The Cramer-Rao bound sets a fundamental limit on estimation accuracy — no unbiased estimator can have lower variance. For joint channel-and-symbol estimation in multi-user uplink systems, the CRB-derived mutual information proxy provides a principled way to allocate power and bandwidth.
The proxy's validity depends on the operating regime.
Using random matrix theory, the paper identifies the asymptotic scaling where the Cramer-Rao bound becomes tight — where the theoretical limit is actually achievable. In that regime, power allocation rules derived from the CRB proxy are optimal. Outside that regime, the same proxy misleads. The gap between theoretical bound and achievable performance opens up, and the allocation rules optimized for the bound produce suboptimal real-world performance.
The bound doesn't change. The physics doesn't change. What changes is the relationship between the bound and what can actually be achieved. At large scale (many antennas, many users, favorable SNR), the CRB is tight and the proxy is reliable. At finite scale, the same mathematical object becomes an unreliable guide.
This is a specific instance of a general phenomenon: a bound's tightness is not a property of the bound alone but of the regime in which you invoke it. The Cramer-Rao bound is always valid — it always provides a lower bound on variance. But “valid lower bound” and “useful design guide” are different claims. A bound that is loose by a factor of ten is technically valid but practically useless for resource allocation.
Fundamental limits are only fundamental relative to the assumptions that derived them. The limit is real. Whether it matters — whether the gap between limit and achievable performance is small enough to make the limit actionable — depends on where you sit in parameter space.