The hardware power-aware Keyword Spotting (KWS) implementation requires small memory footprint, low-complex computation, and high accuracy performances. In this article, three aspects are introduced to satisfy these three stringent requirements. Firstly, a lightweight Binary Residual Neural Network (B-ResNet) is proposed and applied to the small-footprint KWS. The parameters and calculations inside the net-work are greatly downscaled during the binary quantization. Secondly, during the forward propagation, distribution of the binary activation is optimized by our proposed learnable activation function with fix-valued shift initialization. Thirdly, our variable periodic window (PW) for the backward gradient correction (BGC) is also put forward to avoid gradient mismatch and vanishing problems during the back-propagation. These two improvements effectively increase the accuracy performance during the binarization. Our studies in this article are very helpful and promising for the future hardware KWS implementations.