Due to their low complexity, Minimum Mean Squared Error (MMSE) and Zero-Forcing (ZF) emerge as two appealing MIMO receivers. Although they provide asymptotically the same achievable rate as the signal-to-noise ratio (SNR) grows large, a non-vanishing gap between the signal to interference and noise ratio (SINR) obtained through the two receivers exists, affecting the error and outage probability, and the multiuser efficiency. Interestingly, both the SINR and the multiuser efficiency gaps can be compactly expressed as quadratic forms of random matrices, with a kernel that depends solely on the statistics of the interfering streams. By leveraging, we derive the closed-form distribution of such indefinite quadratic forms with random kernel matrix, which turns out to be proportional to the determinant of a matrix containing the system parameters. Then, specializing our result to different fading conditions, we obtain the closed-form statistics of both the SINR gap and the multiuser efficiency gap. Although the focus of this work is on the finite-size statistics, for completeness we also provide some results on the doubly-massive MIMO case. We validate all our derivations through extensive Monte Carlo simulations.

中文翻译：

---

MIMO 线性接收器之间的 SINR 和多用户效率差距

由于其低复杂性，最小均方误差 (MMSE) 和迫零 (ZF) 成为两个吸引人的 MIMO 接收器。尽管随着信噪比 (SNR) 增大，它们提供渐近相同的可实现速率，但通过两个接收器获得的信干噪比 (SINR) 之间存在非零差距，从而影响错误和中断概率和多用户效率。有趣的是，SINR 和多用户效率差距都可以紧凑地表示为随机矩阵的二次形式，其内核仅取决于干扰流的统计数据。通过利用，我们用随机核矩阵推导出这种不定二次形式的封闭形式分布，结果证明它与包含系统参数的矩阵的行列式成正比。然后，将我们的结果专门用于不同的衰落条件，我们获得了 SINR 差距和多用户效率差距的封闭形式统计数据。尽管这项工作的重点是有限大小的统计数据，但为了完整性，我们还提供了一些关于双大规模 MIMO 情况的结果。我们通过广泛的蒙特卡罗模拟验证了我们所有的推导。