Saturday, July 11, 2009

How Wide A Wideband Channel Should Be?

[Frequency Selectivity of A 1.2288MHz, 3GPP2, TSG-C, Working Group 3, C30-20090511-028]

How wide should a channel be before it is called wideband? says it is "responding to or operating at a wide band of frequencies". I guess this is pretty much the one in most people's mind. gives us a more technical definition,"a system is typically described as wideband if the message bandwidth significantly exceeds the channel's coherence bandwidth". Basically it says whether a channel can be called wideband channel or not largely depends on the multiple of coherence bandwidth it has. The question then becomes what is coherence bandwidth and how wide a typical coherence bandwidth can be. For example, should a CDMA2000 channel, which has a bandwidth of 1.22288MHz, be called wideband or not?  Why can a 5.0MHz WCDMA channel usually be called wideband? Let's find out here.

Coherence Bandwidth

Coherence bandwidth is a statistical parameter indicating how fast a channel changes in frequency and the frequency range over which the channel can be considered "flat". Narrower a channel's coherence bandwidth is, more frequency selectivity it has and more frequency diversity gain the communication system can achieve. In general, the channel's "flatness" depends on both the cell size and operating environment. The factors includes, macro-cell or micro-cell, urban or suburban, indoor or outdoor, line-of-sight or no-line-of-sight detection, and detection threshold in a typical receiver design. Fundamentally, the coherence bandwidth of a multi-path channel is an inverse to its delay spread. And the delay spread of a channel can be quantified through the measuring of root mean squared (RMS) delay spread or maximum excess delay spread. Maximum excess delay spread can be taken as an upper bound reference.

As we know, RMS delay spread is known to follow a log-normal distribution, which is similar to that of log-normal shadowing (LNS). In fact, RMS delay spread is correlated to log normal shadowing and its median grows as some power of distance. RMS delay spread has been modeled and simply quantified in the form:

Δ rms = E1/2{ (d - d0)2 } ≈ Δ0 · dε · y

where d is the distance in km, ε is an exponent between 0.5 and 1.0, and y is a log-normal variant. The correlation coefficient value for suburban and urban data was shown to be about -0.75, which indicates that for a strong signal ( positive LNS ), the delay spread is reduced, and for a weak signal condition ( negative LNS ), the delay spread is increased. In [1], Sousa, et. al., reported the 90th percent rms delay spread to be 1.2 μs in suburban Toronto. In [2], Ling, et. al. observed that the 90th percent rms delay spread was 1.7 μs in Lakehurst NAES, New Jesey. In [3],  Baum reported the 77th percent rms delay spread was 1 μs, the 94th percent rms delay spread was 2 μs in Rolling Meadows, Chicago.
Figure 1. The statistic model of delay spread

Now, considering the fundamental chip rate of 1.2288Mcps of CDMA2000 mobile communication standards, a 70%-90% RMS delay spread is between 1-2 chips, which is about a 3dB-coherence bandwidth of 25 – 60 subcarriers with the assumption of 180 subcarriers per 1.2288MHz. Therefore, a CDMA2000 1x channel statistically has 3 ~ 7 coherence bandwidths and it should be called narrowband instead.  For a 5MHz WCDMA channel, 12 ~ 28 coherence bandwidths should be observed.  It can be called wideband. 

Impact of Cyclic Delay Diversity (CCD)

The impact of multiple Tx antennas on channel delay spread also depends on the employed multi-antenna techniques. CCD is one of the most open-loop multi-antenna techniques.  When CCD is employed by the transmitter, the total delay spread will increase. This usually results in more fluctuations in the frequency domain of channel response.

Example: Coherence Bandwidth of OFDM Channels

Figure 2. OFDM Coherence Bandwith

[1] E. Sousa, V. Jovanovic, C. Daigneault, “Delay spread measurements for the digital cellular channel in Toronto”, IEEE Trans. on Vehicular Technology, Nov 1994
[2] J. Ling, D. Chizhik, D. Samardzija, R. Valenzuela, “Wideband and MIMO measurements in wooded and open areas”, Lucent Bell Laboratories,
[3] K. Baum, “Frequency-Domain-Oriented Approaches for MBWA: Overview and Field Experiments”, Motorola Labs, IEEE C802.20-03/19, March 2003
[4] L. Greenstein, V. Erceg, Y. S. Yeh, M. V. Clark, “A New Path-Gain/Delay-Spread Propagation Model for Digital Cellular Channels,” IEEE Transactions on Vehicular Technology, VOL. 46, NO.2, May 1997, pp.477-485.
[5] A. Algans, K. I. Pedersen, P. Mogensen, “Experimental Analysis of the Joint Statistical Properties of Azimuth Spread, Delay Spread, and Shadow Fading,” IEEE Journal on Selected Areas in Communications, Vol. 20, No. 3, April 2002, pp. 523-531.
[6] Spatial Channel Model AHG (Combined ad-hoc from 3GPP & 3GPP2), “Spatial Channel Model Text Description ”, 3GPP, 2003
[7] H. Arslan and T. Yucek, Estimation of Frequency Selectivity for OFDM based New Generation Wireless Communication System, WWC 2004.