Self-supervised learning has been proved to benefit a wide range of speech processing tasks, such as speech recognition/translation, speaker verification and diarization, etc. However, most of these approaches are computationally intensive due to using transformer encoder and lack of sub-sampling. In this paper, we propose a new self-supervised learning model termed as Neural Encoder for Self-supervised Training (NEST). Specifically, we adopt the FastConformer architecture, which has an 8x sub-sampling rate and is faster than Transformer or Conformer architectures. Instead of clustering-based token generation, we resort to fixed random projection for its simplicity and effectiveness. We also propose a generalized noisy speech augmentation that teaches the model to disentangle the main speaker from noise or other speakers. Experiments show that the proposed NEST model improves over existing self-supervised models on a variety of speech processing tasks. Code and checkpoints will be publicly available via NVIDIA NeMo toolkit.