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Worse-Than-Rayleigh Fading: Experimental Results and Theoretical Models David W University of South Carolina Scholar Commons Faculty Publications Electrical Engineering, Department of 4-2011 Worse-than-Rayleigh Fading: Experimental Results and Theoretical Models David W. Matolak University of South Carolina - Columbia, [email protected] Jeff rF olik Follow this and additional works at: https://scholarcommons.sc.edu/elct_facpub Part of the Digital Circuits Commons, Digital Communications and Networking Commons, and the Systems and Communications Commons Publication Info Postprint version. Published in IEEE Communications Magazine, Volume 49, Issue 4, 2011, pages 140-146. © IEEE Communications Magazine, 2011, IEEE Matolak, D., Frolik, J. (2011). Worse-than-Rayleigh Fading: Experimental Results and Theoretical Models. IEEE Communications Magazine, 49(4), 140-146. http://dx.doi.org/10.1109/MCOM.2011.5741158 This Article is brought to you by the Electrical Engineering, Department of at Scholar Commons. It has been accepted for inclusion in Faculty Publications by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. MATOLAK LAYOUT 3/22/11 11:12 AM Page 140 ACCEPTED FROM OPEN CALL Worse-than-Rayleigh Fading: Experimental Results and Theoretical Models David W. Matolak, Ohio University Jeff Frolik, University of Vermont ABSTRACT fading, in most settings, is a direct result of the constructive and destructive addition of multiple This article is motivated by the recent recog- delayed replicas of the transmitted signal as seen nition that channel fading for new wireless appli- at the communications receiver. These multiple cations is not always well described by traditional replicas travel different path lengths and have models used for mobile communication systems. different amplitudes and phases, resulting in a In particular, fading data collected for vehicle- phenomenon known as multipath fading. Model- to-vehicle and wireless sensor network applica- ing such small-scale fading is important in physi- tions has motivated new models for conditions in cal layer (PHY) design, as it helps engineers which channel fading statistics can be worse than design fading countermeasures, such as diversity Rayleigh. We review the use of statistical chan- transmission/reception, forward error correction nel models, describe our example applications, coding and interleaving, and equalization. In this and provide both measured and modeling results article we focus attention on small-scale fading, for these severe fading conditions. with a brief mention of some “medium-scale” or “meso-scale” effects. INTRODUCTION Since the PHY forms the foundation of the communications protocol stack, the transmission To put these severe fading conditions in context, performance of this layer — often measured in we first briefly discuss the importance of channel terms of bit error ratio (BER), or packet error modeling in wireless communication systems. As ratio (PER) — affects all higher layers of the a frame of reference for our modeling results, stack. Some current research (e.g., [2]) has also we review the assumptions and statistics for the begun to “extrapolate” the PHY channel effects classical Rayleigh fading model. This statistical on transmission performance to higher layers for model has long been used as a worst case condi- a more integrated approach to system modeling; tion for mobile communication systems, but as this approach is related to the current topic of we show, it is not always conservative enough for cross-layer design. a number of important applications. Modern wireless communication systems are highly complex. Even at the physical layer, many IMPORTANCE OF CHANNEL MODELING new systems, such as wireless local area net- The importance of accurately modeling the works (WLANs), provide a range of transmis- effects of wireless channels on communication sion and reception options. These options are signals is well established [1]. This includes mod- almost always adaptively employed, and enable eling the effects of propagation path loss, or the system to operate in a range of channel con- attenuation, for the determination of link budget ditions, with different numbers of system users, parameters such as required transmitter power, different data rates, and different transmission achievable link distance, and receiver sensitivity. qualities (so-called quality of service, QoS). Yet In addition to estimating path loss vs. distance, even with such highly reconfigurable systems, the the variation of this propagation path loss over impairments caused by the channel may be large areas, typically tens to hundreds of wave- severe enough to degrade performance signifi- lengths, is also useful to model. This variation is cantly if the channel characteristics are not taken often termed “large-scale” fading, and in built- into account in advance. Such performance up areas is also known as shadowing or obstruc- degradations could include a BER/PER “floor,” tion. wherein the error probability reaches a lower A separate and largely independent channel limit regardless of received power level, and a effect is the phenomenon of “small-scale” fad- large latency (delay). For some protocols this ing. This type of fading occurs on spatial scales large latency can translate to a link outage on the order of one-half wavelength. Small-scale and/or multiple retransmissions. 140 0163-6804/10/$25.00 © 2010 IEEE IEEE Communications Magazine • April 2011 MATOLAK LAYOUT 3/22/11 11:12 AM Page 141 Statistical models are most often employed for characterizing small-scale fading effects. 100 These statistical models do not aim to accurately Two-ray Rayleigh predict fading at any given point in time and Weibull (β = 1.6) space, but rather attempt to faithfully reproduce the variation of channel effects. Deterministic models (e.g., ray tracing) can also be used, yet to 10-1 be accurate, deterministic modeling tends to Worse than ) Rayleigh region require much more computation and a substan- V tial amount of data on the local environment, particularly when channel mobility is high. Thus, 10-2 these models are less “portable” and are often “site specific.” (amplitude < P A FRAME OF REFERENCE: RAYLEIGH FADING A fairly general expression for the received sig- 10-3 nal in a multipath environment is the Two-Wave, Diffuse-Power (TWDP) model [3]. As illustrated Ricean region in Eq. 1, the received signal voltage, Vreceived, is dependent on two specular signal paths (V1 and 10-4 V2) along with L – 2 diffuse (i.e., scattered) -70 -60 -50 -40 -30 -20 -10 0 10 lower-amplitude components. The specular com- V = 10log (r2) (dB) ponents are those of significant magnitude; for 10 example, they may be line of sight (LOS) com- Figure 1. Cumulative distribution functions (cdf) for Rayleigh, Weibull (β = ponents. 1.6), and two-ray fading. The region more benign than Rayleigh is indicated as Ricean. VVjreceived = 1 exp(φl ) L + Vj22exp(φ ) ++ ∑ Vjiiexp(φ ) (1) i=3 tion, the fading becomes more benign since the diffuse component specular components can no longer cancel each other. In the cdf plot of Fig. 1, we see the Ricean region lies below the Rayleigh curve, indicating The case without specular components (i.e., lower probabilities of severe fades. V1 = V2 = 0) is commonly assumed in mobile The Ricean and Rayleigh distributions are systems where an LOS component may not be well discussed in the literature and ubiquitously guaranteed. When L is large there are many used in practice [1]. In this article, however, we reflected components, and the diffuse compo- focus our interest on fading phenomena whose nent of Eq. 1 will be complex with the real and cdf curves lie above the Rayleigh curve; that is, imaginary components well modeled as indepen- the fading is worse than Rayleigh or, synonymous- dent and identically distributed (i.i.d.). For large ly, severe. This is also indicated in Fig. 1 by the enough L, by the central limit theorem these Weibull and two-ray cdfs, which we describe and real and imaginary components are approximat- employ subsequently. ed as zero-mean Gaussian random variables with standard deviation σ. It is well known that the CHANNEL MODELING FOR resulting summation of these components has an EMERGING APPLICATIONS envelope, r = |Vreceived|, with Rayleigh statistics [1]. That is, the probability density function (pdf) Wireless communications is being used in an for the received envelope r is, for r ≥ 0, expanding variety of applications and in new ways. In the traditional mobile setting, connec- r tions to the network often persist for long time fr( ) exp[r22 / (2 )] (2) r = 2 − σ periods, as users more frequently desire an σ “always on” status for their devices. This trans- For mobile systems, the Rayleigh fading lates into wider areas of service, which can mean assumption is a common “default” for worst case a wider variety of environment types, including performance analyses. Integrating the pdf in Eq. within vehicles or pedestrian, in urban, subur- 2 from 0 to r results in the cumulative distribu- ban, and rural settings, both indoor and outdoor. tion function (cdf), commonly plotted on a log- Thus, long-term/wide-area channel models are log scale as in Fig. 1. The cdf is a useful needed for these conditions. Long-term model- representation for fading phenomena, for we can ing implies an abandonment of the typical wide- utilize the curve to ascertain the probability of a sense stationary, uncorrelated scattering particular fade depth. For example, we see from (WSSUS) channel assumptions long used by Fig. 1 that for a Rayleigh channel, the probabili- researchers and system designers since the chan- ty of a 20 dB fade relative to the median received nel statistics will change when observed over a power is 1 percent. Thus a system designer can long enough time period and/or a wide enough assure 99 percent link reliability in this environ- area. Thus, non-stationary (NS) modeling tech- ment if 20 dB of margin is provided. For envi- niques may be required to faithfully represent ronments where there exists a single specular channel fading.
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