) codes in the ician Channel characterized by ionospheric scintillation to improve the performance. Simulation results reveal that the coding gain with DPC codes at 8.4 GHz (X-band) and 3 GHz (Ka-band) are better than convolutional codes, with more than 3. db and.5 db respectively, and the performance degradation of convolutional codes is deeply affected by channel fading, while DPC codes represents an excellent performance of channel fading resistance. Key Words: solar scintillation, rician channel, DPC codes Introduction During the human exploration of space, the communications link is the only way that enables the Earth to send telecommand to and receive telemetry information from the probe, and directly dictates the success or failure of exploration mission. However, the communication link in deep space environment faces a severe challenge, which, first and foremost, is the very-long distance: for geosynchronous satellite, the distance is 36, km, for lunar probe, it reaches 38, km, for Mars probe, it can achieve as long as 384,, km at most. The very-long distance transmission can degrade the signals to serious degree. Meanwhile, the signal propagation is under harsh channel conditions characterized by ionospheric scintillation, multipath propagation and interference, which will affect the communication link furthermore. Severe ionospheric scintillation can even make the t- elecommunication link unavailable. The Earth-Probe link encounters ionospheric scintillation during superior solar conjunction (see Fig. ), when the Sun lies between the Earth and probe. The Earth-Probe distance is at or near maximum and the received signal is at its weakest level. In addition, the intervening charged particles of the solar corona in the signal path produce significant amplitude scintillation, phase scintillation, and spectral broadening effects, which increase as the Sun-Earth- Probe (SEP) angle ( in Fig. ) decreases [4]. Several solutions are provided to deal with the situation, such as the implementation of channel coding, Earth θ Sun Figure : elevant solar conjunction geometry. Probe the increase of antenna aperture and the reduction of project operations, while each of them has its limitation respectively. First, the channel coding method in deep space communication at present is convolutional code, which has insufficient correcting ability in severe condition. Second, the increase of antenna aperture will increase the construction cost as well as the operation complexity. Third, the reduction of project operations, such as invoking command moratoriums, downscaling tracking schedule and lowering data rates, will result in the unreliability of the whole system. In this paper, we proposed to apply low-density parity-check (DPC) codes instead of convolutioanl codes to obtain high error correctability. Noted for its near Shannon limit performance [], [3], DPC codes have been extensively applied in many communication and digital storage systems with high reliability requirements, and these years the applications have ISBN:

2 ( ) ( ) j ( ) w t = s t e θ α ( t) n( t) sc where K S is deterministic signal power (specular signal component); ϕ is a constant phase shift randomly and uniformly distributed over the interval of [ π, π] and n scint (t) is a (filtered) complex Gaussian process generated from scattered signal propagation over random paths (non line-of-sight) due to ionospheric scintillation effects. The signal fluctuation is measured by the scintillation index [4]: var{ α sc (t) = } () {E α sc (t) } Modulated/ coded Input signal Figure : Complex baseband channel simulation model. been expanded to aerospace field, such as Chang e, Chinese unmanned lunar probe launched in November. As ionospheric scintillation can be statistically modeled as ician or ayleigh signal fading with finite signal decoration time and limited coherent bandwidth of transmission channel [], we optimize the DPC codes to get better performance in ician channel. The simulation results reveal that with the application of DPC codes, the coding gain at 8.4 GHz (X-band) and 3 GHz (Ka-band) are better than convolutional codes, with more than 3. db and.5 d- b respectively under solar scintillation condition, and the performance of DPC codes is much less sensitive to the channel fading than convolutional codes. It is extremely useful to improve communication performance for deep space telemetry. Section II addresses the scintillation modeling of the communication channel. Section III describes the optimization studies of DPC codes over ician channel. Section IV presents the simulation and performance analysis of the DPC codes, finally conclusion is in section V. System Model for Solar Scintillation A simulation model of scintillation communication system is depicted in Fig.. Time-varying scintillation coefficient α sc (t) is s- tatistically modeled as a non-zero mean, complex Gaussian random process [8]: α sc (t) = K S e jϕ + n scint (t) () The average signal power received via the scattered paths is proportional to: σnsc E n scint and the total received signal power is presented by: S = (K S +σnsc) P S, where P S E w(t) = E{s(t) } is the transmitted signal power (see Fig. ). Assume that the amplitude scintillation causes no loss in the long-term average received signal power. Then the specular and scattered signal power components must meet the constraint K S + σnsc =. The envelop of the scintillation coefficient SC = α sc (t) has a character of ician distribution, i.e., p rsc () = σ nsc e γ e σnsc I { γ σ nsc }, (3) where γ K S /σ nsc is the ician factor, defined as the ratio of received specular power to random power. The relationship of scintillation index and the ician factor γ can be expressed as [5] γ = ( S 4 )/ ( S 4 )/ (4) Then the parameters K S and σ nsc are related to the scintillation index by K S = ( S 4) / (5) σnsc = ( S 4 )/ (6) Notice that is between and. When, it translates to an ideal non-fading channel, with < <, it is ician fading, and in the limit (no line-of-sight received path), it reduces to the ayleigh fading. The received signal of fading channel in Fig. can be presented by y(t) = α sc (t) w(t) + n(t) = α sc (t) s(t)e jθ(t) + n(t) (7) Where θ(t) is derived from channel estimation, and independent of the concerned signal to noise ratio (S- N); n(t) obeys Gaussian random distribution with zero mean and variance σ ; α sc is normalized ician ISBN:

3 fading factor with E{α sc} = and probability density function (pdf) is given by (3); for binary phase shift keying (BPSK) modulation, s { E s, E s } maps the code symbol x, while E s is the symbol energy []. Assume the ician fading factor α sc is given. Then the conditional pdf of the matched filter output is [] p(y s, α sc ) = πσ e (y sα sc) σ (8) C(Bit/Symbol) Shannon capacity boundary BPSK AWGN BPSK ician BPSK ayleigh The capacity of the channel is defined by (db) C = max p s (s) {I(S; Y A SC)} = max {E p(y s, α sc ) p(s,y,α sc ){log p s(s) z p s(z) (y z, α sc ) }} where E p (x) is the mathematical expectation of variable x with probability distribution of p. The pdf p(s, y, α sc ) can be written as () due to the independency between s and α sc. p(s, y, α sc ) = p(y s, α sc ) p(s) p(α sc ) () If p(s) satisfies the equal-probability distribution, the I(S; Y A SC ) reaches the maximum. C = log ( = s=± E s p(α sc ) p(y s, α sc ) p(y s, α sc ) z=± E s p(y z, α sc ) ) dy dα sc p(α sc ) p(y s = E S, α sc ) (9) p(y z = E s, α sc ) log ( p(y z = E s, α sc ) + p(y z = E s, α sc ) ) () dy dα sc = p(α sc ) p(y s = E s, α sc ) log ( + p(y z = E s, α sc ) p(y z = E s, α sc ) ) dy dα sc The capacity C can be written as () through (8) and (). C = p(α sc ) p(y s = E s, α sc ) () log ( + e yαsc Es/σ ) dy dα sc According to Shannon s second theorem, if the information transmission rate is not larger than the channel capacity C, there exists a coding system such that Figure 3: Shannon channel capacity limit. the information bit can be transmitted over the channel with an arbitrary small frequency of errors. et = C and combine with { N } =C = { E s N } =C (3) the numerical solution of Shannon limit in ician channel can be calculated. Fig. 3 shows the shannon limits in ician, ayleigh and AWGN channel with channel state information of BPSK signal [6]. The rician factor γ is db. The shannon limits of ician and AWGN channel is very close to the shannon channel capacity boundary with low bit rate. 3 The Proposed Communication System with DPC Codes The simulation approach is based on the link model as shown in Fig. 4, with the assumption of an ideal receiver, that is, the assumption of perfect carrier and subcarrier tracking as well as symbol synchronization. The degradation caused by amplitude scintillation is simulated for the case of BPSK modulation with D- PC codes as well as convolutional codes for comparison. The effects due to scintillation are introduced by the relationship between scintillation index and ician parameters K S and σ nsc through (5) and (6). The DPC codes used in the simulation are defined by column weight distribution polynomial λ(x) and row weight distribution polynomial ρ(x) through (4) and (5), with code length n of 3 and code rate r of /. λ(x) = x x x 6 (4) ISBN:

4 Input Data DPC Encoder Convolutional BPSK Modulator =.37 =4 =.37) Before coding =4 =.37) after DPC coding =4 =.37) after convolutional coding Encoder (7,/) Amplitude Scintillation ician Model AWGN BP Output Data Decoder Viterbi Decoder BPSK Demodulator Figure 5: Telecommunication link performance at X- band with = 4. (7,/) Figure 4: Channel simulation model due to solar scintillation. =.3 =5 (S =.3) Before coding 4 =5 =.3) after DPC coding =5 =.3) after convolutional coding ρ(x) =.6754 x x 5 (5) The decoding of received data is based on iterative belief-propagation (BP) algorithm, which is particularly effective for DPC codes. For comparison, the communication performance is simulated with no channel coding as well as (7, /) convolutional codes at both 8.4 GHz (X-band) and 3 GHz (Ka-band). The decoder for convolutional codes uses Viterbi algorithm. 4 Numerical Simulations The simulation performance at X-band is shown in Fig. 5, Fig. 6, Fig. 7 and Fig. 8, where the Sun- Probe distance ( in Fig. ) is varied from 4 to 8 solar radii ( in Fig. ) and the corresponding scintillation index decreases from.37 to.99 [7]. The simulations show that at =, which is usual requirement for deep-space telecommunication link, the link performance of DPC codes is better than convolutional codes with coding gain more than 3. db at least, and with the increase of scintillation index, the performance of convolutional codes degrades seriously, while DPC codes represents an excellent performance of fading resistance. Fig. 9) displays the link performance results at Ka-band, where the probe is assumed to be at perihelion with the Sun-Probe distance = 4 and the scintillation index =.64, which is much smaller than X-band at the same Sun-Probe distance Figure 6: Telecommunication link performance at X- band with = 5. =.37). The link performance of DPC codes is better than convolutional codes with coding gain about.5 db at =. 5 Conclusion DPC codes can give very good performance for communication under solar scintillation condition. In addition, their complexity can be reduced to the admissible level by using semi-random structure. Therefore, DPC codes are very powerful and useful when they are applied to telemetry information transmissions in deep space communications. Acknowledgements: This work was supported in part by National Natural Science Foundation of China (No. 6) and Program for New Century Excel- ISBN:

5 =.6 =6 =.6) Before coding =6 =.6) after DPC coding =6 =.6) after convolutional coding Figure 7: Telecommunication link performance at X- band with = 6. =.99 =8 =.99) before coding =8 =.99) after DPC coding =8 =.99) after convolutional coding Figure 8: Telecommunication link performance at X- band with = 8. =4 =.64) Ka band Before coding After DPC coding After convolutional coding lent Talents in University (NCET). eferences: [] Kullstam P. A. and Keskinen M., Ionospheric Scintillation Effects on UHF Satellite Communications, MICOM,. []. G. Gallager, ow-density Parity Check Codes. Cambridge, MA: MIT Press, 963. [3] D. J. MacKay and. M. Neal, Near Shannon limit performance of low density parity check codes, IEE Electronics etters, vol. 3, no. 8, pp , Aug [4] E. J. Fremou and H. F. Bates, Worldwide behavior of average VHF-UHF scintillation, adio Sci.,vol. 6, pp , Oct. 97. [5] P. Shaft, On the elationship between Scintillation Index and ician Fading, IEEE Trans., Comm., pp.73-73, May 974. [6] Shaoqian i, Principle and Application of DPC codes. Chengdu, China: University of Electronic Science and Technology of China Press, May 6. [7] Y.Feria, M.Belongie, T.McPheeters and H.Tan, Solar Scintillation Effects on Communication inks at Ka-band and X-band, The Telecommunications and Data Acquisition Progress eport 4-9,JP Pasadena,California,May 5,997. [8] Z. Ye and E. Satorius, Channel Modeling and Simulation for Mobile User Objective System (MUOS)-Part I: Flat Scitillation and Fading, ICC 3, pp , Nov. 3. [9] D. Morabito, Solar Corona Amplitude Scintillation Modeling and Comparison to Measurements at X-Band and Ka-Band, JPN Progress eport 4-53, May.5 3. [] Xu Hua, Xu Cheng-qi and Xiaochuan Zheng, Optimization of Irregular DPC codes on ician Channel, Proc. Wireless Communications, Networking and Mobile Computing, 5. [] in Jiaru and Wu Weiling, Performance of Irregular DPC codes on ician-ading Channel Acta Electronic Sinica, vol. 33, no., Jan. 6. Figure 9: Telecommunication link performance at Kaband with = 4. ISBN: