An exact channel impulse response (CIR) for the three-dimensional point-to-sphere absorbing channel under drift has remained unavailable due to symmetry breaking. This letter closes this gap by deriving an exact analytical CIR for a fully absorbing spherical receiver under uniform drift with arbitrary direction. By formulating the problem in terms of joint first-hitting time-location statistics and applying a Girsanov-based measure change, drift effects are isolated into an explicit multiplicative factor, yielding an exact series representation. The resulting CIR provides a rigorous reference model and enables efficient, noise-free evaluation of key channel metrics without relying on Monte Carlo simulations.
翻译:由于对称性破缺,三维点对球吸收信道在漂移条件下的精确信道冲激响应(CIR)一直未能获得。本文通过推导任意方向均匀漂移下完全吸收球接收器的精确解析CIR,填补了这一空白。通过基于联合首次击中时间-位置统计量构建问题,并应用基于Girsanov的测度变换,漂移效应被分离为显式乘法因子,从而得到精确的级数表示。所得CIR提供了严谨的参考模型,并能够在不依赖蒙特卡洛模拟的情况下,高效、无噪声地评估关键信道指标。