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

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Cascade-Net: a New Deep Learning Architecture for OFDM Detection Cascade-Net: a New Deep Learning Architecture for OFDM Detection Qisheng Huang1, Chunming Zhao1, Ming Jiang1, Xiaoming Li1, Jing Liang2 1National Mobile Communications Research Lab., Southeast University, Nanjing 210096, China 2Huawei Technologies CO., LTD. Email:1fqshuang, cmzhao, jiang ming, [email protected], [email protected] Abstract—In this paper, we consider using deep neural network detection [7] and autoencoder for deep modulation [8] [9]. for OFDM symbol detection and demonstrate its performance These specific applications of deep learning in communica- advantages in combating large Doppler Shift. In particular, a tions can be roughly divided into two types. First, using new architecture named Cascade-Net is proposed for detection, where deep neural network is cascading with a zero-forcing the deep unfolding [10] to add trainable parameters to the preprocessor to prevent the network stucking in a saddle point classical methods, through this data driven detection to find a or a local minimum point. In addition, we propose a sliding promoted algorithm. Second, substituting the modified dense detection approach in order to detect OFDM symbols with large neutral network, convolutional neutral network or residual number of subcarriers. We evaluate this new architecture, as well neutral network for the appropriate parts in communications as the sliding algorithm, using the Rayleigh channel with large Doppler spread, which could degrade detection performance in for enhancement. In this paper, we mainly focus on the first an OFDM system and is especially severe for high frequency band usage and enhance the performance of OFDM systems by and mmWave communications. The numerical results of OFDM improving the classical detection. As the primary requirement detection in SISO scenario show that cascade-net can achieve of higher transmitting rate, the neutral networks are usually better performance than zero-forcing method while providing ro- trained off-line and directly applied online with reconfigurable bustness against ill conditioned channels. We also show the better performance of the sliding cascade network (SCN) compared to hardware. sliding zero-forcing detector through numerical simulation. The main contribution of this paper is to propose a new ar- Index Terms—OFDM Detection; Neural networks; Rayleigh chitecture in OFDM detection. As mentioned before, Doppler fading channel; Large Doppler spread. spread can cause severe ICI between subcarriers especially when information are transmitted on high frequency. Inspired I. INTRODUCTION by deep MIMO detection [7], we use similar deep unfolding Orthogonal frequency division multiplexing (OFDM) has method to create a trainable network through modifying ML been widely applied in modern communication. By using fast algorithm in purpose of combating against ICI. However, train- fourier transformation (FFT), this technique can support high ing of deep neutral network can easily get into a saddle point data-rate transmission and achieve high spectral efficiency or local minimum [11], which leads to poor performance in in wireless communications. Recently, application of this high signal-to-noise rate. In this paper, we creatively propose technique in the 5th generation (5G) wireless communication a cascade structure to handle this issue. In cascade network, system has been confirmed [1]. However, this attractive tech- neural network is cascaded to a zero-forcing preprocessor nique is very sensitive to the carrier frequency offset, phase being trained and used as a whole part. The thought of cascade noise, timing offset, and Doppler spread [2], which can break network is similar to transfer learning. By adding parameter- the orthogonality between subcarriers and cause inter-carrier fixed network to a new net, the difficulty of training a new interference (ICI). With growth of the carrier frequency used high-dimension network to converge sharply decreases. In in future broadband wireless access and the speed of modern multi subcarrier scenario, we propose a sliding structure [12] arXiv:1812.00023v1 [eess.SP] 30 Nov 2018 vehicles, the Doppler spread of the wireless channel strongly [13]. Our sliding structure consists of two parts: output area increases which leads to more severe ICI. To deal with this (OA) and guarding area (GA). Through careful analysis of emerging equalization problem, we propose a deep learning adjacent subcarriers’ ICI to the subcarrier being detected, we based method which usually performs better than the classical give out the empirical formula used for designing the length methods, such as zero-forcing and MMSE detection. of GA and OA. This sliding structure ensures the detecting During the past few years, with the development of deep performance of our cascade-net without adding too much learning approach, and the deep learning algorithm, neutral calculation complexity. network architecture has been successfully used in the field II. SYSTEM MODEL AND NEURAL NETWORK FOR of computer vision and language processing, given its ex- DETECTION pressive capacity and convenient optimization capability [3]. Particularly, many practical deep learning models for phys- A. SYSTEM MODEL ical layer communication come out, such like deep channel In our paper we mainly forcus on OFDM detection in estimation [4], deep channel decoding [5] [6], deep MIMO single in single out (SISO) scenario. For convenience, we use frequency-domain model to describe the whole system. HHT Assuming that cyclic prefix (CP) is long enough to eliminate internal symbol interference, transmitting and detection of b wk k wk 1 bk 1 ˆ each OFDM symbol would be independent. Considering an Xk 1 ˆ Xk 1 OFDM system with N subcarriers, the transmitted data in Concat- Concat- t t time-varying multipath channel is x(n). When the transmitted enate k enate k1 signal passes through the channel h(n; l), the received signal can be represented as [14] HYT Layer k Layer k+1 y (n) = h (n; l) ∗ x (n) + w (n) (1) th where ∗ denotes the convolution, L represents the number of Fig. 1. The k layer flowchart of DNT. discrete multipaths, h(n; l) is the time-varying complex gain of the lth path at the nth sample instant generated from Jakes The goal in our detection can be expressed in the following model [15] [16], and w(n) is the additive white Gaussian noise equation: (AWGN). Assuming perfect synchronization at the receiver th 2 side, the demodulated signal on the m subcarrier in the X^ θ(H; Y) = arg min kY − HXk N (6) frequency domain is x2fsymbolsetg L−1 ! where the θ represents the trainable weights and bias. How- X 0 −j2πlk=N ever, the value of X is discrete, which is non-differentiable Y [m] = W [m] + Hl e X [m] l=0 and cannot be optimized. Thus, we enlarge the value set of N−1 L−1 (2) X to C and use hard-decision to achieve the estimation X^ X X m−k −j2πlk=N + X [k] Hl e of sending signal X. Our net’s architecture is proposed using k=0 l=0 deep unfolding [10] given as: k6=m X^ = 0 where X[k] represents the signal transmitted on the kth 0 m−k 2 HT Y 3 subcarrier in the frequency domain, Hl represents the FFT of the time-varying multipath channel tap l, which also 6 ^ 7 zk = wk 4 Xk 5 + bk (7) indicates the ICI characteristics between subcarriers given as: T H HX^ k N−1 1 X X^ = ' (z ) Hm−k = h (n; l) e−j2πn(m−k)=N (3) k+1 tk k l N n=0 th where X^ k is the estimation of sending signal X in the k the second term of (2) indicates the fading coefficient resulting iteration. wk, bk and tk are trainable parameters. Intuitively, from the multipath except interference of other subcarriers. each iteration is a linear combination. The kth iteration can The third term represents the ICI componet on the mth be seen as the forward propagation from kth layer to k + 1th subcarrier let layer(see Fig. 1). After adding trainable parameters. 'tk is a X = [X[1];X[2]; ··· ;X[N]]T piecewise linear soft sign activation function cited from [7]: T ρ (x + t ) ρ (x − t ) Y = [Y [1];Y [2]; ··· ;Y [N]] (4) ' (x) = −1 + k − k (8) tk jt j jt j W = [W [1];W [2]; ··· ;W [N]]T k k Our net uses a normalized multi-loss function [7], which is : the element of H in mth row, kth column be L−1 2 P m−k −j2πlk=N L ^ H e . The transmission of an OFDM X X − X l loss X; X^ (H; Y) = log (k) (9) l=0 θ 2 symbol with N subcarriers can be expressed as: ~ k=1 X − X Y = HX + W (5) where L is the total layer number, X~ is the zero-forcing result In our SISO scenario, matrix H is the frequency domain given as: −1 channel matrix which illustrates the interference and fading X~ = (HT H) HT Y (10) to subcarriers in one OFDM symbol. This special designed loss function [7] uses zero-forcing B. NEURAL NETWORK FOR DETECTION detector as a standard to train the network while applying multi In this section, we achieve our deep detection network loss to prevent network from overfitting. The layer number is (DNT) by adding trainable parameters to the traditional detect- same to the number of iteration in origin ML algorithm. Thus, ing algorithm [5]. Inspired by article: Learning to detect for what DNT do is making use of the trainable parameters to MIMO detection [7], we also choose to unfold ML detection find the best detecting algorithm for ML detection in limited algorithm to a trainable network. iterations. However, as it actually uses all zero vector as the is N and w1 = [I2N×2N ; −IN×N ] where I represents the HHT identity matrix, substituting X^ 0 into X^ k in equation (11) gives: ^ T −1 T X1 = 't1 [w1((H H) )H Y) + b1] (12) ()1 w1 b1 Assuming wk(k > 1) to be the identity matrix, and bk be ˆ Y Concat X1 the zero matrix, the forward propagation of the cascade-net t -enate 1 becomes −1 T T T H ^ Xk = 'tk ('tk−1 ··· ('t2 ('t1 ((H H) H Y))) (13) There, we suppose: tk = tk−1 ··· = t1 = 1, 'tk (x) satisfies 'tk (x) = x in the activation area of the function.
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