Radar-based Human Activity Recognition (HAR) is an attractive alternative to wearables and cameras because it preserves privacy, and is contactless and robust to occlusions. However, dominant Convolutional Neural Network (CNN)- and Recurrent Neural Network (RNN)-based solutions are computationally intensive at deployment, and recent lightweight Vision Transformer (ViT) and State Space Model (SSM) variants still exhibit substantial complexity. In this paper, we present RadMamba, a parameter-efficient, micro-Doppler-oriented Mamba SSM tailored to radar HAR under on-sensor compute, latency, and energy constraints typical of distributed radar systems. RadMamba combines (i) channel fusion with downsampling, (ii) Doppler-aligned segmentation that preserves the physical continuity of Doppler over time, and (iii) convolutional token projections that better capture Doppler-span variations, thereby retaining temporal-Doppler structure while reducing the number of Floating-point Operations per Inference (#FLOP/Inf.). Evaluated across three datasets with different radars and types of activities, RadMamba matches the prior best 99.8% accuracy of a recent SSM-based model on the Continuous Wave (CW) radar dataset, while requiring only 1/400 of its parameters. On a dataset of non-continuous activities with Frequency Modulated Continuous Wave (FMCW) radar, RadMamba remains competitive with leading 92.0% results using about 1/10 of the parameters, and on a continuous FMCW radar dataset it surpasses methods with far more parameters by at least 3%, using only 6.7k parameters. Code: https://github.com/lab-emi/AIRHAR.