Analysis of Fixed Outage Transmission Schemes: A Finer Look at the Full Multiplexing Point

This paper studies the performance of transmission schemes that have rate that increases with average SNR while maintaining a fixed outage probability. This is in contrast to the classical Zheng-Tse diversity-multiplexing tradeoff (DMT) that focuses on increasing rate and decreasing outage probability. Three different systems are explored: antenna diversity systems, time/frequency diversity systems, and automatic repeat request (ARQ) systems. In order to accurately study performance in the fixed outage setting, it is necesary to go beyond the coarse, asymptotic multiplexing gain metric. In the case of antenna diversity and time/frequency diversity, an affine approximation to high SNR outage capacity (i.e., multiplexing gain plus a power/rate offset) accurately describes performance and shows the very significant benefits of diversity. ARQ is also seen to provide a significant performance advantage, but even an affine approximation to outage capacity is unable to capture this advantage and outage capacity must be directly studied in the non-asymptotic regime.

💡 Research Summary

This paper investigates transmission schemes whose rates increase with average signal‑to‑noise ratio (SNR) while keeping the outage probability fixed at a target value ε. Unlike the classic Zheng‑Tse diversity‑multiplexing tradeoff (DMT), which simultaneously raises rate (multiplexing gain r) and reduces outage (diversity order d), the authors focus on the “fixed‑outage” regime where d = 0 for any ε > 0 and the maximum multiplexing gain r_max is achieved. The DMT, however, only predicts the leading term r_max·log₂ P in the high‑SNR expansion of the outage capacity R(P, ε); the constant (O(1)) term, which depends on ε and the system configuration, can dominate performance at realistic SNRs.

The authors therefore adopt an affine high‑SNR approximation
 R(P, ε) ≈ r_max·log₂ P + O(1)
and study three representative families of schemes: antenna diversity (SIMO/MISO), time/frequency diversity (block‑fading across L independent slots), and hybrid automatic repeat request (H‑ARQ).

Antenna Diversity.
For a single‑input multiple‑output (SIMO) or multiple‑input single‑output (MISO) link with Rayleigh fading, the instantaneous mutual information is log₂(1 + P·‖H‖²/N_t). The outage probability is Pr