Elements of information theory
Elements of information theory
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
IEEE Transactions on Information Theory
Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels
IEEE Transactions on Information Theory
On the high-SNR capacity of noncoherent networks
IEEE Transactions on Information Theory
A Coding Theorem for a Class of Stationary Channels With Feedback
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog--defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity--is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity.