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215
Unitary SpaceTime Modulation for MultipleAntenna Communications in Rayleigh Flat Fading
 IEEE Trans. Inform. Theory
, 1998
"... Motivated by informationtheoretic considerations, we propose a signalling scheme, unitary spacetime modulation, for multipleantenna communication links. This modulation is ideally suited for Rayleigh fastfading environments, since it does not require the receiver to know or learn the propagation ..."
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Cited by 307 (19 self)
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Motivated by informationtheoretic considerations, we propose a signalling scheme, unitary spacetime modulation, for multipleantenna communication links. This modulation is ideally suited for Rayleigh fastfading environments, since it does not require the receiver to know or learn the propagation coefficients. Unitary spacetime modulation uses constellations of T \cross M spacetime signals {\Phi_l, l= 1,...L},where T represents the coherence interval during which the fading is approximately constant, and M > M . We design some multipleantenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding. We demonstrate that two antennas have a 6dB diversity gain over one antenna at 15db SNR.
Grassmannian frames with applications to coding and communication
 Appl. Comp. Harmonic Anal
, 2003
"... For a given class F of unit norm frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation 〈fk, fl〉  among all frames {fk}k∈I ∈ F. We first analyze finitedimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal sph ..."
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Cited by 229 (14 self)
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For a given class F of unit norm frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation 〈fk, fl〉  among all frames {fk}k∈I ∈ F. We first analyze finitedimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These bounds yield a simple condition under which Grassmannian frames coincide with unit norm tight frames. We exploit connections to graph theory, equiangular line sets, and coding theory in order to derive explicit constructions of Grassmannian frames. Our findings extend recent results on unit norm tight frames. We then introduce infinitedimensional Grassmannian frames and analyze their connection to unit norm tight frames for frames which are generated by grouplike unitary systems. We derive an example of a Grassmannian Gabor frame by using connections to sphere packing theory. Finally we discuss the application of Grassmannian frames to wireless communication and to multiple description coding.
HighResolution Radar via Compressed Sensing
, 2008
"... A stylized compressed sensing radar is proposed in which the timefrequency plane is discretized into an N ×N grid. Assuming the number of targets K is small (i.e., K ≪ N 2), then we can transmit a sufficiently “incoherent ” pulse and employ the techniques of compressed sensing to reconstruct the ta ..."
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Cited by 156 (9 self)
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A stylized compressed sensing radar is proposed in which the timefrequency plane is discretized into an N ×N grid. Assuming the number of targets K is small (i.e., K ≪ N 2), then we can transmit a sufficiently “incoherent ” pulse and employ the techniques of compressed sensing to reconstruct the target scene. A theoretical upper bound on the sparsity K is presented. Numerical simulations verify that even better performance can be achieved in practice. This novel compressed sensing approach offers great potential for better resolution over classical radar.
Optimal Sequences, Power Control, and User Capacity of Synchronous CDMA Systems with Linear MMSE Multiuser Receivers
 IEEE TRANS. INFORM. THEORY
, 1999
"... There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spreadspectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjuncti ..."
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Cited by 102 (5 self)
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There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spreadspectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjunction with multiuser receivers and the resulting network user capacity is not well understood. In this paper we will focus on a single cell and consider both the uplink and downlink scenarios and assume a synchronous CDMA (SCDMA) system. We characterize the user capacity of a single cell with the optimal linear receiver (MMSE receiver). The user capacity of the system is the maximum number of users per unit processing gain admissible in the system such that each user has its qualityofservice (QoS) requirement (expressed in terms of its desired signaltointerference ratio) met. Our characterization allows us to describe the user capacity through a simple effective bandwidth characterization: Users are allowed in the system if and only if the sum of their effective bandwidths is less than the processing gain of the system. The effective bandwidth of each user is a simple monotonic function of its QoS requirement. We identify the optimal signature sequences and power control strategies so that the users meet their QoS requirement. The optimality is in the sense of minimizing the sum of allocated powers. It turns out that with this optimal allocation of signature sequences and powers, the linear MMSE receiver is just the corresponding matched filter for each user. We also characterize the effect of transmit power constraints on the user capacity.
Structured compressed sensing: From theory to applications
 IEEE TRANS. SIGNAL PROCESS
, 2011
"... Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discretetodiscrete measurement architectures using matrices of randomized nature and signal models based on standard ..."
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Cited by 98 (15 self)
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Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discretetodiscrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuoustime signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.
Iterative construction of optimum signature sequence sets in synchronous CDMA systems
 IEEE Trans. Inform. Theory
, 1989
"... Abstract—Recently, optimum signature sequence sets that maximize the capacity of singlecell synchronous code division multiple access (CDMA) systems have been identified. Optimum signature sequences minimize the total squared correlation (TSC); they form a set of orthogonal sequences, if the number ..."
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Cited by 89 (9 self)
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Abstract—Recently, optimum signature sequence sets that maximize the capacity of singlecell synchronous code division multiple access (CDMA) systems have been identified. Optimum signature sequences minimize the total squared correlation (TSC); they form a set of orthogonal sequences, if the number of users is less than or equal to the processing gain, and a set of Welch bound equality (WBE) sequences, otherwise. We present an algorithm where users update their transmitter signature sequences sequentially, in a distributed fashion, by using available receiver measurements. We show that each update decreases the TSC of the set, and produces better signature sequence sets progressively. We prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain. We observe and conjecture that the algorithm converges to a WBE set when the number of users is greater than the processing gain. At each step, the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error (MMSE) receiver corresponding to that signature sequence. Since the MMSE filter can be obtained by a distributed algorithm for each user, the proposed algorithm is amenable to distributed implementation. Index Terms—Code division multiple access (CDMA), distributed interference avoidance, minimum mean squared error (MMSE), optimum signature sequence sets, Welch bound equality (WBE) sequences. I.
Designing Structured Tight Frames via an Alternating Projection Method
, 2003
"... Tight frames, also known as general WelchBoundEquality sequences, generalize orthonormal systems. Numerous applicationsincluding communications, coding and sparse approximationrequire finitedimensional tight frames that possess additional structural properties. This paper proposes an alterna ..."
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Cited by 84 (10 self)
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Tight frames, also known as general WelchBoundEquality sequences, generalize orthonormal systems. Numerous applicationsincluding communications, coding and sparse approximationrequire finitedimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems, which includes the frame design problem. To apply this method, one only needs to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate
Wireless systems and interference avoidance
 IEEE Trans. Wireless Commun
, 2002
"... Abstract—Motivated by the emergence of programmable radios, we seek to understand a new class of communication system where pairs of transmitters and receivers can adapt their modulation/demodulation method in the presence of interference to achieve better performance. Using signal to interference r ..."
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Cited by 74 (12 self)
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Abstract—Motivated by the emergence of programmable radios, we seek to understand a new class of communication system where pairs of transmitters and receivers can adapt their modulation/demodulation method in the presence of interference to achieve better performance. Using signal to interference ratio as a metric and a general signal space approach, we present a class of iterative distributed algorithms for synchronous systems which results in an ensemble of optimal waveforms for multiple users connected to a common receiver (or colocated independent receivers). That is, the waveform ensemble meets the Welch Bound with equality and, therefore, achieves minimum average interference over the ensemble of signature waveforms. We derive fixed points for a number of scenarios, provide examples, look briefly at ensemble stability under user addition and deletion as well as provide a simplistic comparison to synchronous codedivision multipleaccess. We close with suggestions for future work. Index Terms—Adaptive modulation, codedivision multipleaccess systems, codeword optimization, interference avoidance, multiuser
Design and analysis of transmitbeamforming based on limitedrate feedback
, 2006
"... This paper deals with design and performance analysis of transmit beamformers for multipleinput multipleoutput (MIMO) systems based on bandwidthlimited information that is fed back from the receiver to the transmitter. By casting the design of transmit beamforming based on limitedrate feedback ..."
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Cited by 72 (1 self)
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This paper deals with design and performance analysis of transmit beamformers for multipleinput multipleoutput (MIMO) systems based on bandwidthlimited information that is fed back from the receiver to the transmitter. By casting the design of transmit beamforming based on limitedrate feedback as an equivalent sphere vector quantization (SVQ) problem, multiantenna beamformed transmissions through independent and identically distributed (i.i.d.) Rayleigh fading channels are first considered. The ratedistortion function of the vector source is upperbounded, and the operational ratedistortion performance achieved by the generalized Lloyd’s algorithm is lowerbounded. Although different in nature, the two bounds yield asymptotically equivalent performance analysis results. The average signaltonoise ratio (SNR) performance is also quantified. Finally, beamformer codebook designs are studied for correlated Rayleigh fading channels, and a lowcomplexity codebook design that achieves nearoptimal performance is derived.
Welch's Bound and Sequence Sets for CodeDivision MultipleAccess Systems
 In Sequences II: Methods in Communication, Security and Computer Science
, 1991
"... Welch's bound for a set of M complex equienergy sequences is considered as a lower bound on the sum of the squares of the magnitudes of the inner products between all pairs of these sequences. It is shown that, when the sequences are binary (1 valued) sequences assigned to the M users in a sy ..."
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Cited by 59 (1 self)
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Welch's bound for a set of M complex equienergy sequences is considered as a lower bound on the sum of the squares of the magnitudes of the inner products between all pairs of these sequences. It is shown that, when the sequences are binary (1 valued) sequences assigned to the M users in a synchronous codedivision multipleaccess (SCDMA) system, precisely such a sum determines the sum of the variances of the interuser interference seen by the individual users. It is further shown that Welch's bound, in the general case, holds with equality if and only if the array having the M sequences as rows has orthogonal and equienergy columns. For the case of binary (1 valued) sequences that meet Welch's bound with equality, it is shown that the sequences are uniformly good in the sense that, when used in a SCDMA system, the variance of the interuser interference is the same for all users. It is proved that a sequence set corresponding to a binary linear code achieves Welch's bound with equ...