## Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity (1999)

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Venue: | IEEE Trans. Inform. Theory |

Citations: | 264 - 11 self |

### BibTeX

@ARTICLE{Tse99linearmultiuser,

author = {David N. C. Tse and Stephen V. Hanly},

title = {Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity},

journal = {IEEE Trans. Inform. Theory},

year = {1999},

volume = {45},

pages = {641--657}

}

### Years of Citing Articles

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### Abstract

Multiuser receivers improve the performance of spread-spectrum and antenna-array systems by exploiting the structure of the multiaccess interference when demodulating the signal of a user. Much of the previous work on the performance analysis of multiuser receivers has focused on their ability to reject worst case interference. Their performance in a power-controlled network and the resulting user capacity are less well-understood. In this paper, we show that in a large system with each user using random spreading sequences, the limiting interference effects under several linear multiuser receivers can be decoupled, such that each interferer can be ascribed a level of effective interference that it provides to the user to be demodulated. Applying these results to the uplink of a single power-controlled cell, we derive an effective bandwidth characterization of the user capacity: the signal-to-interference 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 SIR requirement, and simple expressions are derived for three linear receivers: the conventional matched filter, the decorrelator, and the MMSE receiver. The effective bandwidths under the three receivers serve as a basis for performance comparison.

### Citations

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(Show Context)
Citation Context ...nt thrust of work has been on developing multiuser receiver structures which mitigate the interference between users in spread-spectrum systems. These receivers include the optimum multiuser detector =-=[24]-=-, the linear decorrelator [11], [12], and the linear minimum mean-square error (MMSE) receiver [29], [13], [16], [17]. Unlike the conventional matched-filter receiver, these techniques take into accou... |

315 | MMSE Interference Suppression for Direct-Sequence Spread-Spectrum CDMA
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(Show Context)
Citation Context ...tween users in spread-spectrum systems. These receivers include the optimum multiuser detector [24], the linear decorrelator [11], [12], and the linear minimum mean-square error (MMSE) receiver [29], =-=[13]-=-, [16], [17]. Unlike the conventional matched-filter receiver, these techniques take into account the structure Manuscript received January 8, 1998; revised December 11, 1998. This work was supported ... |

309 | Linear multiuser detectors for synchronous code-division multiple-access channels
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- 1989
(Show Context)
Citation Context ...developing multiuser receiver structures which mitigate the interference between users in spread-spectrum systems. These receivers include the optimum multiuser detector [24], the linear decorrelator =-=[11]-=-, [12], and the linear minimum mean-square error (MMSE) receiver [29], [13], [16], [17]. Unlike the conventional matched-filter receiver, these techniques take into account the structure Manuscript re... |

257 | Blind adaptive multiuser detection
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- 1995
(Show Context)
Citation Context ...hange in the spreading sequences occurs at a much slower timescale than the time required to acquire the sequences. (There are known adaptive algorithms for which acquisition can be done blindly; see =-=[6].)-=- However, the performance of the MMSE receiver depends on the initial choice of the sequences and hence is random. The model for random sequences is as follows: let The random variables ’s are indep... |

200 | Near-Far Resistance of Multiuser Detectors in Asynchronous Channels - Lupas, Verdu - 1990 |

191 |
The impact of antenna diversity on the capacity of wireless communication systems
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Citation Context ... the different receivers. The only difference here is that the degrees of freedom are obtained by spatial rather than frequency diversity. These results should be compared with that of Winters et al. =-=[28]-=-, which showed that for a flat Rayleigh fading channel, a combiner which attempts to null out all the interferers will cost one degree of freedom per interferer. This combiner is of course the subopti... |

178 |
Distributions of eigenvalues for some sets of random matrices
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- 1967
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Citation Context ... the eigenvalues depends on the realization of the random entries of and .) The following theorem due to Silverstein and Bai [18], which is a strengthening of an earlier result by Marcenko and Pastur =-=[15]-=-, gives the asymptotic behavior of as and grows. The solution is in terms of the Stieltjes transform, which for any distribution is defined as for Theorem 4.1: As such that , then almost surely conver... |

159 |
A Family of Suboptimum Detectors for Coherent Multiuser Communications
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Citation Context ...nce between users in spread-spectrum systems. These receivers include the optimum multiuser detector [24], the linear decorrelator [11], [12], and the linear minimum mean-square error (MMSE) receiver =-=[29]-=-, [13], [16], [17]. Unlike the conventional matched-filter receiver, these techniques take into account the structure Manuscript received January 8, 1998; revised December 11, 1998. This work was supp... |

155 | On the empirical distribution of eigenvalues of a class of large dimensional random matrices
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Citation Context ...s; since the eigenvalues are random, so is . (The empirical distribution of the eigenvalues depends on the realization of the random entries of and .) The following theorem due to Silverstein and Bai =-=[18]-=-, which is a strengthening of an earlier result by Marcenko and Pastur [15], gives the asymptotic behavior of as and grows. The solution is in terms of the Stieltjes transform, which for any distribut... |

82 |
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Citation Context ...users in spread-spectrum systems. These receivers include the optimum multiuser detector [24], the linear decorrelator [11], [12], and the linear minimum mean-square error (MMSE) receiver [29], [13], =-=[16]-=-, [17]. Unlike the conventional matched-filter receiver, these techniques take into account the structure Manuscript received January 8, 1998; revised December 11, 1998. This work was supported by the... |

78 |
Optimum decision feedback multiuser equalization with successive decoding achieves the total capacity of the Gaussian multiple-accesschannel
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- 1997
(Show Context)
Citation Context ...efore, a one-to-one monotonic relationship between the information-theoretic rate and the achieved SIR. In particular, meeting a target SIR is equivalent to meeting a target rate. • It has been show=-=n [22]-=- that any vertex of the Shannon capacity region of the CDMA channel (1) can be achieved by a combination of successive cancellation and MMSE demodulation. Each vertex corresponds to a particular choic... |

67 |
Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
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- 1993
(Show Context)
Citation Context ... is the orthogonal projection of onto (Proposition 7.1), it follows that . Proposition 7.1 implies that the SIR of user 1 tends to zero in this case. Now consider the case . In this case, Bai and Yin =-=[1]-=- show that the smallest eigenvalue of the random matrix converges almost surely to a strictly positive number; hence is almost surely of full rank when is large. Thus as . But by Proposition 7.1, is t... |

61 | Optimal sequences, power control and capacity of synchronous CDMA systems with linear multiuser receivers
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- 1998
(Show Context)
Citation Context ...roof, it provides little intuition as why Theorem 3.1 is true. In particular, a better understanding of the decoupling phenomenon between interferers is desired. Based on some new results obtained in =-=[27]-=-, we provide a heuristic but more intuitive derivation of (4) in Appendix A, bypassing the mysterious Stieltjes transform characterization of the limiting eigenvalue distribution of random matrices in... |

60 | Optimum multiuser asymptotic efficiency - Verdu - 1986 |

45 | Capacity and power control in spread spectrum macrodiversity radio networlis - Hanly - 1996 |

38 |
User-separating demodulation for code-division multiple-access systems
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- 1994
(Show Context)
Citation Context ...in spread-spectrum systems. These receivers include the optimum multiuser detector [24], the linear decorrelator [11], [12], and the linear minimum mean-square error (MMSE) receiver [29], [13], [16], =-=[17]-=-. Unlike the conventional matched-filter receiver, these techniques take into account the structure Manuscript received January 8, 1998; revised December 11, 1998. This work was supported by the Air F... |

38 | Adaptive power control and MMSE interference suppression
- Ulukus, Yates
- 1998
(Show Context)
Citation Context ...tem saturates and the required power level goes to infinity. A similar result is given in [5]. Now let us turn to the MMSE receiver. To satisfy given target SIR requirements which are feasible, [10], =-=[21]-=-, [2] showed that there is an optimal solution for which the received power of every user is minimized; moreover, they gave an iterative algorithm to compute it. However, here we can give an explicit ... |

37 |
Information capacity of radio networks
- Hanly
- 1993
(Show Context)
Citation Context ...user-capacity constraint on feasible values of is the linear constraint Furthermore, if class users have a maximum power constraint that , for each , then the tighter user-capacity constraint emerges =-=[4]-=-. It seems very reasonable to call the bandwidth of class users, in degrees of freedom per class user. Let us denote this bandwidth by degrees of freedom per class user. We now show that the MMSE filt... |

24 |
Power Control for a Spread Spectrum System with Multiuser Receivers
- Kumar, Holtzman
- 1995
(Show Context)
Citation Context ...he system saturates and the required power level goes to infinity. A similar result is given in [5]. Now let us turn to the MMSE receiver. To satisfy given target SIR requirements which are feasible, =-=[10]-=-, [21], [2] showed that there is an optimal solution for which the received power of every user is minimized; moreover, they gave an iterative algorithm to compute it. However, here we can give an exp... |

22 | resistance of multiuser detectors in asynchronous channels - “Near-far - 1990 |

21 | Randomly selected spreading sequences for coded CDMA
- Grant, Alexander
- 1996
(Show Context)
Citation Context ...er on the SIR for user 1 cannot be seen directly from this formula. In practice, it is often reasonable to assume that the spreading sequences are randomly and independently chosen. (See, e.g., [14], =-=[3]-=-.) For example, they may be pseudorandom sequences, or the users choose their sequences from a large set of available sequences as they are admitted into the network, or the transmitted sequences may ... |

20 | Effective bandwidths and effective interference for linear multiuser receivers in asynchronous systems
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(Show Context)
Citation Context ... of the receiving antenna elements. We will also restrict our analysis to synchronous systems in this paper. Extensions of these results to symbol-asynchronous spread-spectrum systems can be found in =-=[9]-=-. Related results on the performance of multiuser receivers under random spreading sequences were obtained independently in [26], presented simultaneously as a conference version [19] of this work. Th... |

18 |
Performance variability of linear multiuser detection for DS-CDMA
- Honig, Veerakachen
- 1996
(Show Context)
Citation Context ...quel [20] to this paper is devoted to the analysis of such fluctuations, via Central-Limit theorems. It turns out that even the computation of the variance of the fluctuations is nontrivial. See also =-=[7]-=- and [8] for a related study. Two performance measures commonly used in the literature for multiuser receivers are their efficiency and their asymptotic efficiency [25]. In the context of linear recei... |

15 |
Multiuser demodulation: Effective interference, effective bandwidth and capacity
- Tse, Hanly
(Show Context)
Citation Context ...s can be found in [9]. Related results on the performance of multiuser receivers under random spreading sequences were obtained independently in [26], presented simultaneously as a conference version =-=[19]-=- of this work. They considered exclusively the single class case where every user has the same received power and the same rate requirement, and derived Shannon theoretic performance. In the present p... |

13 |
multi-user asymptotic efficiency
- “Optimum
- 1990
(Show Context)
Citation Context ...tuations is nontrivial. See also [7] and [8] for a related study. Two performance measures commonly used in the literature for multiuser receivers are their efficiency and their asymptotic efficiency =-=[25]-=-. In the context of linear receivers, the efficiency for user 1 is defined to be the ratio of the achieved SIR to the SIR when there is no interferer and only background noise. For the MMSE receiver w... |

13 |
Shitz), “Multiuser detection with random spreading and error-correction codes: Fundamental limits
- Verdú, Shamai
- 1997
(Show Context)
Citation Context ...e results to symbol-asynchronous spread-spectrum systems can be found in [9]. Related results on the performance of multiuser receivers under random spreading sequences were obtained independently in =-=[26]-=-, presented simultaneously as a conference version [19] of this work. They considered exclusively the single class case where every user has the same received power and the same rate requirement, and ... |

6 | Shitz), "Multiuser detection with random spreading and errorcorrection codes: fundamental limits", presented at Allerton Conference - Verd'u, Shamai - 1997 |

4 | Joint power control and beamforming for capacity improvement in wireless networks with antenna arrays
- Rashid-Farrokhi, Tassiulas, et al.
- 1996
(Show Context)
Citation Context ...turates and the required power level goes to infinity. A similar result is given in [5]. Now let us turn to the MMSE receiver. To satisfy given target SIR requirements which are feasible, [10], [21], =-=[2]-=- showed that there is an optimal solution for which the received power of every user is minimized; moreover, they gave an iterative algorithm to compute it. However, here we can give an explicit solut... |

3 |
and power control in spread spectrum macro diversity radio networks
- “Capacity
- 1996
(Show Context)
Citation Context ...acity of the conventional receiver when is then users/degree of freedom. (14) Put it another way, as , the system saturates and the required power level goes to infinity. A similar result is given in =-=[5]-=-. Now let us turn to the MMSE receiver. To satisfy given target SIR requirements which are feasible, [10], [21], [2] showed that there is an optimal solution for which the received power of every user... |

3 |
Outage probability of multi-code DS-CDMA with linear interference suppression
- Kim, Honig
- 1998
(Show Context)
Citation Context ...] to this paper is devoted to the analysis of such fluctuations, via Central-Limit theorems. It turns out that even the computation of the variance of the fluctuations is nontrivial. See also [7] and =-=[8]-=- for a related study. Two performance measures commonly used in the literature for multiuser receivers are their efficiency and their asymptotic efficiency [25]. In the context of linear receivers, th... |

1 | detection of direct-sequence CDMA signals: Performance analysis for random signature sequences - “MMSE |

1 |
Fluctuations of performance of multiuser receivers under random signature sequences,” submitted for publication
- Tse, Zeitouni
- 1998
(Show Context)
Citation Context ... is a spread of about 1 dB around the asymptotic limit. Theorem 3.1 gives only the asymptotic limit but does not describe the fluctuation of the SIR around this limit for finitesized system. A sequel =-=[20]-=- to this paper is devoted to the analysis of such fluctuations, via Central-Limit theorems. It turns out that even the computation of the variance of the fluctuations is nontrivial. See also [7] and [... |

1 |
Two philosophies
- Vembu, Viterbi
- 1996
(Show Context)
Citation Context ...e degrees of freedom. Despite significant work done in the area, there is still much debate about the user capacity 1 of the various approaches to deal with multiuser interference. (See, for example, =-=[23]-=-.) One reason is that the performance of multiuser receivers in conjunction with networking-level techniques of power control and resource allocation are less well understood than for more traditional... |