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Channel capacity under subnyquist nonuniform sampling,” submitted to
 IEEE Trans on Information Theory, April 2012. [Online]. Available: http://arxiv.org/abs/1204.6049
"... Abstract — This paper investigates the effect of subNyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear timeinvariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of r ..."
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Abstract — This paper investigates the effect of subNyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear timeinvariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of rightinvertible timepreserving sampling methods which includes irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signaltonoise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling grid employed at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while are typically complicated to realize in practice, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain in this scenario, which is in contrast to the benefits obtained from random mixing in spectrumblind compressive sampling schemes. Index Terms — Nonuniform sampling, irregular sampling, sampled analog channels, subNyquist sampling, channel
Distortion Rate Function of SubNyquist Sampled Gaussian Sources
"... The amount of information lost in subNyquist sampling of a continuoustime Gaussian stationary process is quantified. We consider a combined source coding and subNyquist reconstruction problem in which the input to the encoder is a subNyquist sampled version of the analog source. We first derive ..."
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The amount of information lost in subNyquist sampling of a continuoustime Gaussian stationary process is quantified. We consider a combined source coding and subNyquist reconstruction problem in which the input to the encoder is a subNyquist sampled version of the analog source. We first derive an expression for the mean square error in reconstruction of the process as a function of the sampling frequency and the average number of bits describing each sample. We define this function as the distortionratefrequency function. It is obtained by reverse waterfilling over a spectral density associated with the minimum variance reconstruction of an undersampled Gaussian process, plus the error in this reconstruction. Further optimization to reduce distortion is then performed over the sampling structure, and an optimal presampling filter associated with the statistics of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any uniform sampling scheme. It unifies the ShannonNyquistWhittaker sampling theorem and Shannon ratedistortion theory for Gaussian sources.
1Channel Capacity under SubNyquist Nonuniform Sampling
"... Abstract—This paper investigates the effect of subNyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear timeinvariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of rig ..."
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Abstract—This paper investigates the effect of subNyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear timeinvariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of rightinvertible timepreserving sampling methods which include irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signaltonoise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while typically complicated to realize, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain, which is in contrast to the benefits obtained from random mixing in spectrumblind compressive sampling schemes. Index Terms—nonuniform sampling, irregular sampling, sampled analog channels, subNyquist sampling, channel capacity, Beurling density, timepreserving sampling systems I.
1Backing off from Infinity: Performance Bounds via Concentration of Spectral Measure for Random MIMO Channels
"... Abstract—The performance analysis of random vector channels, particularly multipleinputmultipleoutput (MIMO) channels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of characterizing the exact distribution of the objectiv ..."
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Abstract—The performance analysis of random vector channels, particularly multipleinputmultipleoutput (MIMO) channels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of characterizing the exact distribution of the objective performance metrics. This paper exposes a new nonasymptotic framework that allows the characterization of many canonical MIMO system performance metrics to within a narrow interval under moderatetolarge channel dimensionality, provided that these metrics can be expressed as a separable function of the singular values of the matrix. The effectiveness of our framework is illustrated through two canonical examples. Specifically, we characterize the mutual information and power offset of random MIMO channels, as well as the minimum mean squared estimation error of MIMO channel inputs from the channel outputs. Our results lead to simple, informative, and reasonably accurate control of various performance metrics in the finitedimensional regime, as corroborated by the numerical simulations. Our analysis framework is established via the concentration of spectral measure phenomenon for random matrices uncovered by Guionnet and Zeitouni, which arises in a variety of random matrix ensembles irrespective of the precise distributions of the matrix entries. Index Terms—MIMO, massive MIMO, confidence interval, concentration of spectral measure, random matrix theory, nonasymptotic analysis, mutual information, MMSE I.