Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to $1-{Q}/{N}$. Here, $N$ is the number of symbols transmitted within one fading block, and $Q$ is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as $1-1/N$. Since the capacity pre-log corresponding to symbol-rate sampling is $1-Q/N$, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.Comment: To appear in the IEEE Transactions on Information Theor

A capacity-approaching coded modulation scheme for non-coherent fading channels

Approaching the Shannon limit of the communication channels has been studied by many researchers to efficiently and reliably transmit data through the channels. To solve this problem, various methods and schemes have been proposed for approaching the theoretical limit for Shannon’s channel capacity. Among them, both low-density parity check (LDPC) codes and Turbo codes have been proposed to minimize the bit error rate (BER). Therefore, understanding of LDPC codes and Turbo codes is useful for their applications in modern communication systems. The study about non-coherent channels, which do not require explicit knowledge or estimation of the channel state information, has become a major issue in mobile communication. Specifically, a new signaling scheme called unitary space-time modulation has been invented which is suitable for non-coherent channels. Combining channel coding with unitary space-time modulation is expected to make good performance for non-coherent fading channels. In this thesis, non-coherent capacity of a mobile communication channel in Rayleigh flat fading is calculated for the case of coherence time of length two. Also, LDPC codes and Turbo codes are combined with unitary space-time modulation to enhance the efficiency and reliability of communication over non-coherent fading channels. The performance results are compared to the calculated channel capacity. Simulation results show that both LDPC codes and Turbo codes are well performed for non-coherent fading channels. The LDPC and Turbo coded unitary space-time modulation schemes have BER performance much better than the uncoded modulation schemes and the performance is close to the calculated channel capacity

Capacity of Underspread Noncoherent WSSUS Fading Channels under Peak Signal Constraints

We characterize the capacity of the general class of noncoherent underspread wide-sense stationary uncorrelated scattering (WSSUS) time-frequency-selective Rayleigh fading channels, under peak constraints in time and frequency and in time only. Capacity upper and lower bounds are found which are explicit in the channel's scattering function and allow to identify the capacity-maximizing bandwidth for a given scattering function and a given peak-to-average power ratio.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2007, Nice, Franc

On the Capacity Achieving Covariance Matrix for Frequency Selective MIMO Channels Using the Asymptotic Approach

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In this paper, it is proposed to optimize (w.r.t. the input covariance matrix) a large system approximation of the average mutual information derived by Moustakas and Simon. An algorithm based on an iterative water filling scheme is proposed, and its convergence is studied. Numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information.Comment: presented at ISIT 2010 Conference, Austin, Texas, June 13-18, 2010 (5 pages, 1 figure, 2 tables