# Sphere Bounding Scheme for Probabilistic Robust Constructive Interference Precoding in MISO Downlink Transmission

## TL;DR

This paper introduces a sphere bounding scheme for probabilistic robust constructive interference precoding in MISO downlink, effectively handling channel errors to optimize power and improve transmission reliability.

## Contribution

It develops a novel sphere bounding approach transforming probabilistic constraints into tractable SOC constraints, enhancing robust precoding under imperfect CSI.

## Key findings

- Achieves lower symbol error rate (SER)
- Reduces transmit power
- Maintains high connect probability satisfaction

## Abstract

In this letter, we propose a sphere bounding scheme for probabilistic robust constructive interference (CI) power minimizing precoding, to address the imperfect channel state information (CSI) caused by the channel error (CE), which satisfies the known distribution in single-cell multiuser multipleinput single-output (MISO) downlink transmission. In the proposed scheme, we transform the probabilistic quality of service (QoS) constraints into tractable sphere bounding second-order cone (SOC) constraints through taking two-step tightening, and then we model tightened CI max-min signal-to-noise ratio (SNR) precoding, proving that its lower bound can be solved through tightened CI power minimizing precoding. Besides, in tightened CI power minimizing precoding, we propose the relaxation iteration to relax the connect probability requirement. Finally, we analyze the complexity of our proposed scheme. Numerical results show that our proposed schemes perform well in the satisfaction of the connect probability requirement, resulting in lower symbol error rate (SER) and higher transmit power.