Deep learning for joint channel estimation and feedback in massive MIMO systems(2)

3.channel estimation and feedback network

In this section, two joint channel estimation and feedback networks will be developed, where quantization method will also be discussed. Training strategy of each network will also be described at the end of this section.

3.1 Channel estmation and feedback network(CEFnet)

3.1.1 channel estimation (CE) subnet

To track the instantaneous channel variation, pilot symbol based channel estimation method is adopted. Due to the special structure of the comb pilots, the receiver only extracts the pilot symbols at the pilot locations in frequency domain and then calculates the channel frequency response at the pilot locations. To obtain the estimated channel frequency response at the remaining locations, operations, such as interpolation or transformation, are used then. Conventional pilot-based channel estimation methods can be considered as down sampling, noise-addition and interpolation of the original channel matrix according to the analysis above. In comparison, a low-resolution (LR) image is also considered to be derived from a perfect high resolution (HR) image after a series of down-sampling and noise interference, based on the imaging principle. Image super resolution is to recover the HR images from the LR images, which is similar to the channel estimation optimization process in theoretical sense.

采用梳狀導頻結構，對于中間沒有導頻的頻點采用插值的方式來估計，這對于時間選擇性不強的信道是可行的，而且可以節省導頻數量，增加資料的量。标黃的部分說得很好，但是要是不采用梳狀的導頻呢？？這樣子的解釋理論就有些牽強。

In recent years, deep learning has been widely used to establish the nonlinear mapping from a LR image to a HR one to perform single image super resolution (SISR) [36], [37]. To apply the deep learning based SISR methods for channel estimation in our study, the channel matrix is regaded as a two-dimensional image. The receiver first estimates the channel by the conventional LS algorithm as an initial channel estimate. The estimated channel can be considered as a LR image, with the corresponding ideal channels as the HR one. The channel matrix in the space-frequency domain will first be transformed to the angle-delay domain for the compatibility with the following feedback network. Due to the limited storage capacity and computation complexity of the UEs, it is more practical to deploy a light-weight neural network at the UEs. Therefore, a three-layer super resolution convolutional neural network (SRCNN) is adopted to estimate the channel in our study, which was proposed in [36] to handle the image super resolution problem.

看似簡單，不過已經和專業的機器學習的論文開始結合了。

To measure the information retrieval capacity of a convolutional network, the receptive field metric is used to represent the extent to which each pixel in the output image can perceive the original image. It can also be taken as the area of each pixel in the output feature map mapped to the original image[38]. The reason why the output cannot always perceive all the information of the original image is that the convolutional layer and pooling layer are commonly used and layers are locally connected. The larger the receptive field is, the more the information of the original image the network can obtain, which also means that it may contain more global and higher semantic features. Therefore, the size of the receptive field can be used to roughly judge the context retrieval capacity of each layer. The receptive field of the l-th layer can be calculated as follows, R l = ( R l + 1 − 1 ) × s l + f l R_l=(R_{l+1}-1)\times s_l+f_l Rl​=(Rl+1​−1)×sl​+fl​where R l + 1 R_{l+1} Rl+1​ is the receptive field of the ( l + 1 ) (l+1) (l+1)-th layer, s l s_l sl​ and f l f_l fl​ are the stride and filter size of the l l l-th layer respectively. According to the above equation and the stride of each layer is 1, the receptive field of the CE subnet can be calculated as: R C E n e t = f 1 + f 2 + f 3 − 2 R_{CEnet}=f_1+f_2+f_3-2 RCEnet​=f1​+f2​+f3​−2The calculation result of the receptive field in (8) will help guide the design of our convolutional network module in our simulation to ensure a stronger information retrieval capacity.

說接收域的事情。