ELM-based Frame Synchronization in Burst-Mode Communication Systems with Nonlinear Distortion
IIEEE WIRELESS COMMUNICATIONS LETTERS, VOL. XX, NO. XX, XXX 2020 1
ELM-based Frame Synchronization in Burst-ModeCommunication Systems with Nonlinear Distortion
Chaojin Qing,
Member, IEEE,
Wang Yu, Bin Cai, Jiafan Wang and Chuan Huang,
Member, IEEE
Abstract —In burst-mode communication systems, the qualityof frame synchronization (FS) at receivers significantly impactsthe overall system performance. To guarantee FS, an extremelearning machine (ELM)-based synchronization method is pro-posed to overcome the nonlinear distortion caused by nonlineardevices or blocks. In the proposed method, a preprocessing isfirst performed to capture the coarse features of synchronizationmetric (SM) by using empirical knowledge. Then, an ELM-basedFS network is employed to reduce system’s nonlinear distortionand improve SMs. Experimental results indicate that, comparedwith existing methods, our approach could significantly reducethe error probability of FS while improve the performance interms of robustness and generalization.
Index Terms —frame synchronization, extreme learning ma-chine, non-linear distortion, synchronization metric.
I. I
NTRODUCTION N OWADAYS the burst-mode transmission is pervasivelyapplied in modern communication systems, such as Inter-net of Things (IoT) [1], wireless local area networks (WLAN)[2], etc. In burst-mode communication system (BCS), framesynchronization (FS) is the foundation of the overall systemperformance, and is always assumed to be obtained at thereceiver. However, the BCS has a large number of non-linear devices or blocks, e.g., high power amplifier (HPA),digital to analog converter (DAC), etc., inevitably causingnonlinear distortion [3], [4]. Usually, synchronization precedeschannel estimation, signal demodulation, etc., and thus firstencounters these nonlinear distortions, degrading receiver’s FSperformance (e.g., the error probability performance). Owingto the lack of considerations for nonlinear distortion, theexisting methods (e.g., correlation-based FS [5], etc) are facinggreat challenges.In recent years, machine learning has drawn considerableattention due to its prominent ability to cope with nonlineardistortion [6], [7]. The machine learning, in particular deeplearning (DL) has been applied in wireless communication,e.g., signal detection [7], precoding [8], channel state informa-tion (CSI) feedback [9], channel estimation [10], [11] etc. Yet,
This work is supported in part by the National Key Research and Devel-opment Program (Grant 2018YFB1800800), the Key Projects of EducationDepartment of Sichuan Province (Grant 15ZA0134), and the Major SpecialFunds of Science and Technology of Sichuan Science and Technology PlanProject (Grant 19ZDZX0016) of China.Chaojin Qing, Wang Yu and Bin Cai are with School of ElectricalEngineering and Electronic Information, Xihua University, Chengdu, China.(e-mail: [email protected])Jiafan Wang is with Synopsys Inc., 2025 NE Cornelius Pass Rd, Hillsboro,OR 97124 USA. (email: [email protected])Chuan Huang is with the National Key Laboratory of Science and Tech-nology on Communications, University of Electronic Science and Technologyof China, Chengdu, China (e-mail: [email protected]). very limited works are focused on DL-based FS. One relatedwork [12] investigated the DL-based timing synchronization,yet shows a higher timing error probability than conventionalmatched filtering. In addition, these DL-based approaches suf-fer from many difficulties such as complex parameter tuning,and long-time training [9], etc.Unlike the DL-based approaches, the extreme learningmachine (ELM) is a single-hidden layer feed-forward neu-ral network, i.e., the gradient back-propagation (BP) is notrequired, possessing many advantages, e.g., randomly gener-ating for input weight and hidden bias, fast learning speed(hundreds of times faster than that of BP algorithm), andgood generalization performance, etc., [13], [14]. Inspiredby these advantages, an ELM-based FS is proposed in thispaper to improve the training sequence-based method, e.g.,correlation-based FS [5]. Due to the loss of training sequence’sorthogonality, the training sequence-based FS is difficult toapply in the scenario of nonlinear distortion. In the proposedmethod, a preprocessing is first performed to coarsely capturethe features of synchronization metric (SM) by using empiricalknowledge. Then, an ELM network is employed to alleviatesystem’s nonlinear distortion and improve SMs. Comparedwith the correlation-based FS [5] and recent FS method in[15], the proposed method can effectively reduce the errorprobability of FS for the cases with nonlinear distortion.Furthermore, with the parameter impacts, the proposed methodshows a stable improvement given the change of systemparameters.The remainder of this paper is structured as follows: InSection II, we briefly describe the system model. In SectionIII, the ELM-based FS method is specifically presented, andthe numerical simulation and analysis are given in Section IV,the Section V concludes our work.Notations: Bold lowercase and uppercase letters denotevectors and matrices respectively; italicized letters denotevariables; ( · ) T , ( · ) H , ( · ) − and ( · ) † denote the transpose,conjugate transpose, matrix inversion, MoorePenrose pseu-doinverse, respectively; N is N × vector with N zeroelements; (cid:107)·(cid:107) is the Frobenius norm; | x | denotes the absolutevalue of x and | x | denotes the absolute value operation to theevery elements of vector x .II. SYSTEM MODELConsidering a frame-based BCS, the transmitted frameformat is illustrated in Fig. 1(a), which consists of N s trainingsymbols s = [ s , s , · · · , s N s ] T ∈ C N s × , N g empty symbols TN g , and N d data symbols d = [ d , d , · · · , d N d ] T ∈ C N d × . a r X i v : . [ ee ss . SP ] F e b EEE WIRELESS COMMUNICATIONS LETTERS, VOL. XX, NO. XX, XXX 2020 2 (b). System modelTransmittedframe Nonlinear distortion h delay by x n y (a). Frame format for the burst-mode communication systemGuard Data sequence N s N g N d Training sequence T s T d TN g h ~ Fig. 1: Frame format and system modelTo guarantee the training symbol and data symbol are allocatedthe same transmitted power, E {| s i | } = E {| d j | } = P , i = 1 , , · · · , N s , j = 1 , , · · · , N d , is considered in thispaper. The transmitted frame x ∈ C M × is formed by (cid:104) s T , TN g , d T (cid:105) T , where M is the frame length. Similar to[15], N g empty symbols are employed to mitigate the multi-path channel dispersion. Fig. 1(b) presents the system model,in which the nonlinear distortion (due to the existence ofnonlinear blocks or devices, such as HPA, DAC, etc [3]) isencountered by the frame x , and then the distorted signalsare transmitted. At the receiver, the observation of transmittedtraining sequence s , denoted as y ∈ C M × , can be expressedas follows [15] y = (cid:101) S (cid:101) h + n , (1)where n ∈ C M × is the complex additive white Gaussiannoise (AWGN) vector whose entries are with zero-mean andvariance σ . The M × N complex matrix (cid:101) S , which consists ofthe distorted and shifted version of transmitted frame x , couldbe defined as (cid:101) S = (cid:101) s · · · ... (cid:101) s . . . (cid:101) s N s ... . . . (cid:101) s N s . . .... . . .... . . . , (2)where (cid:101) s i , i = 1 , , · · · , N s stands for the variant of the trainingsymbol s i due to the nonlinear distortion, and N is the sizeof search window. In equation (1), (cid:101) h ∈ C N × represents theextended vector of channel impulse response (CIR), which canbe written as (cid:101) h = , · · · , (cid:124) (cid:123)(cid:122) (cid:125) τ , h T , , · · · , (cid:124) (cid:123)(cid:122) (cid:125) N − L − τ T , (3)where τ is the frame boundary offset to be estimated with ≤ τ ≤ M − N s − . In (3), h = [ h , h , · · · , h L ] T denotesthe finite CIR vector of L samples memory, where h l , l =1 , , · · · , L represents the complex-valued CIR of the l th path.III. ELM FRAME SYNCHRONIZATIONIn this section, a preprocessing for FS is first describedin section III-A, followed by an ELM network (given in TABLE I: Offline training procedureGiven a training set { ( ¯g i , T i ) | i = 1 , , · · · , N t } , hiddenneuron number (cid:101) N and real-valued activation function σ ( · ) ,the training steps are summarized as follows:step 1 : Randomly choose the input weight W ∈ R (cid:101) N × ( M − N s ) and the hidden bias b ∈ R (cid:101) N × .step 2 : According to W and b , calculate the hidden layeroutput H i ∈ R (cid:101) N × and construct a training outputmatrix H ∈ R (cid:101) N × N t as given in (10).step 3 : Use the desired label T i to construct a label matrix T according to (11), and then compute outputweight Υ ∈ R ( M − N s ) × (cid:101) N according to (12).section III-B). According to [12], the error probability ofDL-based timing synchronization is far higher than that ofmatched filtering, while similar behaviors are also observed inFS experiments where the ELM-based networks are employedfor the scenarios with or without nonlinear distortion. Thus,a preprocessing is employed to capture the coarse features ofSM. A. Preprocessing of Frame Synchronization
In the conventional approaches, τ can be estimated by usingcross-correlation based SM [5], [15], i.e., (cid:98) τ cross − correlation = arg max ≤ t ≤ M − N s − (cid:12)(cid:12) s H y t : t + N s − (cid:12)(cid:12) , (4)where y t : t + N s − represents the elements of y from t to t + N s − . In this paper, the existing methods for computingSMs, e.g., cross-correlation based method in [5], are viewedas empirical knowledge . It should be noted that besides thecross-correlation based SM, other SMs could also be appliedin our method with the similar processing. Denoting the cross-correlation based SM as Γ t = (cid:12)(cid:12) s H y t : t + N s − (cid:12)(cid:12) , t = 0 , , · · · , M − N s − , (5)then the SM vector g ∈ R ( M − N s ) × can be given by g = [ Γ , Γ , · · · , Γ M − N s − ] T . (6)For easy operation of ELM network, we normalize g in (6) as ¯g = g / (cid:107) g (cid:107) . (7)Then, ¯g is used as the input of ELM network. We will employELM network for FS to decrease nonlinear distortion andimprove SMs, which is elaborated in the following subsection. B. ELM-based Frame Synchronization
The ELM-based FS includes offline and online procedures,which are elaborated in Table I and Table II, respectively.For offline training, N t samples, i.e., { ( ¯g i , T i ) } , i =1 , , · · · , N t , are collected to form a training set, where T i is the offset label of the i th sample. Denoting the offset of the EEE WIRELESS COMMUNICATIONS LETTERS, VOL. XX, NO. XX, XXX 2020 3
TABLE II: Online procedureWith the learned output weight Υ , the chosen input weight W and hidden bias b , the online running steps of ELMnetwork are summarized as follows:step 1 : Execute the preprocessing of FS to obtain metricvector ¯g , according to (5)–(7).step 2 : Fed ¯g into the trained ELM-based FS network toobtain network output O according to (13).step 3 : From (14), estimate the frame boundary offset, i.e.,obtain the estimation (cid:98) τ . i th sample as τ ( i ) , the label T i can be encoded according toone-hot mode, i.e., T i = , · · · , (cid:124) (cid:123)(cid:122) (cid:125) τ ( i ) , , , · · · , (cid:124) (cid:123)(cid:122) (cid:125) M − N s − τ ( i ) − T . (8)As shown in Table I, during the offline training procedure, theinput weight W ∈ R (cid:101) N × ( M − N s ) and hidden bias b ∈ R (cid:101) N × of ELM network are randomly chosen, where (cid:101) N is the hiddenneuron number. Then, the hidden layer output H i ∈ R (cid:101) N × can be given by H i = σ ( W¯g i + b ) , (9)where σ ( · ) denotes the activation function such as sigmoid,hyperbolic tangent (tanh) , rectified linear units (ReLU) [16],etc. By collecting H i , a training output matrix H ∈ (cid:101) N × N t canbe constructed as H = [ H , H , · · · , H N t ] . (10)From the training set { ( ¯g i , T i ) } , the training labels { T i } canbe used to form a label matrix T ∈ R ( M − N s ) × N t , i.e., T = [ T , T , · · · , T N t ] . (11)According H and T , the output weight Υ ∈ R ( M − N s ) × (cid:101) N canbe given by Υ = TH † . (12)The main task for offline training of ELM network is to learnthe output weight Υ . With the learned output weight Υ , thechosen input weight W and hidden bias b , the ELM networkcan implement online running, which is given in Table II.For online running, the input of ELM-based FS network(i.e., the metric vector ¯g ) is obtained by employing thepreprocessing, i.e., the equations from (5) to (7). Then, ¯g isfed into the trained ELM-based FS network, which producesa network output O ∈ R ( M − N s ) × as O = Υ · σ ( W¯g + b ) . (13)By expressing O as O = [ o , o , · · · , o M − N s − ] T , the esti-mation of frame boundary offset can be given by (cid:98) τ = arg max ≤ j ≤ M − N s − | o j | . (14) Fig. 2: Error probability of FS vs. SNRTo sum up, the ELM-based FS network is employed toimprove SMs, which can overcome multi-path interfere andnonlinear distortion.IV. NUMERICAL SIMULATIONTo verify the proposed ELM-based FS can improve the errorprobability performance, we compared it with the classicalcorrelation-based FS [5] and the recent novel method in [15]when the nonlinear distortion is encountered. Besides, it isalso necessary to validate the robustness and generalization ofthe performance.The basic parameters involved are listed below. The trainingsequence is Zadoff-Chu sequence [17], N s = 32 , M = 160 , N = M − N s = 128 , (cid:101) N = 10 N = 1280 , N t = 10 ,and L = 8 [7]. The decibel (dB) form of signal-noise-ratio(SNR) and the error probability of FS are defined as SN R =10log (cid:0) P/σ (cid:1) [18] and P e = P r ( (cid:98) τ (cid:54) = τ ) , respectively. Themulti-path Rayleigh fading channel with an exponentially-decayed power coefficient (denoted as η ) 0.2 is considered.For fair comparison with [15], the same situation is considered,i.e., except the first path, each of the following L − pathsis set as zero-valued with a probability of 0.5. Note that,the proposed ELM-based FS is applicable regardless of thesparsity of the channel. For nonlinear distortion, we considerthe effects of HPA in this paper. The nonlinear amplitude A ( x ) and phase Φ( x ) are respectively adopted from [19] A ( x ) = α a x β a x , Φ ( x ) = α φ x β φ x . (15)According to [19], α a = 1 . , β a = 0 . , α φ = 2 . , and β φ = 2 . are considered in the simulations.For simplicity, we use “Prop”, “Corr” and “Ref [15]” todenote the proposed ELM-based FS, the correlation-based FSin [5], and the “CL-OMP” FS method in [15], respectively. Inaddition, “FS Learn” is used to denote the FS method that anELM is employed to learn FS from the received observation y in (1), i.e., without the preprocessing procedure given in III-A. A. Error Probability Performance of FS
The effectiveness of the proposed ELM-based FS is val-idated in terms of the error probability curves in Fig. 2. It
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SNR (dB) -2 -1 E rr o r p r obab ili t y o f F S Ref_[15], L=12Ref_[15], L=10Ref_[15], L=8Ref_[15], L=6Ref_[15], L=4Corr, L=12Corr, L=10Corr, L=8Corr, L=6Corr, L=4Prop, L=12Prop, L=10Prop, L=8Prop, L=6Prop, L=4 (a) different values of L SNR (dB) -1 E rr o r p r obab ili t y o f F S Ref_[15], Ns=16Ref_[15], Ns=32Ref_[15], Ns=64Corr, Ns=16Corr, Ns=32Corr, Ns=64Prop, Ns=16Prop, Ns=32Prop, Ns=64
Ref_[15]CorrProp (b) different values of N s SNR (dB) -1 E rr o r p r obab ili t y o f F S Ref_[15], M=192Ref_[15], M=128Ref_[15], M=64Corr, M=192Corr, M=128Corr, M=64Prop, M=192Prop, M=128Prop, M=64
Ref_[15]CorrProp (c) different values of M SNR (dB) -2 -1 E rr o r p r obab ili t y o f F S Ref_[15] (L=8)Ref_[15] (L=6)Ref_[15] (L=4)Corr (L=8)Corr (L=6)Corr (L=4)Prop (online L=8, train L=8)Prop (online L=6, train L=8)Prop (online L=4, train L=8)Prop (online L=6, train L=6)Prop (online L=4, train L=4)Prop (online L=8, train L=4)Prop (online L=6, train L=4) (d) different HPAs
Fig. 3: Impacts of different parameters on error probability of FScould be observed that the error probabilities of “Corr” and“Ref [15]” are much higher than that of “Prop” during therelatively high SNR, e.g.,
SN R ≥ dB. Meanwhile, the errorprobability of “FS Learn” is higher than those of “Corr”,“Ref [15]” and “Prop”. That is, without the preprocessingprocedure given in III-A, the input of ELM network is thereceived observation y in (1) rather than ¯g in (7), andthus cannot work well. It also reflects that the importanceof preprocessing in ELM-based FS. In addition, the recentFS in [15] is almost not applicable due to its poor errorprobability even at a relatively high SNR (e.g., P e ≥ . at SN R = 16 dB), while the proposed ELM-based FS achievesa relatively low error probability to retains the feasibilityfor practical applications for a relatively high SNR (e.g.,
P e ≤ . at SN R = 16 dB). As a whole, the proposed ELM-based FS shows improvement of reducing error probabilitycompared with “Corr” and “Ref [15]”.
B. Robustness Analysis
Usually, the error probability of synchronization is influ-enced by the number of multi-path (i.e., L ), the length oftraining sequence (i.e., N s ), the length of transmitted frame(i.e., M ), and different HPAs (i.e., different values of nonlineardistortion). To illuminate the robustness of improvement undernonlinear distortion, Fig. 3(a), Fig. 3(b), Fig. 3(c) and Fig.3(d) are given to demonstrate the impacts against L , N s , M ,and different HPAs, respectively. Except for the change of theimpact parameters (i.e., only L , N s , M and the parameters ofHPA are changed for Fig. 3(a), Fig. 3(b), Fig. 3(c) and Fig.3(d), respectively), other basic parameters remain the same asFig. 2 during the simulations.
1) Robustness against L : To demonstrate the impact of L on robustness, Fig. 3(a) shows the error probability of FS,where L = 4 , L = 6 and L = 8 are considered. It isobserved from Fig. 3(a), the improvement of reducing errorprobability is more significant with a smaller L . With theincrease of L , the error probabilities increase for all cases (i.e.,“Corr”, “Ref [15]” and “Prop”), due to the stronger multi-pathinterference. Even so, the error probability of “Prop” is muchlower than those of “Corr” and “Ref [15]”, especially for SN R ≥ dB. As a result, compared with those of “Corr” and“Ref [15]”, the proposed ELM-based FS exhibits the robustimprovement of reducing error probability against varying L .
2) Robustness against N s : Fig. 3(b) plots the error prob-ability of FS with different N s (i.e., N s = 16 , N s = 32 and N s = 64 ). From Fig. 3(b), a lower error probabilityof FS can be obtained as N s increases for the cases of“Corr”, “Ref [15]” and “Prop”. This is because a longertraining sequence is more effective for overcoming multi-pathinterference in the given scenario L = 8 . The error probabilityof “Prop” is lower than those of “Corr” and “Ref [15]”,especially for the high SNR regime (e.g., SN R ≥ dB). Byutilizing the proposed ELM-based FS, the error probability islower than those of “Corr” and “Ref [15]”, and the change of N s shows less impact on this improvement.
3) Robustness against M : To validate the effectivenessagainst the impact of M , the error probability curves areillustrated in Fig. 3(c), where M = 192 , M = 128 and M = 64 are considered, respectively. As M decreases, theerror probabilities of “Corr”, “Ref [15]” and “Prop” slightlydecrease due to the reduced locations for index search (since ≤ τ ≤ M − N s − ). From Fig. 3(c), the error probabilityof “Prop” is lower than those of “Corr” and “Ref [15]” givendifferent values of M . This reflects that the error probabilityis reduced and the improvement is robust against varying M .
4) Robustness against different HPAs:
Besides the HPAmentioned above (denoted as HPA1), an additional HPA(denoted as HPA2), which parameters are set as α a = 1 . , β a = 0 . , α φ = 0 . , and β φ = 0 . [19], is also employedin Fig. 3(d) to observe the influence of HPA on “Prop”. From[19], the root mean-square (RMS) errors of nonlinear ampli-tude and phase of HPA1 (HPA2) are 0.012 (0.041) and 0.478(0.508), respectively. According to the RMS errors, HPA1 hasless distortion than HPA2, and thus brings “Prop”, “Corr” and“Ref [15]” lower error probability of FS. Especially, for bothHPA1 and HPA2, the error probability of “Prop” is obviouslylower than those of “Corr” and “Ref [15]”. Therefore, theproposed ELM-based FS can work well with HPA1 and HPA2. C. Generalization Analysis
Fig. 4(a) and Fig. 4(b) present the generalization perfor-mance against L and η (i.e., the decayed power coefficient),respectively.
1) Generalization against L : In Fig. 4(a), the trainednetworks of L = 4 and L = 8 are respectively employedto test the cases where L = 4 , L = 6 , and L = 8 . From EEE WIRELESS COMMUNICATIONS LETTERS, VOL. XX, NO. XX, XXX 2020 5
SNR (dB) -1 E rr o r p r obab ili t y o f F S Ref_[15] ( = 0.3)Ref_[15] ( = 0.2)Corr ( = 0.2)Corr ( = 0.3)Prop (online = 0.3, train = 0.2)Prop (online = 0.2, train = 0.2)Prop (online = 0.3, train = 0.3)
CorrPropRef_[15] (a) against L SNR (dB) -1 E rr o r p r obab ili t y o f F S Ref_[15], HPA2Ref_[15], HPA1Corr, HPA2Corr, HPA1Prop, HPA2Prop, HPA1
Ref_[15]CorrProp (b) against η Fig. 4: Generalization analysis against L and η Fig. 4(a), the performance of error probability is degradedwhen the testing L is not the training L . Even so, the errorprobability of “Prop” is obviously lower than those of “Corr”and “Ref [15]”. Therefore, for the cases where testing L is nottraining L , the “Prop” still improves the error probabilities of“Corr” and “Ref [15]”.
2) Generalization against η : The error probability perfor-mance for the case where the testing η is not the training η as plotted in Fig. 4(b). In Fig. 4(b), the training η is 0.2,while the testing η is 0.3. According to the error probabilityof FS, this influence is not obvious for “Prop”. Besides, theerror probability of “Prop” is obviously lower than those of“Corr” and “Ref [15]”. Thus, the “Prop” possesses a goodgeneralization performance against η .V. CONCLUSIONIn this work, we investigated the ELM-based FS to improvethe performance of burst-mode communication systems. Apreprocessing is first performed to capture the coarse featuresof SM, followed by an ELM network to reduce system’snonlinear distortion and recover SMs. Compared with theexisting methods, the proposed ELM-based FS is validatedwith its robustness and generalization by reducing error prob-ability. In this paper, the difficulty of obtaining desired labelsis simplified by generating them according to the existingchannel model. In our future works, we will consider thedesired FS labels in real channel scenarios to promote theapplication of machine learning-based FS in practical systems(such as IoT, WLAN, etc) with nonlinear-distortion.R EFERENCES[1] Y. Kuo, C. Li, J. Jhang and S. Lin, “Design of a wireless sensor network-based IoT platform for wide area and heterogeneous applications,”
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