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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 154 (13 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.
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 69 (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.
Linear precoding via conic optimization for fixed mimo receivers
 IEEE Trans. on Signal Processing
, 2006
"... We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maxi ..."
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Cited by 50 (3 self)
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We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maximize the worst case SINR subject to a power constraint. We show that both problems can be solved using standard conic optimization packages. In addition, we develop conditions for the optimal precoder for both of these problems, and propose two simple fixed point iterations to find the solutions which satisfy these conditions. The relation to the well known downlink uplink duality in the context of joint downlink beamforming and power control is also explored. Our precoder design is general, and as a special case it solves the beamforming problem. In contrast to most of the existing precoders, it is not limited to full rank systems. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders. 1
Output MAI Distributions of Linear MMSE Multiuser Receivers in DSCDMA Systems
 IEEE TRANS. INFORM. THEORY
, 2001
"... Multipleaccess interference (MAI) in a codedivision multipleaccess (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. In this paper, we study the behavior of the output MAI of the minimum meansquare error (MMSE) receiver employed in t ..."
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Cited by 48 (8 self)
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Multipleaccess interference (MAI) in a codedivision multipleaccess (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. In this paper, we study the behavior of the output MAI of the minimum meansquare error (MMSE) receiver employed in the uplink of a directsequence (DS)CDMA system. We focus on imperfect powercontrolled systems with random spreading, and establish that in a synchronous system 1) the output MAI of the MMSE receiver is asymptotically Gaussian, and 2) for almost every realization of the signatures and received powers, the conditional distribution of the output MAI converges weakly to the same Gaussian distribution as in the unconditional case. We also extend our study to asynchronous systems and establish the Gaussian nature of the output interference. These results indicate that in a large system the output interference is approximately Gaussian, and the performance of the MMSE receiver is robust to the randomness of the signatures and received powers. The Gaussianity justifies the use of singleuser Gaussian codes for CDMA systems with linear MMSE receivers, and implies that from the viewpoints of detection and channel capacity, signaltointerference ratio (SIR) is the key parameter that governs the performance of the MMSE receiver in a CDMA system.
Resource Pooling and Effective Bandwidths in CDMA Networks with Multiuser Receivers and Spatial Diversity
 IEEE Trans. Inform. Theory
, 1999
"... Much of the performance analysis on multiuser receivers for directsequence codedivision multipleaccess (CDMA) systems is focused on worst case nearfar scenarios. The user capacity of powercontrolled networks with multiuser receivers are less wellunderstood. In [1], it was shown that under som ..."
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Cited by 42 (3 self)
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Much of the performance analysis on multiuser receivers for directsequence codedivision multipleaccess (CDMA) systems is focused on worst case nearfar scenarios. The user capacity of powercontrolled networks with multiuser receivers are less wellunderstood. In [1], it was shown that under some conditions, the user capacity of an uplink powercontrolled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. In the present paper, we show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signaltointerference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirement. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of "resource pooling" arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas.
Optimum linear joint transmitreceive processing for MIMO channels with QoS constraints
 IEEE Transactions on Signal Processing
, 2004
"... Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear ..."
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Cited by 23 (3 self)
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Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power (the exact conditions under which the problem becomes unfeasible are given). Although the original problem is a complicated nonconvex problem with matrixvalued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multilevel waterfilling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmitreceive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors that has an important interest for practical systems. Numerical results from simulations are given to support the mathematical development of the problem. Index Terms—Array signal processing, beamforming, joint transmitreceive equalization, linear precoding, MIMO channels, spacetime filtering, waterfilling. I.
Sensor Networks with Mobile Access: Optimal Random Access and Coding
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: SPECIAL ISSUE ON SENSOR NETWORKS
, 2004
"... We consider random access and coding schemes for sensor networks with mobile access (SENMA). Using an orthogonal codedivision multiple access (CDMA) as the physical layer, an opportunistic ALOHA (OALOHA) protocol that utilizes channel state information is proposed. Under the packet capture model ..."
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Cited by 22 (5 self)
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We consider random access and coding schemes for sensor networks with mobile access (SENMA). Using an orthogonal codedivision multiple access (CDMA) as the physical layer, an opportunistic ALOHA (OALOHA) protocol that utilizes channel state information is proposed. Under the packet capture model and using the asymptotic throughput as the performance metric, we show that OALOHA approaches the throughput equal to the spreading gain with an arbitrarily small power at each sensor. This result implies that OALOHA is close to the optimal centralized scheduling scheme for the orthogonal CDMA networks. When side information such as location is available, the transmission control is modified to incorporate either the distribution or the actual realization of the side information. Convergence of the throughput with respect to the size of the network is analyzed. For networks allowing sensor collaborations, we combine coding with random access by proposing two coded random access schemes: spreading code dependent and independent transmissions. In the low rate regime, the spreading code independent transmission has a larger random coding exponent (therefore, faster decay of error probability) than that of the spreading code dependent transmission. On the other hand, the spreading code dependent transmission gives higher achievable rate.
On QuasiOrthogonal Signatures for CDMA Systems
 IEEE Trans. Inform. Theory. [Online]. Available: http://www.ece.utexas.edu/˜rheath/papers/2002/quasicdma
, 2002
"... Codebooks constructed from Welch bound equality sequences are optimal in terms of sum capacity in synchronous CDMA systems. These optimal codebooks depend on both the sequence length as well as the number of active sequences. Thus to maintain optimality a typically different codebook is needed fo ..."
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Cited by 19 (6 self)
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Codebooks constructed from Welch bound equality sequences are optimal in terms of sum capacity in synchronous CDMA systems. These optimal codebooks depend on both the sequence length as well as the number of active sequences. Thus to maintain optimality a typically different codebook is needed for every possible number of active users. Further, all the sequences need to be reassigned as the number of active users changes. This paper describes and analyzes two promising subclasses of Welch bound equality sequences that have good properties when only a subset of sequences is active. One subclass, based on maximum Welch bound equality sequence sets, has equiangular sequences thus each user experiences the same amount of interference. The interference power depends only on the total number of active users. Another subclass, constructed by concatenating multiple orthonormal basis, comes closer to the Welch bound when not all signatures are active. Optimal unions of orthonormal basis are derived. Performance when subsets of sequences are active is characterized in terms of sumsquared correlation, average interference, and condition number of the Gram matrix.
Optimal Sequences for CDMA Under Colored Noise: A SchurSaddle Function Property
 IEEE TRANS. INFORM. THEORY
, 2002
"... We consider direct sequence code division multiple access (DSCDMA), modeling interference from users communicating with neighboring base stations by additive colored noise. We consider two types of receiver structures: first we consider the informationtheoretically optimal receiver and use the sum ..."
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Cited by 17 (0 self)
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We consider direct sequence code division multiple access (DSCDMA), modeling interference from users communicating with neighboring base stations by additive colored noise. We consider two types of receiver structures: first we consider the informationtheoretically optimal receiver and use the sum capacity of the channel as our performance measure. Second, we consider the linear minimum mean square error (LMMSE) receiver and use the signaltointerference ratio (SIR) of the estimate of the symbol transmitted as our performance measure. Our main result is a constructive characterization of the possible performance in both these scenarios. A central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied. We show that the sum capacity is a saddle function:itisconvex in the additive noise covariances and concave in the user received powers. In the linear receiver case, we show that the minimum average power required to meet a set of target performance requirements of the users is a saddle function: it is convex in the additive noise covariances and concave in the set of performance requirements.
Optimal sequences for CDMA with decisionfeedback receivers
 IEEE Trans. Inform. Theory
, 2003
"... Abstract—We consider a symbolsynchronous codedivision multipleaccess (CDMA) system that is equipped with a multiuser decisionfeedback receiver and for which power control is available. The users are each assigned a qualityofservice (QoS) threshold to be guaranteed by the system, and to cover s ..."
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Cited by 14 (0 self)
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Abstract—We consider a symbolsynchronous codedivision multipleaccess (CDMA) system that is equipped with a multiuser decisionfeedback receiver and for which power control is available. The users are each assigned a qualityofservice (QoS) threshold to be guaranteed by the system, and to cover scenarios for which there are multiple classes of users, these are not required to be equal to each other. For an ideal decisionfeedback receiver, it is known that with enough power the system can always meet the users ’ QoS thresholds, so we instead minimize the sum of the users ’ received powers over system designs (i.e., signature sequences, powercontrol policy, and decisionfeedback receiver) which guarantee the QoS requirements. It is found that the optimal design produces two classes of users, those whose sequences and powers satisfy with equality the generalized Welch bound inequality and those oversized users that are mutually orthogonal to each other and the rest of the users. In terms of power and bandwidth savings, the optimal sequences for the decisionfeedback receiver are found to compare very favorably to optimal designs for linear receivers and to random sequences for the decisionfeedback receiver. Index Terms—Codedivision multiple access (CDMA), decisionfeedback receiver, linear minimum meansquareerror (MMSE) receiver, power control, qualityofservice (QoS), signature sequences. I.