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33
Energy and spectral efficiency of very large multiuser MIMO systems
 IEEE TRANS. COMMUN
, 2013
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Nonlinear Estimators and Tail Bounds for Dimension Reduction in l1 Using Cauchy Random Projections
, 2007
"... For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R ∈ RD×k (k ≪ D) whose entries are i.i.d. samples of the standard Cauchy C(0,1). Because of the impossibility result, one can not hope to recover the pai ..."
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Cited by 29 (0 self)
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For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R ∈ RD×k (k ≪ D) whose entries are i.i.d. samples of the standard Cauchy C(0,1). Because of the impossibility result, one can not hope to recover the pairwise l1 distances in A from B = A × R ∈ Rn×k, using linear estimators without incurring large errors. However, nonlinear estimators are still useful for certain applications in data stream computations, information retrieval, learning, and data mining. We study three types of nonlinear estimators: the sample median estimators, the geometric mean estimators, and the maximum likelihood estimators � (MLE). We derive tail bounds for the logn geometric mean estimators and establish that k = O ε2 � suffices with the constants explicitly given. Asymptotically (as k → ∞), both the sample median and the geometric mean estimators are about 80 % efficient compared to the MLE. We analyze the moments of the MLE and propose approximating its distribution of by an inverse Gaussian. Keywords: dimension reduction, l1 norm, JohnsonLindenstrauss (JL) lemma, Cauchy random projections
Performance analysis of ZF and MMSE equalizers for MIMO systems: An indepth study of the high SNR regime
 IEEE Trans. Inf. Theory
, 2011
"... This paper presents an indepth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multiinput multioutput (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprisi ..."
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Cited by 25 (2 self)
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This paper presents an indepth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multiinput multioutput (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprising analytical results in terms of the wellknown performance metrics of output signaltonoise ratio (SNR), uncoded error and outage probabilities, diversitymultiplexing (DM) gain tradeoff, and coding gain. Contrary to the common perception that ZF and MMSE are asymptotically equivalent at high SNR, we show that the output SNR of the MMSE equalizer (conditioned on the channel realization) is ρmmse = ρzf + ηsnr, where ρzf is the output SNR of the ZF equalizer, and that the gap ηsnr is statistically independent of ρzf and is a nondecreasing function of input SNR. Furthermore, as snr → ∞, ηsnr converges with probability one to a scaled F random variable. It is also shown that at the output of the MMSE equalizer, the interferencetonoise ratio (INR) is tightly upper bounded by ηsnr. Using the decomposition of the output SNR of MMSE, we can approximate its uncoded error as well ρzf as outage probabilities through a numerical integral which accurately reflects the respective SNR gains of the MMSE equalizer relative to its ZF counterpart. The ɛoutage capacities of the two equalizers, however, coincide
Compressed counting
 CoRR
"... We propose Compressed Counting (CC) for approximating the αth frequency moments (0 < α ≤ 2) of data streams under a relaxed strictTurnstile model, using maximallyskewed stable random projections. Estimators based on the geometric mean and the harmonic mean are developed. When α = 1, a simple cou ..."
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Cited by 21 (13 self)
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We propose Compressed Counting (CC) for approximating the αth frequency moments (0 < α ≤ 2) of data streams under a relaxed strictTurnstile model, using maximallyskewed stable random projections. Estimators based on the geometric mean and the harmonic mean are developed. When α = 1, a simple counter suffices for counting the first moment (i.e., sum). The geometric mean estimator of CC has asymptotic variance ∝ ∆ = α − 1, capturing the intuition that the complexity should decrease as ∆ = α−1  → 0. However, the previous classical algorithms based on symmetric stable random projections[12, 15] required O ( 1/ɛ 2) space, in order to approximate the αth moments within a 1 + ɛ factor, for any 0 < α ≤ 2 including α = 1. We show ( that using the geometric mean estimator, CC 1 requires O log(1+ɛ) + 2 √ ∆ log3/2 ( √∆)) + o space, as ∆ → (1+ɛ) 0. Therefore, in the neighborhood of α = 1, the complexity of CC is essentially O (1/ɛ) instead of O ( 1/ɛ 2). CC may be useful for estimating Shannon entropy, which can be approximated by certain functions of the αth moments with α → 1. [10, 9] suggested using α = 1 + ∆ with (e.g.,) ∆ < 0.0001 and ɛ < 10 −7, to rigorously ensure reasonable approximations. Thus, unfortunately, CC is “theoretically impractical ” for estimating Shannon entropy, despite its empirical success reported in [16]. 1
A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large Dimensional Signals
, 2008
"... This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio ..."
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Cited by 18 (8 self)
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This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiantenna as well as spread spectrum transmission models. The expression of the deterministic approximation of the SINR in the large dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.
LowComplexity Decoding via Reduced Dimension MaximumLikelihood Search
"... Abstract—In this paper, we consider a lowcomplexity detection technique referred to as a reduced dimension maximumlikelihood search (RDMLS). RDMLS is based on a partitioned search which approximates the maximumlikelihood (ML) estimate of symbols by searching a partitioned symbol vector space ra ..."
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Cited by 12 (0 self)
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Abstract—In this paper, we consider a lowcomplexity detection technique referred to as a reduced dimension maximumlikelihood search (RDMLS). RDMLS is based on a partitioned search which approximates the maximumlikelihood (ML) estimate of symbols by searching a partitioned symbol vector space rather than that spanned by the whole symbol vector. The inevitable performance loss due to a reduction in the search space is compensated by 1) the use of a list tree search, which is an extension of a single best searching algorithm called sphere decoding, and 2) the recomputation of a set of weak symbols, i.e., those ignored in the reduced dimension search, for each strong symbol candidate found during the list tree search. Through simulations onquadrature amplitude modulation (QAM) transmission in frequency nonselective multiinputmultioutput (MIMO) channels, we demonstrate that the RDMLS algorithm shows near constant complexity over a wide range of bit error rate (BER) (10 1 10 4), while limiting performance loss to within 1 dB from ML detection. Index Terms—Dimension reduction, list tree search, maximumlikelihood (ML) decoding, minimum mean square error (MMSE), multiple input multiple output (MIMO), sphere decoding, stack algorithm. I.
Diversity of MMSE MIMO receivers
 Princeton University, Rice University
"... Abstract—In most multipleinput multipleoutput (MIMO) systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high signaltonoise ratio. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The M ..."
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Cited by 10 (3 self)
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Abstract—In most multipleinput multipleoutput (MIMO) systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high signaltonoise ratio. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The MIMO minimum mean square error (MMSE) receiver does not follow this pattern and exhibits a varying diversity in its family of error curves. This paper analyzes this interesting behavior of the MMSE MIMO receiver and produces the MMSE MIMO diversity at all rates. The diversity of the quasistatic flatfading MIMO channel consisting of any arbitrary number of transmit and receiveantennasisfullycharacterized, showing that full spatial diversity is possible if and only if the rate is within a certain bound which is a function of the number of antennas. For other rates, the available diversity is fully characterized. At sufficiently low rates, the MMSE receiver has a diversity similar to the maximum likelihood receiver (maximal diversity), while at high rates, it performs similarly to the zeroforcing receiver (minimal diversity). Linear receivers are also studied in the context of the MIMO multipleaccess channel. Then, the quasistatic frequency selective MIMO channel is analyzed under zeropadding and cyclicprefix (CP) block transmissions and MMSE reception, and lower and upper bounds on diversity are derived. For the special case of SIMO under CP, it is shown that the aforementioned bounds are tight. Index Terms—Diversity, linear receiver, minimum mean square error (MMSE), multipleinput multipleoutput (MIMO).
Cacheenabled opportunistic cooperative mimo for video streaming in wireless systems
 IEEE Transactions on Signal Processing
, 2014
"... Abstract—We propose a cacheenabled opportunistic cooperative MIMO (CoMP) framework for wireless video streaming. By caching a portion of the video files at the relays (RS) using a novel MDScoded random cache scheme, the base station (BS) and RSs opportunistically employ CoMP to achieve spatial mu ..."
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Cited by 6 (0 self)
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Abstract—We propose a cacheenabled opportunistic cooperative MIMO (CoMP) framework for wireless video streaming. By caching a portion of the video files at the relays (RS) using a novel MDScoded random cache scheme, the base station (BS) and RSs opportunistically employ CoMP to achieve spatial multiplexing gain without expensive payload backhaul. We study a two timescale joint optimization of power and cache control to support realtime video streaming. The cache control is to create more CoMP opportunities and is adaptive to the longterm popularity of the video files. The power control is to guarantee the QoS requirements and is adaptive to the channel state information (CSI), the cache state at the RS and the queue state information (QSI) at the users. The joint problem is decomposed into an inner power control problem and an outer cache control problem. We first derive a closedform power control policy from an approximated Bellman equation. Based on this, we transform the outer problem into a convex stochastic optimization problem and propose a stochastic subgradient algorithm to solve it. Finally, the proposed solution is shown to be asymptotically optimal for high SNR and small timeslot duration. Its superior performance over various baselines is verified by simulations. Index Terms—Wireless video streaming, Dynamic cache control, Opportunistic CoMP, Power control I.
Very sparse stable random projections, estimators and tail bounds for stable random projections
, 2006
"... [36] proposed stable random projections, now a popular tool for data streaming computations, data mining, and machine learning. For example, in data streaming, stable random projections offer a unified, efficient, and elegant methodology for approximating the lα norm of a single data stream, or the ..."
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Cited by 5 (2 self)
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[36] proposed stable random projections, now a popular tool for data streaming computations, data mining, and machine learning. For example, in data streaming, stable random projections offer a unified, efficient, and elegant methodology for approximating the lα norm of a single data stream, or the lα distance between a pair of streams, for any 0 < α ≤ 2. [16] and [18] applied stable random projections for approximating the Hamming norm and the maxdominance norm, respectively, using very small α. Another application is to approximate all pairwise lα distances in a data matrix to speed up clustering, classification, or kernel computations. Given that stable random projections have become successful in various applications, this paper will focus on three different aspects in improving the current practice of stable random projections. Firstly, we propose very sparse stable random projections to significantly reduce the processing and storage cost, by replacing the αstable distribution with a mixture of a symmetric αPareto distribution (with probability β, 0 < β ≤ 1) and a point mass at the origin (with a probability 1 − β). This leads to a significant 1 βfold speedup for small β. We analyze the rate of convergence as a function of β, α, and the data regularity conditions. For example, when α = 1 and the data have bounded second moments, then
1 BER and Outage Probability Approximations for LMMSE Detectors on Correlated MIMO Channels
, 810
"... This paper is devoted to the study of the performance of the Linear Minimum MeanSquare Error receiver for (receive) correlated MultipleInput MultipleOutput systems. By the random matrix theory, it is wellknown that the SignaltoNoise Ratio (SNR) at the output of this receiver behaves asymptotic ..."
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Cited by 3 (1 self)
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This paper is devoted to the study of the performance of the Linear Minimum MeanSquare Error receiver for (receive) correlated MultipleInput MultipleOutput systems. By the random matrix theory, it is wellknown that the SignaltoNoise Ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to + ∞ at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the Bit Error Rate and the outage probability, especially for small system dimensions, Li et al. proposed convincingly to assume that the SNR follows a generalized Gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this article, this technique is generalized to (receive) correlated channels, and closedform expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.