## Wireless systems and interference avoidance (2002)

Venue: | IEEE Trans. Wireless Commun |

Citations: | 52 - 12 self |

### BibTeX

@ARTICLE{Rose02wirelesssystems,

author = {Christopher Rose and Sennur Ulukus and Roy D. Yates},

title = {Wireless systems and interference avoidance},

journal = {IEEE Trans. Wireless Commun},

year = {2002},

volume = {1},

pages = {415--428}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 code-division multiple-access. We close with suggestions for future work. Index Terms—Adaptive modulation, code-division multiple-access systems, codeword optimization, interference avoidance, multiuser

### Citations

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Citation Context ... (t; t) is an autocorrelation function, R is symmetric and positive semi-definite. This implies that R has non-negative eigenvalues and an associated full set of orthonormal eigenvectors which spansN =-=[17]-=-. The receiver observes the signal r(t) = bS(t) +Z(t) (10) Rose, Ulukus and Yates: Interference Avoidance in Wireless Systems 4 as input on the interval [0; T ]. Projecting the received signal onto th... |

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Citation Context ...VOL. 1, NO. 3, JULY 2002 The terms in the left-hand sum are nonnegative, thus, Trace , which is convex in the . Since we require and , application of standard constrained optimization techniques [37]–=-=[39]-=- provides a classical waterfilling result. Defining the “water level” as with as defined in the theorem statement, we have when and otherwise. Thus Trace (38) thereby, proving the first part of the th... |

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Citation Context ...r users' known signature waveforms and additive white Gaussian noise, the vectorsc with componentssc n =ss n =l n is a scaled version of the well known minimum mean squared error (MMSE) linear filter =-=[19]-=- and the decision rule (12) is the MMSE multiuser detector. We see that the filter output (and decision statistic) X =sc >sr = nsc nsr n = N n=1ss 2 n l n ! b+ N n=1ss nsz n l n (14) contains both sig... |

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Citation Context ...imple measures of multi-base performance. For a synchronous CDMA (S-CDMA) system with randomly chosen N-chip signature sequences, the user capacity with simple matched filters is upper bounded by N=g =-=[40]-=-. For a system employing interference Rose, Ulukus and Yates: Interference Avoidance in Wireless Systems 18 avoidance with matched filters, we have determined that at convergence, the user capacity is... |

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Citation Context ...be implemented by blind techniques at the receiver along with a feedback channel to the transmitter. Specifically, in the MMSE algorithm, the receiver for user k could be a blind adaptive MMSE filter =-=[35]-=- based on the observable Z k =R k +s 2 I. Likewise, for the eigen-algorithm, D of equation (27) is maximized when x > R k x, the sum interference experienced by user k with new codeword x, is minimize... |

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Citation Context ...hanges. Nonetheless, recent results show that interference avoidance methods seem to be robust and are applicable to dispersive systems, asynchronous systems and multiple antenna systems as well [41]–=-=[50]-=-. As noted, we have found the speed and stability with which codeword ensembles converge surprising. Especially intriguing is the seemingly certain convergence to an optimal set when starting from a r... |

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Citation Context ... and thesz n are mutually uncorrelated. If the F n (t) do not span the signal space, then error-free reception is possible by first augmenting the basis set to span the signal space (via Gram-Schmidt =-=[18]-=- for example) and then noting that there will be no interference energy projected onto these augmented basis functions which carry non-zero signal energy. Thus, with no loss of generality we assume th... |

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Citation Context ...re waveforms S i (t). Without loss of generality, we assume each S i (t) has unit energy. The relationship between signature selection and multiuser system capacity has been studied in several papers =-=[10, 20, -=-21]. In [20], it is shown that for a set of users' rates R 1 ; : : : ; RM belonging to the information theoretic achievable rate region C , the sum capacity is C s = max (R 1 ;;R M )2C M i=1 R i = 1 2... |

114 |
An algorithm for combined cell-site selection and power control to maximize cellular spread spectrum capacity
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Citation Context ...eless systems of the near future will have elements which adapt dynamically to changing patterns of interference by adjusting modulation and processing methods in much the same way that power control =-=[6]-=-–[10], is used today, albeit on a possibly slower time scale. Furthermore, if the release of 300 MHz of unlicensed spectrum in the 5-GHz range [11] is any indication, one might expect there to be an a... |

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Citation Context ...s sI N +SS > (22) Then we define the eigenvalues of sI N +SS > as l i , i = 1; N and rewrite sum capacity as C s = N 2 log s+ 1 2 N i=1 log l i (23) essentially as was done in both [21] and [26]. Now consider TSC. We first note that if fl i g are the eigenvalRose, Ulukus and Yates: Interference Avoidance in Wireless Systems 7 ues of s 2 I N +SS > then Trace[(sI N +SS > ) 2 ] = N i=1 l 2 i (2... |

92 | Stochastic power control for cellular radio systems
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Citation Context ...essive. We close this section with a caveat. Studies of convergence rate based on perfect information are chimeric. In practical systems where information is imperfect, stochastic convergence studies =-=[8]-=- are necessary, and as a general rule, the convergence rate is much slower. Nonetheless, perfect information can often be used to suggest an upper bound on convergence properties. That is, were conver... |

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Citation Context ...re waveforms S i (t). Without loss of generality, we assume each S i (t) has unit energy. The relationship between signature selection and multiuser system capacity has been studied in several papers =-=[10, 20, -=-21]. In [20], it is shown that for a set of users' rates R 1 ; : : : ; RM belonging to the information theoretic achievable rate region C , the sum capacity is C s = max (R 1 ;;R M )2C M i=1 R i = 1 2... |

69 | Iterative construction of optimum signature sequence sets in synchronous cdma systems
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Citation Context ...g where L is the eigenvalue matrix of Z k . It is known that codewords might be adapted for single users to obtain better mean square error (MSE) performance [30,31]. The following theorem, proven in =-=[9, 30, 32-=-], shows that the MMSE algorithm is indeed an interference avoidance algorithm. Theorem 1 Replacing s k with c k yields D 0, with equality iff c k = s k . Historically, the MMSE algorithm for codewor... |

61 | Optimal sequences, power control and capacity of synchronous CDMA systems with linear multiuser receivers
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Citation Context ...re waveforms S i (t). Without loss of generality, we assume each S i (t) has unit energy. The relationship between signature selection and multiuser system capacity has been studied in several papers =-=[10, 20, -=-21]. In [20], it is shown that for a set of users' rates R 1 ; : : : ; RM belonging to the information theoretic achievable rate region C , the sum capacity is C s = max (R 1 ;;R M )2C M i=1 R i = 1 2... |

51 | CDMA codeword optimization: interference avoidance and convergence via class warfare
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Citation Context ... subpoptimal fixed points seem to be avoided by starting from initially random codewords and that convergence to optimum can be forced by a modification of the greedy interference avoidance procedure =-=[28, 29]-=-. 5 Discussion 5.1 Eigen-Algorithm: numerical examples Here we provide example applications of interference avoidance to the scenarios analyzed in this paper. FIGURE 3 shows CDMA chip sequences for fi... |

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Citation Context ...ONS, VOL. 1, NO. 3, JULY 2002 The terms in the left-hand sum are nonnegative, thus, Trace , which is convex in the . Since we require and , application of standard constrained optimization techniques =-=[37]-=-–[39] provides a classical waterfilling result. Defining the “water level” as with as defined in the theorem statement, we have when and otherwise. Thus Trace (38) thereby, proving the first part of t... |

43 | Welch’s bound and sequence sets for code-division multiple access systems
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Citation Context ...of the squared cross correlations, which we will call total squared correlation (TSC). TSC = Trace[(SS > ) 2 ] = M i=1 M j=1 (s > i s j ) 2 M 2 =N (21) For a simple derivation of the bound (21), see [=-=24, 2-=-5]. Note that sequence sets satisfying (20) satisfy the bound (21) with equality. We observe that the set of sequences satisfying either equation (19) for M N or equation (20) for M N has the proper... |

28 | A software radio architecture for linear multiuser detection - Seskar, Mandayam - 1999 |

27 | Iterative signature adaptation for capacity maximization of CDMA systems
- Ulukus, Yates
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Citation Context ...Theorem 1 Replacing s k with c k yields D 0, with equality iff c k = s k . Historically, the MMSE algorithm for codeword ensemble optimization is the first proposed interference avoidance algorithm [=-=9, 32, 33-=-]. The question of convergence is addressed next where we find that the eigen-algorithm and the MMSE algorithm share a number of common properties: Both algorithms decrease the TSC monotonically. Sin... |

21 |
Control, Multiuser Detection and Interference Avoidance in CDMA Systems
- Ulukus, “Power
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(Show Context)
Citation Context ...g where L is the eigenvalue matrix of Z k . It is known that codewords might be adapted for single users to obtain better mean square error (MSE) performance [30,31]. The following theorem, proven in =-=[9, 30, 32-=-], shows that the MMSE algorithm is indeed an interference avoidance algorithm. Theorem 1 Replacing s k with c k yields D 0, with equality iff c k = s k . Historically, the MMSE algorithm for codewor... |

21 |
Linear adaptive transmitterreceiver structures for asynchronous CDMA systems
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Citation Context ...e decorrelated space and then renormalizing where L is the eigenvalue matrix of Z k . It is known that codewords might be adapted for single users to obtain better mean square error (MSE) performance =-=[30,31-=-]. The following theorem, proven in [9, 30, 32], shows that the MMSE algorithm is indeed an interference avoidance algorithm. Theorem 1 Replacing s k with c k yields D 0, with equality iff c k = s k ... |

18 |
Performance variability of linear multiuser detection for DS-CDMA
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(Show Context)
Citation Context ...e decorrelated space and then renormalizing where L is the eigenvalue matrix of Z k . It is known that codewords might be adapted for single users to obtain better mean square error (MSE) performance =-=[30,31-=-]. The following theorem, proven in [9, 30, 32], shows that the MMSE algorithm is indeed an interference avoidance algorithm. Theorem 1 Replacing s k with c k yields D 0, with equality iff c k = s k ... |

16 | Interference avoidance and multiaccess vector channels - Popescu, Popescu, et al. - 2007 |

14 | User capacity of asynchronous CDMA systems with optimum signature sequences,” submitted to - Ulukus, Yates - 2001 |

13 | Interference Avoidance and Dispersive Channels. A New Look at Multicarrier Modulation
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(Show Context)
Citation Context ... investigation. Of particular interest will be some of the issues raised previously, principal among them, whether interference avoidance can be used effectively with dispersive channels. Recent work =-=[41]-=- where a version of multicarrier modulation is adopted suggests the answer is yes. 6 Summary and Conclusion Starting from a general signal space foundation, we have derived a class of interference avo... |

13 | Iterative construction of optimum sequence sets in synchronous CDMA systems
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(Show Context)
Citation Context ... k might not all be equal as required for SS > = (M=N)I. We now examine the nature of such suboptimal fixed points in more detail. 3 The convergence properties of the MMSE algorithm are described in [=-=9, 32, 34]-=-. In this paper, our focus will be on the eigen-algorithm, or more generally, on any greedy algorithm which always chooses codeword replacements which increase its SIR when at all possible. Or equival... |

12 | Fading channels and interference avoidance
- Popescu, Rose
- 2001
(Show Context)
Citation Context ...ffective in situations where the wireless channel is changing significantly over, say 1000 or 10000, bit intervals, though there are hints that even in such circumstances, IA affords some improvement =-=[42]-=-. Regardless, a fixed wireless environment might be most appropriate for application of interference avoidance methods. We note that despite the assumption of perfect channels used in this paper, wire... |

11 |
On welch's bound for the correlation of a sequence set
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Citation Context ...of the squared cross correlations, which we will call total squared correlation (TSC). TSC = Trace[(SS > ) 2 ] = M i=1 M j=1 (s > i s j ) 2 M 2 =N (21) For a simple derivation of the bound (21), see [=-=24, 2-=-5]. Note that sequence sets satisfying (20) satisfy the bound (21) with equality. We observe that the set of sequences satisfying either equation (19) for M N or equation (20) for M N has the proper... |

10 | Special issue on software radio - Chen, Prasad, et al. - 1999 |

10 | Optimization of CDMA signature sequences in multipath channels - Concha, Ulukus - 2001 |

10 | New approach to multiple antenna systems - Dimitrie, Rose - 2001 |

10 |
Codeword Quantization for Interference Avoidance
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(Show Context)
Citation Context ...vergence seen in practice without escape methods remains elusive. The issue of codeword representation and fidelity in a real software/universal radios has been considered only empirically at present =-=[51, 52]. Specifically, inst-=-ead of uniform-amplitude codeword "chips", interference avoidance presumes real-valued "chips" or more generally, real-valued coefficients for a set of orthonormal signal basis fun... |

9 | Sum capacity and interference avoidance: convergence via class warfare
- Rose
- 2000
(Show Context)
Citation Context ...at the function described in equation (23) is Schur concave while that of equation (24) is Schur convex [27]. Since any constraints on the eigenvalues must be identical, and in fact form a convex set =-=[26, 28, 29]-=-, we can conclude that any set fl i g which maximizes equation (23) must also minimize equation (24) and vice versa. 3 Therefore, minimization of TSC is completely equivalent to maximization of C s . ... |

8 | Multiaccess Dispersive Channels: Maximizing Sum Capacity and Interference Avoidance - Popescu, Rose |

7 | Software defined radio architectures for interference cancellation in DS-CDMA systems - Seskar, Mandayam - 1999 |

6 | Optimum signature sequence sets for asynchronous CDMA systems - Ulukus, Yates - 2000 |

5 |
On the Convergence of the MMSE Algorithm for Interference Avoidance
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- 2000
(Show Context)
Citation Context ...sfying SS > = (M=N)I N . Alternatively, both algorithms could theoretically converge to a local minimum for TSC. In [9, 32,33] mild conditions are derived under which the MMSE algorithm converges. In =-=[34]-=- MMSE interference avoidance is shown to always converge stochastically to the optimum signature set. Empirically, Rose, Ulukus and Yates: Interference Avoidance in Wireless Systems 9 the eigen-algori... |

5 |
Total Capacity of Vector Channels
- Viswanath, Anantharam
- 1999
(Show Context)
Citation Context ...id the fixed users where possible. We also note that the implied minimization of ensemble TSC (including the fixed user signatures) is equivalent to maximization of information theoretic sum capacity =-=[28, 29,-=- 36]. Formally, we let the set fa k j1 k Lg be the set of signal vectors associated with waveform-agile users. Let ff i j1 i M Lg be the signal vectors associated with fixed-waveform users. Greedy... |

4 | A Monolithic CMOS - Sheng, Allmon, et al. - 1998 |