This paper describes the implementation of a computationally efficient embedded system on an Field Programmable Gate Array (FPGA) platform for real-time brain activity estimation with multiple channels. The brain signals from multiple channels are considered as output of independent linear systems with unknown parameters representing the brain activity in corresponding channels. Multiple adaptive Recursive Least-Squares Estimation (RLSE) cores are implemented in FPGA to independently estimate the brain activity in each channel concurrently. The proposed RLSE-FPGA system provides dedicated (no time or resource sharing) and parallel processing environment. The universal asynchronous receiver transmitter core is also developed to communicate the measured and estimated parameters supported by storage facility programmed as shared memory. The computational precision is guaranteed by deploying a 32-bit floating point core for all the variables. The validation carried out by real Functional Near-Infrared Spectroscopy dataset and comparative analysis with the previously reported result, demonstrates the effectiveness of the proposed system. The computational cost endorses the effectiveness of concurrent processing of multiple channelsꞌ data in a sample before the arrival of the next sample. The proposed methodology has potential in real-time medical, military and industrial applications.