Objective: Translational efforts on spike-signal-based implantable brain-machine interfaces (BMIs) are increasingly aiming to minimise bandwidth while maintaining decoding performance. Developing these BMIs requires advances in neuroscience and electronic technology, as well as using low-complexity spike detection algorithms and high-performance machine learning models. While some state-of-the-art BMI systems jointly design spike detection algorithms and machine learning models, it remains unclear how the detection performance affects decoding. Approach: We propose the co-design of the neural decoder with an ultra-low complexity spike detection algorithm. The detection algorithm is designed to attain a target firing rate, which the decoder uses to modulate the input features, preserving statistical invariance. Main results: We demonstrate a multiplication-free fixed-point spike detection algorithm with nearly perfect detection accuracy and the lowest complexity among studies we have seen. By co-designing the system to incorporate statistically invariant features, we observe significantly improved long-term stability, with decoding accuracy degrading by less than 10% after 80 days of operation. Our analysis also reveals a nonlinear relationship between spike detection and decoding performance. Increasing the detection sensitivity improves decoding accuracy and long-term stability, which means the activity of more neurons is beneficial despite the detection of more noise. Reducing the spike detection sensitivity still provides acceptable decoding accuracy whilst reducing the bandwidth by at least 30%. Significance: Our findings regarding the relationship between spike detection and decoding performance can provide guidance on setting the threshold for spike detection rather than relying on training or trial-and-error. The trade-off between data bandwidth and decoding performance can be effectively managed using appropriate spike detection settings. We demonstrate improved decoding performance by maintaining statistical invariance of input features. We believe this approach can motivate further research focused on improving decoding performance through the manipulation of data itself (based on a hypothesis) rather than using more complex decoding models.