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Register a new userMutual Information of IID Complex Gaussian Signals on Block Rayleigh-faded Channels
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Added by
Nihar Jindal
Publication date
2010
fields
Informatics Engineering
and research's language is
English
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We present a method to compute, quickly and efficiently, the mutual information achieved by an IID (independent identically distributed) complex Gaussian input on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and MIMO (multiple-input multiple-output) settings. Operationally, the mutual information thus computed represents the highest spectral efficiency that can be attained using standard Gaussian codebooks. Examples are provided that illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified by the use of multiple transmit antennas. These examples are further enriched by comparisons with the channel capacity under perfect channel-state information at the receiver, and with the spectral efficiency attained by pilot-based transmission.
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This paper concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals $L$ over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more.
Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all signal-to-noise ratios (SNRs). The comparison between the obtained bound and a high SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.
We study the problem of recovering a block-sparse signal from under-sampled observations. The non-zero values of such signals appear in few blocks, and their recovery is often accomplished using a $ell_{1,2}$ optimization problem. In applications such as DNA micro-arrays, some prior information about the block support, i.e., blocks containing non-zero elements, is available. A typical way to consider the extra information in recovery procedures is to solve a weighted $ell_{1,2}$ problem. In this paper, we consider a block sparse model, where the block support has intersection with some given subsets of blocks with known probabilities. Our goal in this work is to minimize the number of required linear Gaussian measurements for perfect recovery of the signal by tuning the weights of a weighted $ell_{1,2}$ problem. For this goal, we apply tools from conic integral geometry and derive closed-form expressions for the optimal weights. We show through precise analysis and simulations that the weighted $ell_{1,2}$ problem with optimal weights significantly outperforms the regular $ell_{1,2}$ problem. We further examine the sensitivity of the optimal weights to the mismatch of block probabilities, and conclude stability under small probability deviations.
The focus of this paper is an information-theoretic study of retransmission protocols for reliable packet communication under a secrecy constraint. The hybrid automatic retransmission request (HARQ) protocol is revisited for a block-fading wire-tap channel, in which two legitimate users communicate over a block-fading channel in the presence of a passive eavesdropper who intercepts the transmissions through an independent block-fading channel. In this model, the transmitter obtains a 1-bit ACK/NACK feedback from the legitimate receiver via an error-free public channel. Both reliability and confidentiality of secure HARQ protocols are studied by the joint consideration of channel coding, secrecy coding, and retransmission protocols. In particular, the error and secrecy performance of repetition time diversity (RTD) and incremental redundancy (INR) protocols are investigated based on good Wyner code sequences, which ensure that the confidential message is decoded successfully by the legitimate receiver and is kept in total ignorance by the eavesdropper for a given set of channel realizations. This paper first illustrates that there exists a good rate-compatible Wyner code family which ensures a secure INR protocol. Next, two types of outage probabilities, connection outage and secrecy outage probabilities are defined in order to characterize the tradeoff between the reliability of the legitimate communication link and the confidentiality with respect to the eavesdroppers link. For a given connection/secrecy outage probability pair, an achievable throughput of secure HARQ protocols is derived for block-fading channels. Finally, both asymptotic analysis and numerical computations demonstrate the benefits of HARQ protocols to throughput and secrecy.
To provide an efficient approach to characterize the input-output mutual information (MI) under additive white Gaussian noise (AWGN) channel, this short report fits the curves of exact MI under multilevel quadrature amplitude modulation (M-QAM) signal inputs via multi-exponential decay curve fitting (M-EDCF). Even though the definition expression for instanious MI versus Signal to Noise Ratio (SNR) is complex and the containing integral is intractable, our new developed fitting formula holds a neat and compact form, which possesses high precision as well as low complexity. Generally speaking, this approximation formula of MI can promote the research of performance analysis in practical communication system under discrete inputs.
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