Deciwavelength-Scale Fade Mitigation

Jeff Frolik School of Engineering, University of Vermont, Burlington, USA

Abstract—This work presents empirical results illustrating that mitigation of the deepest fades produced by environments expected for machine-to-machine (M2M) systems can be readily accomplished with antenna elements spaced at intervals as small as λλ /10. Results are presented for laboratory measurements collected between 5 and 6 GHz. The implication of this work is that compact antenna diversity schemes, which are less than optimal, can still be highly effective in improving M2M link reliability.

Index Terms—propagation, multipath, measurement.

I. INTRODUCTION Advances in wireless embedded systems have enabled new

low-energy, low-cost devices that can be located throughout the environments we live. Systems are now being designed for machine-to-machine (M2M) communications for the purpose of autonomous energy control, system health monitoring, etc. Given the breadth of foreseen applications, it is clear that the environments in which M2M systems will be deployed will vary greatly. They will also have constraints distinct from other wireless systems. First, they will tend to be attached to or embedded within fixed infrastructure and as a result may not be able to use mobility to counteract fading. Also, to maintain low-cost and to ensure ease of deployment, M2M hardware will need to be compact in size. Jointly, these aspects motivate the work presented herein. Specifically, this work investigates, using empirical data, the spatial diversity needed to mitigate the deep channel fades that may be experienced by M2M systems.

II. TESTING CONDITIONS In considering possible M2M environments, we created

one that was capable of producing worse-than-Rayleigh (also referred to as hyper-Rayleigh) channel conditions. These conditions can occur when the environment creates two strong signal components that either add constructively or destructively over changes in frequency, space, or time [1]. Hyper-Rayleigh channels have been measured in airframes, in vehicles, and have been noted in historical data collected in buildings [2]; all environments comparable to those foreseen for possible M2M systems.

Our experimental setup was a short-range (~1 m) link having a clear line-of-sight (LOS) component and a secondary component coming off of a ~1 m x ~1 m reflecting metal plate (Fig. 1). While most unlicensed sensing hardware currently operates in the 2.4 GHz band, this empirical study considers the band of frequencies from 5.0 to 6.0 GHz that captures the 5.2/5.3 GHz U-NII and 5.7 GHz ISM bands. In comparison to operating in the 2.4 GHz band, operating at these higher

frequencies has benefits beyond simply additional available bandwidth. Specifically, the shorter transmission range at these higher frequencies is suited to the envisioned spatially dense M2M networks and allows for greater reuse of frequencies. Furthermore, the higher operational frequencies allow for more compact, by approximately a factor of two, antenna designs.

Fig. 1. Short-range test setup. Transmit (TX) antenna is movable in the XY plane over a 12 cm x 12 cm square. Receive (RX) is fixed in position. Initial position of the TX antenna is ~20 cm from the reflecting plate. Reflecting plate is positioned in parallel to the Y-axis.

A transmit antenna (a bicone design) was initially placed ~0.2 m (i.e., ~4λ) from the reflecting plate and the fixed receive antenna (also a bicone) was located ~0.5 m from this surface. Using a vector network analyzer (Agilent 8722ES), S21 data was measured for the channel between the antennas at 1601 points from 5.0 GHz to 6.0 GHz. This S21 data was collected at 1600 different locations on a 40 by 40 horizontal grid at 3 mm intervals. The physical extent for which the transmit antenna was moved corresponds to an approximately 12 cm square (or ~2.2λ square at 5.5 GHz). These measurements resulted in over 2.5 million S21 data points in total. It should be noted that most of the results presented herein are based on measurements taken with transmit and receive antennas oriented in a cross-polarized manner. While one might conclude this configuration would be a worst-case scenario, our recent work [3] demonstrated that for environments producing hyper-Rayleigh fading conditions, cross-polarized links are statistically more benign (i.e., tending to Rayleigh) than co-polarized links.

III. TEST RESULTS In §III.A, we present a representative single-frequency case to illustrate that radio propagation conditions for M2M environments can be potentially quite harsh; that is, producing

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very deep fades. In §III.B, we show that such deep fades can be effectively mitigated, even if the approach is suboptimal. We then present in §III.C the effectiveness of deciwavelength-scale selection diversity across all measured frequencies and for different antenna polarization configurations.

A. Example Measurement at a Single Frequency Fig. 2 provides a gray-scale image plot of S21 data collected across the mapped square area at 5.76 GHz. S21 values range from a maximum -37.3 dB to a null of -98.6 dB. This plot normalizes the data by the median value of -45.3 dB, resulting in a maximum relative fade of -53.4 dB.

Fig. 2. Normalized S21 data collected over a 12 cm x 12 cm area at increments of 3 mm. Data was collected a 5.76 GHz with transmit and receive antennas cross-polarized. NULL is -53.4 dB relatived to the median S21 value.

Fig. 3. Change in signal strength (i.e., S21) as a function of position relative to the NULL location.

For this example case, the fading occurs in bands nearly parallel to the reflecting plate and the null is relegated to a very small region. This null location and/or depth will change as function of frequency and the environment; factors that are mostly likely beyond the control of an individual M2M device. That being said, a device could employ a spatial

diversity scheme using a multi-element antenna design to mitigate such deep fades. To ascertain the null sensitivity to location for the considered data set, Fig. 3 shows the S21 value relative to the null as a function of change in position in both X (left/right) and Y (up/down) directions. As one would expect, the greater the change in position the greater the diversity ‘gain’. We observe however that the most signficant gains (> 30 dB) are achieved in the first λ/10 of movement. Therefore we are motivated to explore deciwavelength-scale antenna diversity.

B. Mitigation Using Deciwavelength-Scale Spatial Diversity Fig. 4 presents the cumulative distribution function, cdf, of the fading statistics for three different cases. The first case is that of the measured data from Fig. 2. With the exception of the null, the data set follows a near Rayleigh distribution as has been seen in other studies on depolarizing/multipath environments. The two other cases assume the M2M devices (leveraging, for example, RSSI measurements) can select (i.e., switch) between one of two antenna elements spaced at λ/10.

Fig. 4. Fading statistics presented as a cdf for the measured data presented in Fig. 2. With the exception of the NULL measurement, data follows near Rayleigh fading statistics. Ricean fading statistics are found for the diversity scenarios where the received signal can be chosen from one of two different antenna elements spaced at ~λ/10 (i.e., 6 mm) in either the X or Y directions.

Fig. 4 illustrates that not only does selection diversity at ~λ/10 mitigate the deepest of fades, but is also improves the overall fading statistics to Rician (K = ~ 1 dB and 3 dB, for Y- and X-direction element spacing, respectively). Using this diversity scheme, the mean received power also improves by 0.4 dB and 1.3 dB, respectively. Note that the theoretical mean gain is 1.76 dB when selecting between two i.i.d. Rayleigh channels [4]. However, this well-known result assumes elements are spaced in theory by at least λ/2, but in practice they may be spaced at intervals approaching 10λ.

C. Results Collected Across the 5-6 GHz Band As noted, the results presented thus far were based on

measurements conducted at a single frequency (i.e., 5.76 GHz). Frequency selective fading effects in this environment tend to be very narrowband and thus we should ascertain the

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fading behavior and deciwavelength-scale mitigation performance across a wider band. To present the results across 5 to 6 GHz, we leverage the 10% fade depth metric (10%FD) that was recently proposed for characterizing fading environments [5]. The 10%FD is that value (in dB) relative to the median received signal strength (or S21 value) below which the received signal falls for 10% of the measurements across time, space or frequency. In comparison to parametric models, the 10%FD has the advantage of being readily calculated from empirical data or found directly from cdf curves.

Fig. 5. Using the 10% fade depth metric to show the effectiveness of using M=2 selection diversity when elements are spaced in the Y-direction at the deciwavelength-scale (6 mm). Each curve represents over 2.5 million measurements across space (1600 locations) and frequency (1601).

The 10%FD metric, calculated across space for each of the 1601 frequencies measured is shown as a cdf in Fig. 5 (solid line), where for reference we also provide a vertical marker for Rayleigh fading (-8.2 dB). This curve indicates that for ~18% of the frequencies, the measurements across space exhibited fading worse than Rayleigh. However, employing deciwavelength-scale selection diversity (dashed line) between two elements improves the overall channel conditions significantly. While the mean overall gain is only 0.5 dB, the key benefit is that now all frequencies experience fading more benign than Rayleigh.

In Fig. 6, we present results for a second cross-polarized case, xpol2, in which the transmit antenna is orthogonal to its original orientation and to the receive antenna. We find these results mimic those presented in Fig. 5; that is, an environment where it was not uncommon for channels to be worse-than-Rayleigh (4.4% of the cases) is consistently more benign when employing M=2 selection diversity (again, at a deciwavelength scale).

Finally, we consider the copolarized case and see from Fig. 6 that as a function of location and frequency the channel takes on a wide range of fading conditions ranging from the most benign (upper right point of the curve where the 10%FD = -1.0 dB) to extremely severe (lower left where the 10%FD = -19.2 dB). These results are consistent with the constructive and deconstructive conditions intended by the test environment. In

particular, the test setup is capable of creating fading conditions that reach or exceed the two-ray scenario (noted by the marker at -13.1 dB). Our diversity results for the co-polarized configuration do show significant improvement. For example, the percentage of scenarios that are worse-than-Rayleigh is reduced from 20% to 9%. That being said, it is clear that the channel still leaves much to be desired.

Fig. 6. 10% fade depth of co-polarized and cross-polarized communication links across 1600 locations and 1601 frequencies between 5.0 and 6.0 GHz. As before, the selection diversity is between two elements spaced in the Y-direction at an interval of 6 mm.

IV. CONCLUSION Herein, we have empirically shown that significant

mitigation of fading channels can be accomplished using a selection diversity scheme where individual antenna elements are spaced at the deciwavelength scale (i.e., at intervals of λ/10 or less). The implications are that a simple and compact selection diversity scheme, albeit suboptimal, not only can mitigate the deepest of fades but also significantly improves the overall link conditions for M2M applications. For systems that are space constrained, these results show promise. While we have explicitly suggested choosing between two different antenna elements, the deciwavelength spatial change also suggests an approach where a single element is mechanically moved, but this is an area for future work.

REFERENCES [1] J. Frolik, “A case for considering hyper-Rayleigh fading channels,”

IEEE Trans. Wireless Comm., Vol. 6, No. 4, April 2007. [2] J. Frolik, “On appropriate models for characterizing hyper-Rayleigh

fading,” IEEE Trans. Wireless Comm., Vol. 7, No. 12, December 2008. [3] J. Frolik, V. Sipal and D. Edwards, “Leveraging depolarization to

increase the link reliability for wireless sensors operating in hyper-Rayleigh environments,” IEEE Sensors Journal, IEEE Early Access October 2013.

[4] A. Molisch, Wireless Communications, 2 ed. West Sussex, UK: Wiley & IEEE, 2011.

[5] J. Frolik, A practical metric for fading environments, IEEE Wireless Communications Letters, Vol. 2, No. 2, April 2013.

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