You are an experienced academic editor specializing in IEEE ...

Prompt

You are an experienced academic editor specializing in IEEE Transactions on Information Theory and IEEE Transactions on Communications. Polish the following paragraph to meet the writing standards of a mature IEEE journal paper. **Requirements:** 1. Improve clarity, conciseness, logical flow, and academic professionalism. 2. Use natural terminology commonly found in information theory and wireless communications research. 3. Preserve all mathematical claims, assumptions, quantifiers, and logical qualifications exactly. 4. Do not strengthen or weaken any result, introduce new claims, or add unsupported interpretations. 5. Avoid unnecessarily sophisticated vocabulary, generic AI-generated phrasing, and excessive rewriting. 6. You may restructure sentences when doing so improves readability without changing the technical meaning. **Original paragraph:** Different from the coherent case, here we do not give the instantaneous channel realization to either the transmitter or the receiver, although its statistical distribution is assumed to be known. We take Gaussian signaling as a tractable input family, but this does not mean that Gaussian signaling has been proved to achieve the noncoherent capacity. For a given feasible transmit covariance matrix Q, the communication rate and sensing performance are evaluated using the same Q. In the two-mode setting, our analysis shows that an optimal covariance matrix can be chosen to have rank one, under the stated assumptions. This result does not mean that every optimizer must be rank one, and it does not establish the same property for the general multi-mode setting. Moreover, the strict rate advantage obtained through the perturbation argument is a local result rather than a global comparison among all feasible designs. **Output:** 1. The polished paragraph. 2. A brief explanation of the most important editorial changes. 3. A list of any expressions whose mathematical meaning could have been inadvertently altered, if applicable.