Most wireless channels are sparse, so sparse channel-based methods can be used for channel estimation and feedback with much better estimation accuracy and much lower feedback overhead. However, certain wireless channels can be non-sparse, for which sparse channel-based methods may cause degraded estimation quality and increased feedback overhead. Means of detecting the channel sparseness are described that provide simple and effective channel sparseness indicators and safeguard against the mismatch between non-sparse channels and sparse channel-based methods. Various fallback options can be used under non-sparse channels such that estimation degradation and feedback overhead are both minimized. Fake multipath removal in continuous time-domain parameter extraction, a sparse channel-based method, is also described that further improves estimation quality and reduces feedback overhead.