## Bandwidth Scaling for Fading Multipath Channels (1999)

Citations: | 85 - 12 self |

### BibTeX

@MISC{Medard99bandwidthscaling,

author = {M. Medard and R. Gallager},

title = {Bandwidth Scaling for Fading Multipath Channels},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

We show that very large bandwidths on fading multipath channels cannot be effectively utilized by spread spectrum systems that (in a particular sense) spread the available power uniformly over both time and frequency. The approach is to express the input process as an expansion in an orthonormal set of functions each localized in time and frequency. The fourth moment of each coefficient in this expansion is then uniformly constrained. We show that such a constraint forces the mutual information to 0 inversely with increasing bandwidth. Simply constraining the second moment of these coefficients does not achieve this effect. The results suggest strongly that conventional direct sequence CDMA systems do not scale well to extremely large bandwidths. To illustrate how the interplay between channel estimation and symbol detection affects capacity, we present results for a specific channel and CDMA signaling scheme.

### Citations

1483 |
Information Theory and Reliable Communication
- Gallager
- 1968
(Show Context)
Citation Context ...ise waveforms are all equivalent in terms of probability of decoding error. For WGN fading multipath channels, there is an old, rather surprising, result due to Kennedy (see, for example, [14], [26], =-=[8]-=-, [32], [1]) saying that the infinite bandwidth capacity of the channel is the same as the infinite bandwidth capacity of the Manuscript received September 23, 1999; revised September 15, 2001. The ma... |

1119 |
Microwave Mobile Communications
- Jakes
- 1980
(Show Context)
Citation Context ...ll bandwidth constraint . 1 � is also often defined as the time ( at which �‚@HY (A� drops to some fixed fraction of ‚�@HY (A� . The fraction is assigned various values between HXQU and HXW [4], [6], =-=[12]-=-. This does not suffice here since we need a measure involving how �‚@HY (A� goes to zero with (.sMÉDARD AND GALLAGER: BANDWIDTH SCALING FOR FADING MULTIPATH CHANNELS 847 Let be the impulse response o... |

714 | Optimal Filtering - Anderson, Moore - 1979 |

527 |
Principles of Spread Spectrum Communications
- Viterbi
- 1995
(Show Context)
Citation Context ...commercial wireless telephony, and CDMA is particularly attractive for future integrated systems. CDMA is also being deployed in ultrawide-band systems as overlays over licensed spectrum. As shown in =-=[35]-=-, [11], [27], [15], CDMA has many system strengths for cellular systems, taking advantage of the idle periods in voice and data, and being robust to out-of-cell interference and noise other than WGN. ... |

375 | Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading
- Marzetta, Hochwald
- 2002
(Show Context)
Citation Context ...el multipath, and the effect of specular components is analyzed. These results also depend critically on our assumption of finite frequency coherence, which rules out flat-fading models as treated in =-=[16]-=-. Finally, for a perspective and survey of known results for a wide variety of models of fading channels, see [5]. The main reason for interest in this result lies in its application to DS-CDMA system... |

291 | Fading channels: Information-theoretic and communications aspects - Biglieri, Proakis, et al. - 1998 |

193 |
On the capacity of a cellular CDMA system
- Gilhousen, Jacobs, et al.
- 1991
(Show Context)
Citation Context ...cial wireless telephony, and CDMA is particularly attractive for future integrated systems. CDMA is also being deployed in ultrawide-band systems as overlays over licensed spectrum. As shown in [35], =-=[11]-=-, [27], [15], CDMA has many system strengths for cellular systems, taking advantage of the idle periods in voice and data, and being robust to out-of-cell interference and noise other than WGN. Also, ... |

192 | The Effect upon Channel Capacity in Wireless Communications of Perfect and Imperfect - Medard - 2000 |

146 |
On channel capacity per unit cost
- Verdu
- 1990
(Show Context)
Citation Context ..., respectively. Later related results appear in [33], [29], [30], [31]. In [30], the results in this paper are considered using an output fourth-order constraint and a capacity per unit cost approach =-=[34]-=-. In [31], a peak signal constraint going to is considered. In [33], the type of results in this paper are shown to depend strongly on having no specular component in the channel multipath, and the ef... |

134 | Theory of spreadspectrum communications - a tutorial - Pickholtz, Schilling, et al. - 1982 |

114 | Capacity and Mutual Information of Wideband Multipath Fading Channels
- Telatar, Tse
- 2000
(Show Context)
Citation Context ... memoryless fading model were presented in [18], [19], using WGN signals and direct-sequence (DS) code-division multiple-access (CDMA) (DS-CDMA) signals, respectively. Later related results appear in =-=[33]-=-, [29], [30], [31]. In [30], the results in this paper are considered using an output fourth-order constraint and a capacity per unit cost approach [34]. In [31], a peak signal constraint going to is ... |

94 |
Fading Dispersive Communication Channels
- Kennedy
- 1969
(Show Context)
Citation Context ...al pseudo-noise waveforms are all equivalent in terms of probability of decoding error. For WGN fading multipath channels, there is an old, rather surprising, result due to Kennedy (see, for example, =-=[14]-=-, [26], [8], [32], [1]) saying that the infinite bandwidth capacity of the channel is the same as the infinite bandwidth capacity of the Manuscript received September 23, 1999; revised September 15, 2... |

93 |
Shitz), “Fading channels: Information-theoretic and communications aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ...ption of finite frequency coherence, which rules out flat-fading models as treated in [16]. Finally, for a perspective and survey of known results for a wide variety of models of fading channels, see =-=[5]-=-. The main reason for interest in this result lies in its application to DS-CDMA systems. The CDMA standard (IS-95) is one of the major systems currently deployed for commercial wireless telephony, an... |

89 |
Channels with block interference
- McEliece, Stark
- 1984
(Show Context)
Citation Context ... identically distributed with that of all other slices. The assumptions of flat fading within each frequency slice and independence between slices is the frequency analog of block fading in time (see =-=[17]-=-,s850 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 4, APRIL 2002 [16]), where the channel is assumed constant within each time block and independent between time blocks. Under the assumption ... |

71 | Theory of spread-spectrum communications—a tutorial
- Pickholtz, Schilling, et al.
- 1982
(Show Context)
Citation Context ...ystem strengths for cellular systems, taking advantage of the idle periods in voice and data, and being robust to out-of-cell interference and noise other than WGN. Also, as shown in [22], [7], [28], =-=[24]-=-, CDMA has many system strengths for military systems, including anti-jam and low-probability-of-intercept capabilities. CDMA signals, however, closely resemble WGN over the available spectrum. Thus, ... |

43 | Energy limited channels: Coding, multiaccess, and spread spectrum - Gallager - 1987 |

21 | Capacity and Reliability Function for Small Peak Signal Constraints
- Hajek, Subramaniam
- 2002
(Show Context)
Citation Context ... model were presented in [18], [19], using WGN signals and direct-sequence (DS) code-division multiple-access (CDMA) (DS-CDMA) signals, respectively. Later related results appear in [33], [29], [30], =-=[31]-=-. In [30], the results in this paper are considered using an output fourth-order constraint and a capacity per unit cost approach [34]. In [31], a peak signal constraint going to is considered. In [33... |

17 |
Correlation bandwidth and delay spread multipath propagation statistics for 910-MHz urban mobile radio channels
- Cox, Leck
- 1975
(Show Context)
Citation Context ...overall bandwidth constraint . 1 � is also often defined as the time ( at which �‚@HY (A� drops to some fixed fraction of ‚�@HY (A� . The fraction is assigned various values between HXQU and HXW [4], =-=[6]-=-, [12]. This does not suffice here since we need a measure involving how �‚@HY (A� goes to zero with (.sMÉDARD AND GALLAGER: BANDWIDTH SCALING FOR FADING MULTIPATH CHANNELS 847 Let be the impulse resp... |

16 |
Shitz), “The capacity of discrete-time Rayleigh fading channels
- Faycal, Trott, et al.
- 1997
(Show Context)
Citation Context ...ms are all equivalent in terms of probability of decoding error. For WGN fading multipath channels, there is an old, rather surprising, result due to Kennedy (see, for example, [14], [26], [8], [32], =-=[1]-=-) saying that the infinite bandwidth capacity of the channel is the same as the infinite bandwidth capacity of the Manuscript received September 23, 1999; revised September 15, 2001. The material in t... |

13 |
Bandwidth scaling for fading channels
- Gallager, Medard
(Show Context)
Citation Context ...er become increasMÉDARD AND GALLAGER: BANDWIDTH SCALING FOR FADING MULTIPATH CHANNELS 841 ingly nonuniform or to become increasingly “peaky” in distribution. The results here were first presented in =-=[10]-=-. Some related results for a memoryless fading model were presented in [18], [19], using WGN signals and direct-sequence (DS) code-division multiple-access (CDMA) (DS-CDMA) signals, respectively. Late... |

12 |
Spreading in block-fading channels
- Médard, Tse
(Show Context)
Citation Context ...the spectrum. In order to evaluate the effectiveness of this technique, one must first determine the range of bandwidths for which the type of signaling addressed in this paper is advantageous. While =-=[21]-=- begins to address this issue for channels which are block-fading in time and frequency, finding tight bounds for advantageous spreading regimes for more general channels is an open problem. The model... |

10 |
Spread Spectrum Systems, 2 nd Ed
- Dixon
- 1984
(Show Context)
Citation Context ... has many system strengths for cellular systems, taking advantage of the idle periods in voice and data, and being robust to out-of-cell interference and noise other than WGN. Also, as shown in [22], =-=[7]-=-, [28], [24], CDMA has many system strengths for military systems, including anti-jam and low-probability-of-intercept capabilities. CDMA signals, however, closely resemble WGN over the available spec... |

8 |
The effect of frequency selective fading on the binary error probabilities of incoherent and differentially coherent matched filter receivers
- Bello, Nelin
- 1963
(Show Context)
Citation Context ... the overall bandwidth constraint . 1 � is also often defined as the time ( at which �‚@HY (A� drops to some fixed fraction of ‚�@HY (A� . The fraction is assigned various values between HXQU and HXW =-=[4]-=-, [6], [12]. This does not suffice here since we need a measure involving how �‚@HY (A� goes to zero with (.sMÉDARD AND GALLAGER: BANDWIDTH SCALING FOR FADING MULTIPATH CHANNELS 847 Let be the impulse... |

8 |
Wireless Personal Communications
- SCHNEIDERMAN
- 1994
(Show Context)
Citation Context ...ireless telephony, and CDMA is particularly attractive for future integrated systems. CDMA is also being deployed in ultrawide-band systems as overlays over licensed spectrum. As shown in [35], [11], =-=[27]-=-, [15], CDMA has many system strengths for cellular systems, taking advantage of the idle periods in voice and data, and being robust to out-of-cell interference and noise other than WGN. Also, as sho... |

8 |
Coding and multiaccess for the energy limited Rayleigh fading channel
- Telatar
- 1988
(Show Context)
Citation Context ...aveforms are all equivalent in terms of probability of decoding error. For WGN fading multipath channels, there is an old, rather surprising, result due to Kennedy (see, for example, [14], [26], [8], =-=[32]-=-, [1]) saying that the infinite bandwidth capacity of the channel is the same as the infinite bandwidth capacity of the Manuscript received September 23, 1999; revised September 15, 2001. The material... |

7 |
limited channels: Coding, multiaccess, and spread spectrum
- “Energy
- 1998
(Show Context)
Citation Context ...the impulsive signaling schemes of [14] and [32]. While the infinite bandwidth capacity for an additive WGN channel is approached reasonably rapidly as bandwidth increases, the results in [32], using =-=[9]-=- indicate that the infinite bandwidth capacity for fading channels is approached impractically slowly. Thus, there is a large operating regime where the constrained fourth moment signals of this paper... |

7 |
The capacity of time varying multiple user channels in wireless communications
- Medard
- 1995
(Show Context)
Citation Context ...TH CHANNELS 841 ingly nonuniform or to become increasingly “peaky” in distribution. The results here were first presented in [10]. Some related results for a memoryless fading model were presented in =-=[18]-=-, [19], using WGN signals and direct-sequence (DS) code-division multiple-access (CDMA) (DS-CDMA) signals, respectively. Later related results appear in [33], [29], [30], [31]. In [30], the results in... |

7 | Shitz), "The capacity of discrete-time Rayleigh fading channels - Faycal, Trott, et al. - 1997 |

5 |
on mutual information for DS-CDMA spreading over independent fading channels,” preprint
- Medard, “Bound
(Show Context)
Citation Context ...NNELS 841 ingly nonuniform or to become increasingly “peaky” in distribution. The results here were first presented in [10]. Some related results for a memoryless fading model were presented in [18], =-=[19]-=-, using WGN signals and direct-sequence (DS) code-division multiple-access (CDMA) (DS-CDMA) signals, respectively. Later related results appear in [33], [29], [30], [31]. In [30], the results in this ... |

4 |
Coding theorem for stationary, asymptotically memoryless, continuous-time channels
- Kadota, Wyner
- 1972
(Show Context)
Citation Context ...straint is placed on the input variables for this channel, then the maximum mutual information is significantly degraded for large , in fact approaching at least as as . Coding theorems and converses =-=[13]-=-, [23] apply to these mutual informations in much the same way as with more conventional channels, so, in what follows, we deal exclusively with mutual informations. With a bandwidth , there are compl... |

4 | Capacity and reliability function per fourth moment cost for WSSUS channel
- Subramanian, Hajek
- 1999
(Show Context)
Citation Context ...yless fading model were presented in [18], [19], using WGN signals and direct-sequence (DS) code-division multiple-access (CDMA) (DS-CDMA) signals, respectively. Later related results appear in [33], =-=[29]-=-, [30], [31]. In [30], the results in this paper are considered using an output fourth-order constraint and a capacity per unit cost approach [34]. In [31], a peak signal constraint going to is consid... |

3 |
effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” submitted to
- “The
(Show Context)
Citation Context ...bability . The frequency slices can now be analyzed independently, so we drop the subscript and analyze an arbitrary single frequency slice. For each such slice, we adopt a Gauss–Markov channel model =-=[20]-=-. Here each time sample evolves as (74) where is a random variable representing the innovations process. The random variables are i.i.d. Gaussian with zero mean and variance . From (74), we see that S... |

3 |
der Meulen, “Information transmission over channels with additive-multiplicative noise
- Pinsker, Prelov, et al.
- 1998
(Show Context)
Citation Context ...er structure and depends only on the fourth moment constraint above. Our results depend on having no side information, so that the channel state estimation depends only on input and output. Reference =-=[25]-=- analyzes a situation with a different assumption about estimate and estimation error. II. A MODEL FOR FADING MULTIPATH CHANNELS First we will look at a system in which the input is band-limited to so... |

3 |
Communication Over Fading Dispersive Channels.” M.I.T. Research Laboratory of Electronics
- Richters
- 1967
(Show Context)
Citation Context ...udo-noise waveforms are all equivalent in terms of probability of decoding error. For WGN fading multipath channels, there is an old, rather surprising, result due to Kennedy (see, for example, [14], =-=[26]-=-, [8], [32], [1]) saying that the infinite bandwidth capacity of the channel is the same as the infinite bandwidth capacity of the Manuscript received September 23, 1999; revised September 15, 2001. T... |

2 |
Correlation functions in a tapped delay line model of the orbital dipole channel
- Bello
- 1963
(Show Context)
Citation Context ... paths whose delay is approximately . We expect these path responses to be uncorrelated with those paths at some other delay . With this assumption, in (3) simplifies to (44) One of the standard ways =-=[3]-=- of representing fading multipath channels is by the two-frequency correlation function , defined as the correlation between the response at time to a sinusoid of unit power at the carrier frequency a... |

2 | Spread Spectrum Systems, Second Edition - Dixon - 1984 |

2 | Capacity and reliability function for small peak signal constraints - Subramanian, Hajek |

1 |
CDMA vs. GSM,” presented at
- Madsen
(Show Context)
Citation Context ...s telephony, and CDMA is particularly attractive for future integrated systems. CDMA is also being deployed in ultrawide-band systems as overlays over licensed spectrum. As shown in [35], [11], [27], =-=[15]-=-, CDMA has many system strengths for cellular systems, taking advantage of the idle periods in voice and data, and being robust to out-of-cell interference and noise other than WGN. Also, as shown in ... |

1 |
Spread Spectrum Design
- Nicholson
- 1988
(Show Context)
Citation Context ..., CDMA has many system strengths for cellular systems, taking advantage of the idle periods in voice and data, and being robust to out-of-cell interference and noise other than WGN. Also, as shown in =-=[22]-=-, [7], [28], [24], CDMA has many system strengths for military systems, including anti-jam and low-probability-of-intercept capabilities. CDMA signals, however, closely resemble WGN over the available... |

1 |
Channels with asymptoticaly decreasing memory and anticipation
- Pfaffelhuber
- 1971
(Show Context)
Citation Context ...t is placed on the input variables for this channel, then the maximum mutual information is significantly degraded for large , in fact approaching at least as as . Coding theorems and converses [13], =-=[23]-=- apply to these mutual informations in much the same way as with more conventional channels, so, in what follows, we deal exclusively with mutual informations. With a bandwidth , there are complex inp... |

1 |
fading channels: Signal burstiness and capacity
- “Broad-band
- 2002
(Show Context)
Citation Context ...fading model were presented in [18], [19], using WGN signals and direct-sequence (DS) code-division multiple-access (CDMA) (DS-CDMA) signals, respectively. Later related results appear in [33], [29], =-=[30]-=-, [31]. In [30], the results in this paper are considered using an output fourth-order constraint and a capacity per unit cost approach [34]. In [31], a peak signal constraint going to is considered. ... |

1 | The E#ect of Frequency Selective Fading on the Binary Error Probabilities of Incoherent and Di#erentially Coherent Matched Filter Receivers - Bello, Nelin - 1963 |

1 | CDMA vs. GSM," presented to the Telecommunications Policy Research Conference - Madsen |

1 | Channels with Asymptoticaly Decreasing Memory and Anticipation - Pfaelhuber - 1971 |

1 | der Meulen, "Information Transmission over Channels with Additive-multiplicative Noise - Pinsker, Prelov, et al. - 1998 |

1 | Hajek,"Broadband Fading Channels: Signal Burstiness and Capacity," submitted to - Subramanian, B |