Sphere detector with low complexity Euclidean distance computation based on affine transform modulation

The foreseen scale of connected autonomous and low power consumption devices in the near future is a challenging aspect for the next generation of mobile communication networks. As the number of available connection resources is limited, frequency‐time multiplexing may not be sufficient to meet the expected demand for capacity, where scheduling solutions might incur in undesired latency levels and also increase the power expenditure to meet a more stringent synchronisation. In this scenario, spatial multiplexing based on multi‐user multiple‐input multiple‐output can extend the uplink capacity at the cost of inter‐antenna interference at the base station, requiring more complex detection schemes. The sphere detector can mitigate the inter‐antenna interference, achieving close‐to‐optimum bit error rate performance with average polynomial complexity that still challenges the field programmable gate array implementation in terms of resources and area. To further reduce the sphere detector complexity, the authors introduce the concept of affine transform modulation, which allows us to describe the received signal in terms of the sequence of transmitted bits per symbol. The authors demonstrate that this approach allows to evaluate the Euclidean distance in the sphere detector algorithm in terms of the transmitted bits, replacing the complex inner product by a complex accumulator in its extensively accessed core function. The approach proposed in this paper leads to a considerable complexity reduction in terms of FLOPs for low‐order modulations while attaining the conventional sphere detector performance.