On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.Comment: IEEE Transactions on Communications, 201

Some fundamental issues in receiver design and performance analysis for wireless communication

Ph.DDOCTOR OF PHILOSOPH

The Impact of Hard-Decision Detection on the Energy Efficiency of Phase and Frequency Modulation

The central design challenge in next generation wireless systems is to have these systems operate at high bandwidths and provide high data rates while being cognizant of the energy consumption levels especially in mobile applications. Since communicating at very high data rates prohibits obtaining high bit resolutions from the analog-to-digital (A/D) converters, analysis of the energy efficiency under the assumption of hard-decision detection is called for to accurately predict the performance levels. In this paper, transmission over the additive white Gaussian noise (AWGN) channel, and coherent and noncoherent fading channels is considered, and the impact of hard-decision detection on the energy efficiency of phase and frequency modulations is investigated. Energy efficiency is analyzed by studying the capacity of these modulation schemes and the energy required to send one bit of information reliably in the low signal-to-noise ratio (SNR) regime. The capacity of hard-decision-detected phase and frequency modulations is characterized at low SNR levels through closed-form expressions for the first and second derivatives of the capacity at zero SNR. Subsequently, bit energy requirements in the low-SNR regime are identified. The increases in the bit energy incurred by hard-decision detection and channel fading are quantified. Moreover, practical design guidelines for the selection of the constellation size are drawn from the analysis of the spectral efficiency--bit energy tradeoff.Comment: To appear in the IEEE Transactions on Wireless Communication

Artificial-Noise-Aided Physical Layer Phase Challenge-Response Authentication for Practical OFDM Transmission

Recently, we have developed a PHYsical layer Phase Challenge-Response Authentication Scheme (PHY-PCRAS) for independent multicarrier transmission. In this paper, we make a further step by proposing a novel artificial-noise-aided PHY-PCRAS (ANA-PHY-PCRAS) for practical orthogonal frequency division multiplexing (OFDM) transmission, where the Tikhonov-distributed artificial noise is introduced to interfere with the phase-modulated key for resisting potential key-recovery attacks whenever a static channel between two legitimate users is unfortunately encountered. Then, we address various practical issues for ANA-PHY-PCRAS with OFDM transmission, including correlation among subchannels, imperfect carrier and timing recoveries. Among them, we show that the effect of sampling offset is very significant and a search procedure in the frequency domain should be incorporated for verification. With practical OFDM transmission, the number of uncorrelated subchannels is often not sufficient. Hence, we employ a time-separated approach for allocating enough subchannels and a modified ANA-PHY-PCRAS is proposed to alleviate the discontinuity of channel phase at far-separated time slots. Finally, the key equivocation is derived for the worst case scenario. We conclude that the enhanced security of ANA-PHY-PCRAS comes from the uncertainty of both the wireless channel and introduced artificial noise, compared to the traditional challenge-response authentication scheme implemented at the upper layer.Comment: 33 pages, 13 figures, submitted for possible publicatio

On the BICM Capacity

Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor

Communications over fading channels with partial channel information : performance and design criteria

The effects of system parameters upon the performance are quantified under the assumption that some statistical information of the wireless fading channels is available. These results are useful in determining the optimal design of system parameters. Suboptimal receivers are designed for systems that are constrained in terms of implementation complexity. The achievable rates are investigated for a wireless communication system when neither the transmitter nor the receiver has prior knowledge of the channel state information (CSI). Quantitative results are provided for independent and identically distributed (i.i.d.) Gaussian signals. A simple, low-duty-cycle signaling scheme is proposed to improve the information rates for low signal-to-noise ratio (SNR), and the optimal duty cycle is expressed as a function of the fading rate and SNR. It is demonstrated that the resource allocations and duty cycles developed for Gaussian signals can also be applied to systems using other signaling formats. The average SNR and outage probabilities are examined for amplify-and-forward cooperative relaying schemes in Rayleigh fading channels. Simple power allocation strategies are determined by using knowledge of the mean strengths of the channels. Suboptimal algorithms are proposed for cases that optimal receivers are difficult to implement. For systems with multiple transmit antennas, an iterative method is used to avoid the inversion of a data-dependent matrix in decision-directed channel estimation. When CSI is not available, two noncoherent detection algorithms are formulated based on the generalized likelihood ratio test (GLRT). Numerical results are presented to demonstrate the use of GLRT-based detectors in systems with cooperative diversity