Semi-blind Joint Data Equalization and Channel ... - IEEE Xplore

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*State Key Lab. of Integrated Services Networks Xidian University. Shannxi Xi'an ... suggested for adaptive modulation and coding (AMC) of MBC system in this ...
Semi-blind Joint Data Equalization and Channel Estimation for Meteor Burst Communication Zan Li*, Member IEEE, Jian Shen**, Jueting Cai*** and Jueping Cai* *State Key Lab. of Integrated Services Networks Xidian University Shannxi Xi’an, China, 710071 [email protected] ** China Electronics Systems Engineering Corporation Beijing,China *** Huawei Technologies Co.Ltd Shenzhen, China, 518129

Abstract According to the analysis of MBC (meteor burst communication) mechanism, a model of signal processing based on the structure of data frame is suggested for adaptive modulation and coding (AMC) of MBC system in this paper. There are two distinct modes of operation for signal processing: acquisition and tracking. The acquisition mode is a training period to initialize the channel estimation by frame header. The tracking mode is jointly to equalize payload data and to trace channel, where the principle of persurvivor processing (PSP) for maximum likelihood sequence detection (MLSD) is performed. A suboptimal method called D-PSP is adopted to save the computational time and memory size, which agrees with the slow-fading characteristic of meteor channel and makes the MLSD possible for adaptive modulation and coding of MBC system. Computer simulation results are included to support our development.

For joint channel estimation and equalization, persurvivor processing (PSP) [3-7] provide a general framework for the approximation of maximum likelihood sequence detection (MLSD) for unknown or time-varying channels, by incorporating channel estimation into the Viterbi algorithm (VA), which provides superior performance and robustness. However, for very short active duration of meteor bursts, the perfect precise VA becomes computationally prohibitive for adaptive modulation and coding (AMC) of MBC system.

2. Mechanism of MBC

1. Introduction Meteor burst communication (MBC) systems fill a unique niche in the area of communications. It less susceptibility to jamming, low probability of interception and more rapid blackout recovery when compared can support reliable communication with superiorities of nuclear survivability, to HF or satellite systems for civil and military applications [1] [2]. Due to the nature of meteor channel, MBC transmit messages in an intermittent manner, so its acceptance is hampered by the channel’s low throughput and long message waiting time. One way to improve MBC performance is adaptively to change information rates with the signal-to-noise ratio (SNR). For meteor burst communications, the medium experiences multipath propagation which induces the intersymbol interference (ISI), thus resulting in both data detection and channel estimation problems at the receiver side.

Fig.1 Adaptive modulation and coding for MBC system

The forward scattering of radio waves from ionized trails of meteors provides reliable communication channel with path lengths from 300 to 2000 km and in the frequency band of 40 to 100 MHz [8][9]. Meteor trails are conveniently classified as either “underdense” or “overdense”. Even though shorter in duration, underdense bursts are more prevalent and constitute most of the meteor burst channels. The rapid decay of underdense meteor trails results in low throughput and long message waiting time. Fortunately, system throughput can be significantly improved using varied rate transmission with the exponential decay of

This Work is supported by the National Natural Science Foundation of China under Grant No: 60402040 and Grant No. 60532060 .and also supported by the Natural Science Foundation of Shannxi Province China under Grant No. 2005F29.

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underdense trails. To simplify MBC systems, the signal bandwidth should be kept invariant during the decaying time, but AMC is adopted with signal setting from 16QAM to 2PSK corresponding to the data rate from 64kbps to 2kbps with varying received SNR (Fig.1).

modulation scheme for each data frame, and consequently the signal processing includes two operation modes according to the frame structure, described as follows.

Fig.3 System model of acquisition

A. Acquisition

Fig.2 Throughput versus frame length for MBC system

It is obvious that, an appropriate frame length is one important issue to fully utilize meteor channel and improve the throughput of MBC. We can divide the electron line density into D grades from q0 toqD-1, assuming N(q0) is the number of meteor bursts with their electron line densities belonging to q0 during time T. Then the number of meteor bursts whose electron line densities are among qd (d=1,2,…D-1) can be calculated as q N (qd ) = 0 ∗ N (q0 ) (1) qd So the sum of the weighted throughput of MBC system is obtained G=

D −1

∑ throughput (q ) * N (q d

d)

(2)

d =0

where throughput (qd ) represents the throughput of data transmitted by meteor bursts with electron line densities belonging to qd . Thus we can get the relation of throughput G with the frame length, thereby determine the optimal length of data frame. Fig.2 plots the throughput versus the frame length under typical MBC distance of 800 km and 1000 km respectively. In MBC system, the data frame is composed of two parts, the header data and the payload data. The 32-bit header includes the identification of modulation type for the frame.

3. The semi-blind Joint data and channel estimation For the very short duration of meteor bursts, a typical semi-blind algorithm of joint data and channel estimation needs to be exploited with low computation complexity. As mentioned above, the AMC mechanism that is coincident with the meteor channel characteristics is performed by adaptive optimal

For each data frame, the frame header is used to estimate the equivalent meteor channel parameters before payload data equalization. The system model of acquisition is shown in fig.3, where the adaptive recursive least squares (RLS) algorithm or adaptive least mean square (LMS) algorithm is adopted for channel estimation [10]. In fig.3, the input xk is the training sequence, e.g. frame header, and rk denotes the complex additive white Gauss noise (AWGN) with     power spectrum N0 / 2 at time k. Let hk = {hk ,L−1, hk,L−2 ,hk ,0}T now be the estimation of the channel parameters vector hk = {hk , L −1, hk ,L − 2  hk ,0 }T with L representing the channel memory length and (⋅)T standing for the matrix transposition, then  the output of channel estimation yk is given by yk = hkT X k , where Xk = {X k −( L−1) , Xk −(L−2) ,X k }T . As dk denotes the desired output of channel estimation, the error ek = d k - yk can be easily attained. Without loss of generality, the transfer function H(z) of equivalent meteor channel is considered to be constant during each frame header transmission because of the slow-fading characteristic of meteor channel. Thus the system Mean Square Error (MSE) is ξk = E[| ε k |2 ] = E[(dk − yk )* (dk − yk )]    = E[| dk |2 ] + hkH E[ X k* X kT ]hk − 2Re{hkT E[dk* X k ]} (3)    = E[| dk |2 ] + h H Rh − 2Re{hT M } where R = E[ X k* X kT ] = E[ X * X T ] , M = E[dk* X k ] = E[d * X ] , ()⋅ ∗ and ()⋅ H stand for complex conjugation and Hermitian transposition respectively. The MSE can be further written as ξ k = φdd (0) +





∑∑

l =−∞ m =−∞

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∑ hˆ φ

(4

l dx (-l )

l =−∞

) where φxx (n) =

E[ x*k xk + n ]

and φxd (n) =

E[ x*k d k + n ]

.

Let ∂E[| ε k |2 ]/ ∂hˆ = 0 , so the optimal weight vector ˆ hopt can be obtained. For each tap weight, we have 2

∂E[ ε k ] =2 ∂ hˆ k



∑ hˆ φ

m xx ( k

m =−∞

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hˆl∗ hˆmφ xx (l - m) - 2

- m) - 2φ xd (k ) = 0

(5)

Taking the Z-transform of (5), the following equation holds Hˆ opt ( Z ) = Φ xd (Z ) / Φ xx ( Z ) (6) and

φxx (n) = E[( Dk hk' )∗ ( Dk + n hk' + n )]

(10) As the input sk is independent of AWGN signal rk , the corresponding Z-transform can be expressed as Φ xd (Z ) = H ( Z ) H ′∗ (Z )Φ SS (Z ) + H ′∗ ( Z )Φ rr ( Z ) 2

Φ xd (Z ) = H ( Z )Φ xx (Z ) + Φ xr ( Z )

(7) For the independence of input xk from AWGN signal nk , we finally obtain Hˆ opt ( Z ) = H (Z )( (8) It may well be stated that the parameters of MBC channel can be acquired during the training period in terms of minimizing the system MSE, with the result not affected by AWGN.

B. Tracking

Φ xx ( Z ) = H ( Z )

2

2

H ′( Z ) Φ SS ( Z ) + H ′( Z ) Φrr ( Z )

(12) Substituting (11) and (12) into (6), it is easily shown that the optimal weight vector is Hˆ opt ( Z ) = 1/ H ′( Z ) (13) In stationary cases, the transfer function of equalizer is the reciprocal of that of the equivalent meteor channel, i.e. H ′(Z ) = 1/ H ( Z ) . Thereby the accurate channel parameters can be obtained by Hˆ opt (Z ) = H ( Z ) . C. The algorithm of joint data and channel estimation

Fig.4 System model of data equalization and channel tracing

Fig.5 The D-PSP algorithm of joint data and channel estimation

Following the acquisition, the equalizer is used to detect payload data corrupted by AWGN and ISI. Meanwhile, channel tracing should be executed to update the channel coefficients for the slow timevarying meteor channel. Fig. 4 gives the system model for payload data equalization and channel tracing. The corresponding denotations in Fig.4 follow the definition in Fig.3, so are their assumption conditions. A little difference is that the equalizer input sk is payload data received following the frame header, and the output of equalizer is denoted as sk . For channel tracing, sk is similar to the input xk in Fig.3 expressed as xk = DkΤhk' , where D k = { d k - ( L -1) , d k - ( L - 2 ) ,  d k }Τ and hk' = {hk′ , L -1 , hk′ , L -2 ,  hk′ ,0 }Τ are the equivalent impulse response of equalizer. The desired output of channel tracing d k is obtained by d k = SkΤ hk + rk , where Sk = {sk -( L -1) , sk -( L -2)  sk }Τ . Thus the cross-correlation φ xd (n ) and the auto-correlation φxx (n) are given by φxd (n ) = E[( Dk hk' )∗ d k + n ] (9)

The above sections gave the system model and its theoretical analysis for the operation modes of acquisition and tracking. In the tracking mode, the data and channel estimation are jointly executed. Although the performance of PSP can approach that of known channel MLSD [4][5], its computational complexity is rapidly increased with M for adaptive MPSK modulation scheme, so it becomes time-consuming for the very short active duration of meteor channel. Based on the analysis of PSP, a fast algorithm, called D-PSP (dimension-down PSP), is suggested in this section. Using D-PSP algorithm, the channel parameters of one state in the trellis diagram are estimated, and simultaneity survivors are also rapidly searched. Based upon the previous state, the same are done to the next one. In this way, the received data are reliably detected. As shown in fig.4, the model concerned is a discrete-time symbol-spaced signal, defined by d k = S kT hk + rk k = 0,1, 2 (14) where the notations are consistent with that of Fig.4. The digital data sequence {sk } is assumed independent and uniformly distributed over a finite alphabet S of MPSK signals, i.e. sk ∈ S . The component equation of (14) may be written in vector form as Dk = S K hk + Rk (15) where Dk = {d k , d k -1  d 0 }Τ , Rk = {rk , rk -1  r0 }Τ and T S k = {S k , S k −1 ,  S 0 } . The (( k + 1) × L) Toeplitz matrix S k consists of elements from the M-ary alphabet S . Due to the white Gaussian nature of the observation noise, the joint-ML data and channel estimations are found by performing the following minimization min Dk − SK hk

S k ,hk

IEEE

2

(16)

The metric to be minimized for all hk and Sk is the residual least-squares (LS) error Γ k ( Sk ) of the persequence channel estimation [5]

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(11)

2

Γ k (Sk ) = ( I − Sk SkI ) Dk

2

(17)

The pseudo-inverse of Sk is denoted by SkI and is given by SkI = ( SkΤ Sk ) −1 SkΤ when Sk has rank L. For issues of numerical stability and performance, an exponentially weighted LS fit 2 Γ k (Sk ) = Wk1/ 2 ( I − Sk SkI ) Dk

with Wk = diag (1, w, w2  wk ) in consideration, where w is the weighted coefficient. Assuming that Sk -1 has rank L, the metric can be computed recursively via Γ k (Sk ) = wΓ k ( S k -1 ) + (1 − S kΤ g k )[d k − S kΤ hˆk -1 ] (18) where hˆk is computed via RLS channel estimation and gk is the associated Kalman gain vector (KGV) for the RLS estimator. The recursion in (18) allows joint data and channel estimation problem to be viewed as a tree search problem, which is referred to as both a generalization and theoretical foundation of the PSP technique. Based on the PSP principles, combining the algorithm with a reduced complexity approximation according to the characteristic of meteor channel may be a promising approach to obtain reliable semi-blind data receiving. It is well known that, with the typical fading rate about 1 Hz for the slow-fading meteor channel, the symbol decision has a great correlation with that of the preceding one. For this reason, based on channel estimation (CE) of the survivor entering μk , a near-optimal channel estimation of the path leaving μk can be achieved by the D-PSP algorithm, with the maximum of the possible reduced dimensions N to be L-1. For the PSP algorithm, there are ML states of μk = {μk,1, μk,2 ,μk,M L } at time k, representing the tentative decisions of L symbols of {sk , sk -1 sk -( L-1) } (Fig.5 (a)). However, there are only ML-N states of μk ={μk,1, μk,2,μk,ML-N } for the D-PSP method with reduced dimension N, which represent the tentative decisions of L-N symbols of {sk , sk-1 sk-( L- N-1) } (Fig.5(b)),and the residual N decisions are determined by the tentative decisions retained in μk -1 . Let μk →μk+1 denote the transition from μk to μ k +1 , and hˆ( μk ) = {hˆk , L−1, hˆk , L-2 ,hˆk ,0 }Τ represent the estimation of the slowly time-varying meter channel vector h( μk ) = {hk , L -1 , hk , L -2  hk ,0 }Τ for the particular state μk . Define λN (μk → μk +1 ) as the transition metrics of the D-PSP approach with reduced dimension N at time k that λN (μk → μk +1 ) = FN [ μk → μk +1 , d k +1 , hˆ( μk )] (19) According to the principle of PSP, hˆ( μk ) is updated by RLS estimator through the following: e( μ ) = d − hˆ Η ( μ ) Sˆ ( μ ) (20) k

k

k -1

N

k

p( μk -1 ) SˆN ( μk ) g (μ k ) = w + SˆNΗ ( μk ) p( μk -1 ) SˆN ( μk ) p( μk ) =

1 [ p(μk -1 ) − g ( μk )SˆNΗ ( μk ) p( μk -1 )] w

(21) (22)

hˆ( μk ) = hˆ(μk -1 ) + g (μ k )e∗ (μ k ) (23) where p(μk ) is the corresponding correlation matrix and SˆN (μk ) = {sˆk-( L-1) , sˆk-( L-2) sˆk }Τ represents the tentative decisions for symbol sequence vector Sk = {sk-(L-1) , sk -(L-2) sk }Τ corresponding to state μk for the D-PSP approach with reduced dimension N. Based on the above parameters recursion, the accumulated survivor metrics Γ(μk+1) is then determined by the minimization over the current states μ k +1 that Γ(μk +1 ) = min[Γ(μk ) + λN (μk → μk +1 )] μk

= min[Γ(μk ) + FN [μk → μk +1 , dk +1 , hˆ(μk )]} μk

Substituting FN [μ k → μk +1 , d k +1 , hˆ( μk )] = d k +1 − hˆ( μk )Τ SˆN ( μk +1 )

into (24) yields 2

Γ(μk +1 ) = min[Γ(μk ) + d k +1 − hˆ(μk )Τ SˆN (μk +1 ) ] μk

= min[Γ(μk ) + d k +1 − μk

IEEE

L−1



2

(25)

hˆk ,i sˆk +1−i ]

i =0

It is obvious that, the recursive computation of (25) coincides with the principle of PSP in (18). In the DPSP algorithm, the tentative decisions of SˆN (μk+1) ={sˆk+1-(L-1) sˆk , sˆk+1}Τ at time ( k + 1) are obtained by ( μ ) + Sˆ (μ ) Sˆ (μ ) = Sˆ (26) N

k +1

N , Map

k +1

N ,Trace

k +1

where SˆN , Map ( μk +1 ) = [sˆk +1−( L − N −1) , sˆk , sˆk +1 ] is the tentative decisions of L − N symbols directly mapped by state μ k +1 , while SˆN ,Trace ( μk +1 ) = [sˆk +1-( L -1) , sˆk +1−( L − N ) ] is that of the rest L symbols retained in μk , and is achieved by survivor path tracing with depth N , denoted by (27) SˆN , Trace (μk + 1) = Path _ trace[μk - N → μk ] As discussed above, the equivalent meteor channel parameters at time k are estimated from (20) to (23), and then the accumulated metrics Γ( μk +1 ) of state μ k +1 can be calculated by (24) to (27), through which the survivor of μ k +1 is determined. Based upon this, the relative settings of meteor channel coefficients hˆ( μk +1 ) are then updated at time (k + 1) . It is found that if N, the reduced dimension, is appropriately chosen in D-PSP algorithm for each data frame of M-ary PSK signals, and digital signal processor (DSP) can spend almost the same computational time and memory size for signal processing. Therefore, the relatively good performance of data receiving can be achieved with the restricted DSP resources being fully used.

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(24)

2

4. Simulation results and analysis A. Simulations of acquisition

In MBC system, the Yagi-Uda antenna is adopted and the locations of the master stations and the remote stations are fixed. So the performance of the adaptive MLSD receiver for MBC can be evaluated experimentally with Doppler Effect not taken into account. It is reasonable to consider that the meteor channel is invariable during the transmission of every 32-bit frame header for the slow-varying meteor channel. Given the complex multi-path channel hk = {hk ,0 , hk ,1 hk ,L−1}Τ = { hk ,0 e jθ0 , hk ,1 e jθ1  hk ,L-1 e jθL−1 }Τ where the memory length L equals 4, the simulations of channel estimation are performed for various channel parameters hk ,i e jθi (i = 1, 2  L − 1) . Then the average MSE of channel estimation according to (28) is plotted in Fig.6, where J is the observation times. J ⎡ L −1 2⎤ 1 MSE = hk ,i − hˆk ,i ⎥ (28) ⎢ L * J j =1 ⎣⎢ i =0 ⎦⎥

∑∑

schemes are almost the same. It is shown that the MSE of channel estimation is determined by the ratio of Es/N0 rather than Eb/N0. In Fig.6, the MSE descends straightly with the increase of SNR for constant channel parameters. Owing to the additional disturbance introduced by slow-varying channel in the practical MBC system, the actual MSE curve will decrease to a certain degree, and then it will be held above a minimum floor even if SNR increases. A comparison between a given particular channel and its estimation in the case where Es/N0 equals 15dB of 16QAM scheme is also illustrated in Fig.7. B. Simulations of joint payload data and channel estimation

In this section, the validity of the proposed D-PSP approach is verified experimentally since the theoretical comparison with the analogous PSP algorithms is not easy to be attained [5-7]. The Watterson channel model recommended by CCIR is adopted for simulation, in which the relationship of the fading rate fr with the random sequences shift rate fc of the equivalent multi-path Rayleigh fading channel is given by (29) with m denoting the length of the shift register. 4.4 f c f r = 1.47 ∗ (29) 2π (2m + 1) 2

Fig.6 The average MSE of channel estimation

Fig.8 Performance of various algorithms of QPSK

Fig.7 (a) the actual channel parameters (b) the estimated channel parameters

As Fig.6 shows, the MSE curve of QPSK nearly coincides with that of 16QAM, which indicates that the acquisition performances for different modulation

Meanwhile, the amplitude of the channel vector decays exponentially according to the character of meteor channel [8][9]. With the typical fading rate fr=1Hz and memory length L=4 for MBC, the system simulation results of channel acquisition combined with the joint data and channel tracing for QPSK and 16QAM schemes are plotted in fig.8 and fig.9 respectively. With the bit rate of 32kbps and 64kbps, the sampling rate of 5 points per symbol, the carrier frequency of 40MHz and the AWGN introduced the system simulations are performed without any processing of interleaving and error-correct codes. For convenient comparison, the performance of bit-error rate (BER) for PSP, MSP[7] and full-state Viterbi algorithm with known channel are also depicted in Fig.8-9.

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It is reasonable to look at the BER of known channel in the above two figures as the upper bound of performances for comparison. As shown in Fig.8-9, the performance of D-PSP method with N=1 for various modulations is nearly close to that of PSP, while the BER of D-PSP methods with N=2 for QPSK and 16QAM symbols degrade by only 0.5dB and 0.8dB respectively than those of PSP. The performance of MSP is intervenient between that of N=2 and N=3 of D-PSP methods, whereas its computational complexity grows exponentially with the increase of modulation phase number M. For all the D-PSP methods, the BER of QPSK is less than 1× 10 −3 when Es/N0 is higher than 10.5dB, while the BER of 16QAM is also below 1× 10 −3 when Es/N0 is higher than 17.5dB. In this situation, the system can further achieve a BER of 10-6 with symbol interleaving and 1/2 code rate of Turbo codes or convolution codes, which is an ultimate value to realize the reliable data transmission for MBC.

communications using spread spectrum multiple access technique. Proceedings of the Eighteenth National Radio Science Conference, Egypt, 2001. 451-458. [3] Zhenyu Zhu, Hamid R. Sadjadpour. An adaptive Per-survivor processing algorithm. IEEE Trans on Comm., 2002, 50(11): 1716-1718. [4] Alessandro Vanelli-Coralli, Paola Salmi. A performance review of PSP for joint phase/frequency and data estimation in future broadband satellite networks. IEEE Journal on Selected Areas in Communications, 2001,19(12): 2298-2309. [5] Keith M. Chugg. Blind acquisition characteristics of PSP-based sequence detectors. IEEE Journal on Selected Areas in Communications, 1998,16(8): 1518-1529. [6] Riccardo Raheli, Andreas Polydoros, Ching-Kae Tzou. Persurvivor processing: A general approach to MLSE in uncertain environments. IEEE Trans on Comm., 1995,43(2/3/4): 354364. [7] G Castellini, F Conti, E Del, Re, L Pierucci. A continuously adaptive MLSE receiver for mobile communications: algorithm and performance. IEEE Trans on Comm., 1997, 45(1): 80-89. [8] A. Fukuda. Meteor burst communications. Tokyo: Corona Publishing Co. Ltd., 1997. 1-10. [9] Schanker, Jacob Z. Meteor burst communications. Boston: Artech House Inc., 1990. 89-93. [10] Simon Haykin. Adaptive Filter Theory (Fourth Edition). Beijing: Publishing House of Electronics Industry, 2002. 436444.

Fig.9 Performance of various algorithms of 16QAM

5. Conclusions The present work emphasizes the practicability of MBC system operating with a variable transmission data rate. This paper theoretically presents the system model of channel acquisition and the model of joint data and channel tracing based on the mechanism of MBC. In the tracking mode, the D-PSP method of joint data and channel estimation is introduced that is consistent with the characteristics of meteor channel, with a recursive computation of the ML metrics viewed as an application of the previously developed principle of PSP. Simulation results suggest that the proposed method can reduce the computational complexity and memory size effectively. Thereby, the semi-blind MLSD receiver can be achieved for MBC system exhibiting near-optimal performance. REFERENCES [1]

[2]

Khaled Mahmud, Kaiji Mukumoto, Akira Fukuda. A bandwidth efficient variable rate transmission scheme for meteor burst communications. IEICE Trans on Comm., 2001, 11(E84-B): 2956-2966. Aly, A.F., Shafie, A.A., Korrat, S.R. Meteor burst

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