Cascade-Net: a New Deep Learning Architecture for OFDM Detection

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1 : a New Deep Learning Architecture for OFDM Detection Qisheng Huang 1, Chunming Zhao 1, Ming Jiang 1, Xiaoming Li 1, Jing Liang 1 Nationa Mobie Communications Research Lab., Southeast University, Nanjing 10096, China Huawei echnoogies CO., LD. Emai: 1 {qshuang, cmzhao, jiang ming, xmi}@seu.edu.cn, jingiang@huawei.com arxiv: v1 [eess.sp] 30 Nov 018 Abstract In this paper, we consider using deep neura network for OFDM symbo detection and demonstrate its performance advantages in combating arge Dopper Shift. In particuar, a new architecture named is proposed for detection, where deep neura network is cascading with a zero-forcing preprocessor to prevent the network stucking in a sadde point or a oca minimum point. In addition, we propose a siding detection approach in order to detect OFDM symbos with arge number of subcarriers. We evauate this new architecture, as we as the siding agorithm, using the Rayeigh channe with arge Dopper spread, which coud degrade detection performance in an OFDM system and is especiay severe for high frequency band and mmwave communications. he numerica resuts of OFDM detection in SISO scenario show that cascade-net can achieve better performance than zero-forcing method whie providing robustness against i conditioned channes. We aso show the better performance of the siding cascade network (SCN) compared to siding zero-forcing detector through numerica simuation. Index erms OFDM Detection; Neura networks; Rayeigh fading channe; Large Dopper spread. I. INRODUCION Orthogona frequency division mutipexing (OFDM) has been widey appied in modern communication. By using fast fourier transformation (FF), this technique can support high data-rate transmission and achieve high spectra efficiency in wireess communications. Recenty, appication of this technique in the 5th generation (5G) wireess communication system has been confirmed [1]. However, this attractive technique is very sensitive to the carrier frequency offset, phase noise, timing offset, and Dopper spread [], which can break the orthogonaity between subcarriers and cause inter-carrier interference (ICI). With growth of the carrier frequency used in future broadband wireess access and the speed of modern vehices, the Dopper spread of the wireess channe strongy increases which eads to more severe ICI. o dea with this emerging equaization probem, we propose a deep earning based method which usuay performs better than the cassica methods, such as zero-forcing and MMSE detection. During the past few years, with the deveopment of deep earning approach, and the deep earning agorithm, neutra network architecture has been successfuy used in the fied of computer vision and anguage processing, given its expressive capacity and convenient optimization capabiity [3]. Particuary, many practica deep earning modes for physica ayer communication come out, such ike deep channe estimation [4], deep channe decoding [5] [6], deep MIMO detection [7] and autoencoder for deep moduation [8] [9]. hese specific appications of deep earning in communications can be roughy divided into two types. First, using the deep unfoding [10] to add trainabe parameters to the cassica methods, through this data driven detection to find a promoted agorithm. Second, substituting the modified dense neutra network, convoutiona neutra network or residua neutra network for the appropriate parts in communications for enhancement. In this paper, we mainy focus on the first usage and enhance the performance of OFDM systems by improving the cassica detection. As the primary requirement of higher transmitting rate, the neutra networks are usuay trained off-ine and directy appied onine with reconfigurabe hardware. he main contribution of this paper is to propose a new architecture in OFDM detection. As mentioned before, Dopper spread can cause severe ICI between subcarriers especiay when information are transmitted on high frequency. Inspired by deep MIMO detection [7], we use simiar deep unfoding method to create a trainabe network through modifying ML agorithm in purpose of combating against ICI. However, training of deep neutra network can easiy get into a sadde point or oca minimum [11], which eads to poor performance in high signa-to-noise rate. In this paper, we creativey propose a cascade structure to hande this issue. In cascade network, neura network is cascaded to a zero-forcing preprocessor being trained and used as a whoe part. he thought of cascade network is simiar to transfer earning. By adding parameterfixed network to a new net, the difficuty of training a new high-dimension network to converge sharpy decreases. In muti subcarrier scenario, we propose a siding structure [1] [13]. Our siding structure consists of two parts: output area (OA) and guarding area (GA). hrough carefu anaysis of adjacent subcarriers ICI to the subcarrier being detected, we give out the empirica formua used for designing the ength of GA and OA. his siding structure ensures the detecting performance of our cascade-net without adding too much cacuation compexity. II. SSEM MODEL AND NEURAL NEWORK FOR DEECION A. SSEM MODEL In our paper we mainy forcus on OFDM detection in singe in singe out (SISO) scenario. For convenience, we

2 use frequency-domain mode to describe the whoe system. Assuming that cycic prefix (CP) is ong enough to eiminate interna symbo interference, transmitting and detection of each OFDM symbo woud be independent. Considering an OFDM system with N subcarriers, the transmitted data in time-varying mutipath channe is x(n). When the transmitted signa passes through the channe h(n, ), the received signa can be represented as [14] y (n) = h (n, ) x (n) + w (n) (1) where denotes the convoution, L represents the number of discrete mutipaths, h(n, ) is the time-varying compex gain of the th path at the n th sampe instant generated from Jakes mode [15] [16], and w(n) is the additive white Gaussian noise (AWGN). Assuming perfect synchronization at the receiver side, the demoduated signa on the m th subcarrier in the frequency domain is [m] = W [m] + + N 1 k=0 k m L 1 =0 ( L 1 ) H 0 e jπk/n X [m] =0 X [k] H m k e jπk/n () where X[k] represents the signa transmitted on the k th subcarrier in the frequency domain, H m k represents the FF of the time-varying mutipath channe tap, which aso indicates the ICI characteristics between subcarriers given as: H m k = 1 N N 1 n=0 h (n, ) e jπn(m k)/n (3) the second term of () indicates the fading coefficient resuting from the mutipath except interference of other subcarriers. he third term represents the ICI componet on the m th subcarrier et X = [X[1], X[],, X[N]] = [ [1], [],, [N]] W = [W [1], W [],, W [N]] (4) the eement of H in m th row, k th coumn be L 1 H m k e jπk/n. he transmission of an OFDM =0 symbo with N subcarriers can be expressed as: = HX + W (5) In our SISO scenario, matrix H is the frequency domain channe matrix which iustrates the interference and fading to subcarriers in one OFDM symbo. B. NEURAL NEWORK FOR DEECION In this section, we achieve our deep detection network (DN) by adding trainabe parameters to the traditiona detecting agorithm [5]. Inspired by artice: Learning to detect for MIMO detection [7], we aso choose to unfod ML detection agorithm to a trainabe network. HH Xˆ k 1 H wk bk wk 1 b k 1 Concatenate Concatenate t k t k 1 Layer k Layer k+1 Fig. 1. he k th ayer fowchart of DN. he goa in our detection can be expressed in the foowing equation: Xˆ k 1 ˆX θ (H, ) = arg min HX (6) x {symboset} N where the θ represents the trainabe weights and bias. However, the vaue of X is discrete, which is non-differentiabe and cannot be optimized. hus, we enarge the vaue set of X to C and use hard-decision to achieve the estimation ˆX of sending signa X. Our net s architecture is proposed using deep unfoding [10] given as: ˆX 0 = 0 H z k = w k ˆX k H H ˆX k ˆX k+1 = ϕ tk (z k ) + b k where ˆX k is the estimation of sending signa X in the k th iteration. w k, b k and t k are trainabe parameters. Intuitivey, each iteration is a inear combination. he k th iteration can be seen as the forward propagation from k th ayer to k + 1 th ayer(see Fig. 1). After adding trainabe parameters. ϕ tk is a piecewise inear soft sign activation function cited from [7]: ϕ tk (x) = 1 + ρ (x + t k) t k ρ (x t k) t k Our net uses a normaized muti-oss function [7], which is : ( ) L X ˆX oss X; ˆX θ (H, ) = og (k) k=1 X X (9) where L is the tota ayer number, X is the zero-forcing resut given as: X = (H H) 1 H (10) his specia designed oss function [7] uses zero-forcing detector as a standard to train the network whie appying muti oss to prevent network from overfitting. he ayer number is same to the number of iteration in origin ML agorithm. hus, what DN do is making use of the trainabe parameters to find the best detecting agorithm for ML detection in imited iterations. However, as it actuay uses a zero vector as the (7) (8)

3 HH is N and w 1 = [I N N, I N N ] where I represents the identity matrix, substituting ˆX 0 into ˆX k in equation (11) gives: ˆX 1 = ϕ t1 [w 1 ((H H) 1 )H ) + b 1 ] (1) () 1 Concat -enate w 1 b 1 t1 ˆX 1 Assuming w k (k > 1) to be the identity matrix, and b k be the zero matrix, the forward propagation of the cascade-net becomes H ˆX k = ϕ tk (ϕ tk 1 (ϕ t (ϕ t1 ((H H) 1 H ))) (13) ZF data preprocessor Fig.. he cascade structure. Layer 1 of DN initiaization of ˆX k, training of DN faces huge difficuty for converging. III. CASCADE NE AND SLIDING DEEC ALGORIHM A. CASCADE-NE As mentioned before, the DN using zero vector as initiaization may suffer from sow convergence. o sove this probem, we proposed a cascade structure. In cascade-net, the DN is cascaded to a ZF data preprocessor (see Fig. ). o the DN, the initiaizing vector is no onger a zero but roughy processed data providing by ZF detector. In singe DN detector, it has to perform the work of estimating the sending signa from the very beginning, however, in cascadenet its work changes to compete sending signa detection based on the resuts of ZF detector. In another word, the first part of the cascade-net competes the coarse detection whie the second part performs the detaied detection. his idea is inspired by transfer earning. In transfer earning, earning on a target probem is sped up by using the weights obtained from a network trained for a reated source task [17]. he parameter fixed network competes parts of work for a new earning target. Simiary, what detectors shared in OFDM symbo detection is restoring sending signa from receiving signa. hus, cascade-net shoud have promoted performance on convergence. he forward propagation of cascade-net (CN) can be expressed as: ˆX 0 = (H H) 1 H H z k = w k ˆX k + b k H H ˆX k ˆX k+1 = ϕ tk (z k ) (11) where ˆX 0 is the data preprocessor output and the input of the secondary DN. In fact, a cascade-net wi not worse than a singe zeroforcing detector. If number of subcarriers in an OFDM symbo here, we suppose: t k = t k 1 = t 1 = 1, ϕ tk (x) satisfies ϕ tk (x) = x in the activation area of the function. As the consteation points have aready been normaized before transmitting, their imaginary parts and rea parts are ess than 1. herefore, noninear opponents wi not affect the fina harddecision of the consteation point. At this time, the output of the cascade-net equas to a singe zero-forcing detector. In another word, zero-forcing detector is one of the soutions to the training of this net. Now, we can concude that by cascading a zero-forcing detector as a data preprocessor, the training mission changes to find a better detector with the basis of zero-forcing detection. In the DN, a normaized oss function is used for evauation. However, in cascade-net this operation is redundant, as the first eve is zero-forcing detector, the cascade-net nativey consider the zero-forcing resuts as a standard, the optimization of cascade-net is continuing earning from zeroforcing detection to ML detection. hus, in cascade-net, we directy use Eucidean distance as the oss function, which is: ( ) oss X; ˆX θ (H, ) = B. SLIDING SRUCURE L og (k) X ˆX (14) k=1 In modern communication system, number of subcarriers in one OFDM symbo can be very arge. herefore, using one cascade-net to earn the detection of such a OFDM symbo requires dramatic cacuation resource which is hard to be reaized. However, ICI between subcarriers has strong correation among them which indicates the possibiity of peforming the whoe detection step by step. In fact, ICI to one subcarrier is mainy caused by imited number of adjacent subcarriers, therefore we propose a siding detecting structure [1] for detection of those OFDM symbos with arge number of subcarriers. Different from the cassica ICI canceation method [18], siding window (SW) consists of two parts: guarding area (GA) and output area (OA). GA is used to hep OA compete the ICI canceation, which means the detection resut in this part wi not be output. hen, SW keeps siding unti finishing the detection of the whoe symbo. he structure of SW and the detecting process are shown in Fig. 3. Design of these two parts is based on the signa to interference power ratio and feasibiity of cacuation. In previous section, we introduce cascade-net for OFDM detection. Siding cascaded-net is appying siding window to cascade structure, which means each SCN wi consist of two parts: zero-forcing data preprocessor and deep detection

4 H Channe matrix Fixed position Screening training Siding Guarding Area ABLE I HE PARAMEERS USED FOR DEECION. Scenario: N = 3 f Nd = 0.16 or 0.18 Labe Moduation Learning Rate Layers Vaue QPSK Labe BatchSize Vaue 500 Siding 频域滑动窗 Siding Output Area 10 1 DN fnd=0.16 ZF fnd=0.16 CN fnd=0.16 DN fnd=0.18 ZF fnd=0.18 CN fnd=0.18 N-subcarrier OFDM symbo Fig. 3. he structure and appication of SCN. BER 10 network. he training to SCN is finding proper parameters to optimize the detection performance with submatrix of H and as feed-in data. We treat each SCN as a CN for OFDM symbo detection with subcarriers where correspond to the ength of SCN. After proper training, SCN detects subcarriers in each side and keeps siding unti it competes detection of the receiving OFDM symbo shown in Fig. 3. Suppose ˆX scn θ (H, ) to be the converged SCN detector with proper training. After times siding, the symbos to be detected nsip, and the SCN detector output X out can be expressed as: ] nsip = [ ( 1) ( 1) X nsip = ˆX scn θ (H nsip, nsip ) X out = [X G+1 X G+... X G ] (15) where G correspond to the ength of GA in SCN, H nsip represents the sub-matrix used in -times detection. GA incudes those subcarriers which corresponds to main interference to subcarriers in OA. herefore, GA is used to assist OA competing ICI canceation. Next, we give out the specific detais about the GA design. In fact, interference of k th subcarrier to the m th is a decreasing function. It indicates that interference to a specific subcarrier concentrates on imited number of adjacent subcarriers. Based on this idea, the empirica formua we proposed is: x = min{ arg { 1 x >f N N sin πx sin πx /N = αβ}} (16) G = x f Nd where β indicates the owest interference power considered in one SW whie α is used to compensate for unequa ampitude moduation. he ength of output area mainy depends on the capabiity of the cacuation resource. o SCN the signa in GA is used to assist the detection of signa in OA. In another word, we actuay do not care about the output of GA. hus, the oss function shoud aso ony SNR(dB) Fig. 4. BER versus SNR of 3-subcarrier OFDM symbo detection on QPSK with f Nd = 0.16 or 0.18 focus on the performance of OA. Based on this idea, the oss function used to train SCN is now promoted to this form: oss(x out ; ˆX scn θ (H, )) = L og(k) X out ˆX out k=1 (17) where X out and ˆX out represents the signa in output area. IV. LEARNING O DEEC AND NUMERICAL RESULS In this section, we compare the detection performance of CN to DN and cassica ZF detector. he deep detectors are trained off-ine and appied onine. Our simuation is based on the assumption that receiver can get accurate channe information. o prevent our network from miss adjustment, we dismiss the channe matrix with condition number arger than in training phase. he signa to noise rate (SNR) of the data in training set depends on the range of SNR whie detecting. If the detecting range is 15dB to 35dB, the SNR used for training shoud be = 5dB. he trainabe parameter w k is initiaized using truncated norm function with mean 0 and variance 1. b k is initiaized with 0.01, and t k is initiaized with 1. We use tensorfow to construct our network, and appy Adam agorithm as optimizer. ABLE I shows the parameters for the detection of OFDM symbos with 3 subcarriers transmitted in 4 paths fading channe [19] with normaized Dopper shift f Nd = 0.16 or 0.18 constructed by Jakes mode. he resut shown in Fig. 4. iustrates that when signato-noise ratio is around 0dB, the performance of DN is much better than cassica zero-forcing detector, however when

5 ABLE II HE PARAMEERS USED FOR DEECION. Scenario: N = 56 f Nd = 0.16 or 0.18 Labe Moduation Output Area Guarding Area Vaue QPSK 16 8 Labe Learning Rate Layers BatchSize Vaue BER DN fnd=0.16 ZF fnd=0.16 SCN fnd=0.16 DN fnd=0.18 ZF fnd=0.18 SCN fnd= SNR(dB) Fig. 5. BER versus SNR of 56-subcarrier OFDM symbo detection on QPSK with f Nd = 0.16 or 0.18 SNR goes up the constrained iteration eads to the decine of DN s performance. o CN, due to the first eve of data preprocessor, it aways achieves a better performance than zero-forcing detector. In SCN, the cacuation compexity of matrix inverse woud be Θ ( S 3), whie the compexity of siding detector is inear. hus, the output part shoud be as short as possibe. o reach a compromise between compexity and detection deay, we suggest the ength of the output part O to be 8 or 16. he tota ength of SCN equas O + G. he tota siding times per detection is N O. One more thing shoud be taken into consideration in SCN training is the seecting of sub-matrices. We get the submatrices H from the fixed ocation p to p + in channe matrices H (shown in Fig. 3). his method is practica as the statistica characteristic of the channe is ergodicity. ABLE II shows the hyper-parameters for the detection of OFDM symbos with subcarrier N = 56 transmitted in the same fading channe as above. he GA ength is designed using the method mentioned equation (16). he resuts in Fig. 5. shows that both cassica siding detector and deep siding detector have the error foor. However, after using deep siding detector, the detector performance is obviousy promoted. SCN makes further promotion because the error foor of it is the owest. V. CONCLUSION In this paper, we propose a cascade network for detection of OFDM symbo transmitted in channe with arge Dopper shift and provide a siding structure for the detection of muti-subcarrier OFDM symbo. Simuations based on QPSK indicate that our network performs better than cassica zeroforcing detector. Moreover, it has a better performance than singe deep detection network in high signa-to-noise ratio. hough perfect channe information is assumed in our simuation, cascade-net is robust against inaccurate channe estimation. In fact, siding structure coud aso be used in the first eve (data preprocessor) of SCN for further reduction of computationa compexity of data preprocessor. VI. ACKNOWLEDGMEN REFERENCES [1] G. Berardinei, K. Pajukoski, E. Lähetkangas, R. Wichman, O. irkkonen, and P. E. Mogensen, On the potentia of OFDM enhancements as 5g waveforms. in VC Spring, 014, pp [] W. Hou, W. e, S. Feng, and F. Ke, Iterative channe estimation and successive ICI canceation for OFDM systems over douby seective channes, Wireess persona communications, vo. 55, no., pp , 010. [3]. Wang, C.-K. Wen, H. Wang, F. Gao,. Jiang, and S. Jin, Deep earning for wireess physica ayer: Opportunities and chaenges, China Communications, vo. 14, no. 11, pp , 017. [4] H. e, G.. Li, and B. H. Juang, Power of deep earning for channe estimation and signa detection in OFDM systems, IEEE Wireess Communications Letters, vo. 7, no. 1, pp , 018. [5]. Gruber, S. Cammerer, J. Hoydis, and S. ten Brink, On deep earningbased channe decoding, in Information Sciences and Systems, st Annua Conference on. IEEE, 017, pp [6] E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and. Beery, Deep earning methods for improved decoding of inear codes, IEEE Journa of Seected opics in Signa Processing, vo. 1, no. 1, pp , 018. [7] N. Samue,. Diskin, and A. Wiese, Deep MIMO detection, arxiv preprint arxiv: , 018. [8] M. Kim, N. I. Kim, W. Lee, and D. H. Cho, Deep earning-aided SCMA, IEEE Communications Letters, vo., no. 4, pp , 018. [9] S. Li, C. Häger, N. Garcia, and H. Wymeersch, Achievabe information rates for noninear fiber communication via end-to-end autoencoder earning, arxiv preprint arxiv: , 018. [10] J. R. Hershey, J. L. Roux, and F. Weninger, Deep unfoding: Modebased inspiration of nove deep architectures, Computer Science, 014. [11] I. Goodfeow,. Bengio, and A. Courvie, Deep Learning. he MI Press, 016. [1] W. G. Jeon, K. H. Chang, and. S. Cho, An equaization technique for orthogona frequency-division mutipexing systems in time-variant mutipath channes, IEEE ransactions on Communications, vo. 47, no. 1, pp. 7 3, [13] N. Farsad and A. Godsmith, Neura network detection of data sequences in communication systems, arxiv preprint arxiv: , 018. [14] M. Kim, W. Lee, and D.-H. Cho, A nove papr reduction scheme for OFDM system based on deep earning, IEEE Communications Letters, vo., no. 3, pp , 018. [15] R. Carke, A statistica theory of mobie-radio reception, Be system technica journa, vo. 47, no. 6, pp , [16] W. C. Jakes and D. C. Cox, Microwave Mobie Communications. IEEE Press, [17] L.. Pratt, Discriminabiity-based transfer between neura networks, in Advances in neura information processing systems, 1993, pp [18]. Zhao and S. G. Haggman, Intercarrier interference sef-canceation scheme for OFDM mobie communication systems, IEEE ransactions on Communications, vo. 49, no. 7, pp , 00. [19] R. Baraj, echniques for determining covariance measures based on correation criteria, Jun , US Patent 9,071,318.

Co-channel Interference Suppression Techniques for STBC OFDM System over Doubly Selective Channel

Co-channel Interference Suppression Techniques for STBC OFDM System over Doubly Selective Channel Co-channe Interference Suppression Techniques for STBC OFDM System over Douby Seective Channe Jyoti P. Patra Dept. of Eectronics and Communication Nationa Institute Of Technoogy Rourkea-769008, India E