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62
Optimal sequences and sum capacity of synchronous CDMA systems.
 IEEE Trans. Inform. Theory,
, 1999
"... Abstract The sum capacity of a multiuser synchronous CDMA system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed in ..."
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Cited by 140 (7 self)
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Abstract The sum capacity of a multiuser synchronous CDMA system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed in
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.
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 92 (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.
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 77 (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 75 (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.
Life Beyond Bases: The Advent of Frames (Part I)
, 2007
"... Redundancy is a common tool in our daily lives. Before we leave the house, we double and triplecheck that we turned off gas and lights, took our keys, and have money (at least those worrywarts among us do). When an important date is coming up, we drive our loved ones crazy by confirming “just onc ..."
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Cited by 72 (8 self)
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Redundancy is a common tool in our daily lives. Before we leave the house, we double and triplecheck that we turned off gas and lights, took our keys, and have money (at least those worrywarts among us do). When an important date is coming up, we drive our loved ones crazy by confirming “just once more” they are on top of it. Of course, the reason we are doing that is to avoid a disaster by missing or forgetting something, not to drive our loved ones crazy. The same idea of removing doubt is present in signal representations. Given a signal, we represent it in another system, typically a basis, where its characteristics are more readily apparent in the transform coefficients. However, these representations are typically nonredundant, and thus corruption or loss of transform coefficients can be serious. In comes redundancy; we build a safety net into our representation so that we can avoid those disasters. The redundant counterpart of a basis is called a frame [no one seems to know why they are called frames, perhaps because of the bounds in (25)?]. It is generally acknowledged (at least in the signal processing and harmonic analysis communities) that frames were born in 1952 in the paper by Duffin and Schaeffer [32]. Despite being over half a century old, frames gained popularity only in the last decade, due mostly to the work of the three wavelet pioneers—Daubechies, Grossman, and Meyer [29]. Framelike ideas, that is, building redundancy into a signal expansion, can be found in pyramid
Generalised Welch Bound Equality Sequences Are Tight Frames
 IEEE Transactions on Informtion Theory
, 2003
"... This paper shows what are called Welch bound equality (WBE) sequences by the signal processing community are precisely the isometric/equal norm/normalized/uniform tight frames which are currently being investigated for a number of applications, and in the real case are the spherical 2–designs of com ..."
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Cited by 34 (2 self)
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This paper shows what are called Welch bound equality (WBE) sequences by the signal processing community are precisely the isometric/equal norm/normalized/uniform tight frames which are currently being investigated for a number of applications, and in the real case are the spherical 2–designs of combinatorics. Recent applications include wavelet expansions, Grassmannian frames, frames robust to erasures, and quantum measurements. This is done by giving an elementary proof of a generalisation of Welch’s inequality to vectors which need not have equal energy, and then showing that equality occurs in this exactly when the vectors form a tight frame.
Mutually Unbiased Bases are Complex Projective 2Designs
 PROC. 2005 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY
, 2005
"... Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for system of prime power dimension d, it is unknown whether this bound can be achieved for any nonpri ..."
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Cited by 31 (1 self)
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Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for system of prime power dimension d, it is unknown whether this bound can be achieved for any nonprime power dimension. In this paper we demonstrate that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2designs with angle set {0, 1/d}. We also give a new and simple proof that symmetric informationally complete POVMs are complex projective 2designs with angle set {1/(d+1)}.
Ensuring Convergence of the MMSE Iteration for Interference Avoidance to the Global Optimum
, 2003
"... Viswanath and Anantharam [1] characterize the sum capacity of multiaccess vector channels. For a given number of users, received powers, spreading gain, and noise covariance matrix in a codedivision multipleaccess (CDMA) system, the authors of [1] present a combinatorial algorithm to generate a se ..."
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Cited by 29 (1 self)
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Viswanath and Anantharam [1] characterize the sum capacity of multiaccess vector channels. For a given number of users, received powers, spreading gain, and noise covariance matrix in a codedivision multipleaccess (CDMA) system, the authors of [1] present a combinatorial algorithm to generate a set of signature sequences that achieves the maximum sum capacity. These sets also minimize a performance measure called generalized total square correlation (TSC ).
Iterative signature adaptation for capacity maximization of cdma systems
 In Allerton Conf. on Comm., Control and Computing
, 1998
"... For single cell synchronous code division multiple access (CDMA) systems, both the information theoretic capacity and the network capacity have been identi ed. In both cases, it was shown that if the number of users, N, is no more than the processing gain, L, then orthogonal signatures are optimal w ..."
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Cited by 26 (9 self)
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For single cell synchronous code division multiple access (CDMA) systems, both the information theoretic capacity and the network capacity have been identi ed. In both cases, it was shown that if the number of users, N, is no more than the processing gain, L, then orthogonal signatures are optimal while if N>L, then signatures which satisfy the Welch bound on the total squared correlation with equality (called WBE sequences) are optimal. This paper presents an algorithm which iteratively updates the signatures in a distributed fashion, starting from an initial set of signatures. Under mild conditions on the initial set of signatures, we prove that the algorithm converges to a set of orthogonal signatures if N L and to a WBE set if N>L. At each step, the algorithm replaces one signature from the set with the normalized linear MMSE receiver lter corresponding to that signature. Since the MMSE lter can be obtained by a distributed algorithm for each user, the algorithm is amenable to distributed implementation. 1