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Providing wireline availability and reliability in non-line-of-sight (non-LOS) wireless environments presents a particular set of challenges. Difficulties lie in the fact that the received signal power at a location in space is not constant, but is instead random in nature. The depth of the fades is a function of how non-LOS the wireless link actually is. This truism of wireless communications underscores one of the wireless industry's greatest challenges in enabling both fixed and mobile broadband wireless connectivity. Recently commercially developed multiple antenna technologies are demonstrating notable success in defeating early systems' LOS limitations. The advantages of multiple antenna technology are best understood in terms of the obstacles they address.

“What exactly constitutes non-LOS operation?” is a common question. The answer to what seems like an easy question required the intervention of an engineering standards body, namely the IEEE 802.16. IEEE 802.16 is the engineering committee working on standards for fixed wireless “last-mile” access for frequencies under 10 GHz. Six IEEE 802.16a channel models now explicitly define non-LOS. Each of these models quantifies identifying non-LOS characteristics such as Rician K-factor¹ and delay spread². The channel models range from near-LOS (IEEE 802.16a-1) to pure non-LOS (IEEE 802.16a-4-6). The IEEE 802.16 website (http://grouper.ieee.org/groups/802/16/meetings/mtg14/report.html) can provide additional details on the channel models.

In all wireless communication, as a signal is launched from an antenna the energy spreads out in many directions. As a consequence, the power available to a receive antenna decreases with distance.

This phenomenon is termed propagation loss or path loss. In non-LOS links, in addition to the path loss, the signal reflects and refracts off buildings, autos, trees and other topographic obstacles, and arrives at the receiver with disparate delays. At some locations, these multipath delays are such that a signal's reflections add up in phase, improving the signal-to-noise ratio (SNR), and thus resulting in good reception quality. At other locations, the delays are such that the signal's paths add out of phase, producing multipath fades. Non-LOS wireless links therefore bring about phenomena that cause outages if not properly designed for.

A narrow-band received signal power under pure non-LOS links is a Rayleigh distributed random variable in space and time. The signal level for pure LOS links, on the other hand, is relatively constant with additive noise. There exists a family of distributions that captures the continuum of signal level configurations from pure LOS with additive Gaussian noise to non-LOS. It is termed Rician. The parameter that “moves” a Rician distribution from Gaussian for LOS to Rayleigh for non-LOS is the above-mentioned K-factor (see Figure 1).

As previously mentioned, in LOS links, the received signal power is predictable and its variation around a nominal level (in time and space) is minimal. Therefore, only minimal margins³ for wireline availability are necessary. This is shown in Figure 2.

In near-LOS links, received signal strength starts to vary in space and in time as a result of multiple signal reflections from buildings, trucks or other natural and man-made obstacles adding together constructively as well as destructively. In this fashion, a “standing wave” is formed.

The amount of received signal strength variation depends on the degree of “non-line-of-sightedness.” In Figure 3, it is assumed that LOS power is three times the power of all reflections for a Rician K-factor of 3 or 5 dB. Some extra transmit power/margins are required to guarantee a particular level of availability. An outage occurs when the received signal on an antenna falls below a predetermined level for a period of time.

As can be seen in Figure 4, true non-LOS links exhibit much deeper fades.

In fixed wireless channels, the aforementioned “standing wave” moves slowly in space, and thus the locations of peaks, valleys and fades move. The rate of channel condition changes is referred to as “Doppler shift” or simply Doppler. Fixed wireless links exhibit orders of magnitude lower Doppler relative to mobile links. The reason for this is that driving in a car through the standing wave is what causes the fast Doppler characteristics of mobile links. In fixed wireless, neither the transmitter nor the receiver is moving. Wind, autos and other man-made and natural obstacles that change the multipath profile with time result in the Doppler shift in fixed wireless links.

Slow Doppler presents a different set of challenges than fast, mobile Doppler. A mobile link's physical layer features such as modulation, coding and interleaving are designed to get information to the receiver through fast fades. Slow Doppler produces slow fades. The combination of a single antenna in a deep fade and slow Doppler is likely to result in an outage. Data interleaving does not help in this case, and neither does the forward error correction (FEC) coding, because no signal is getting through.

The only way to successfully overcome the effects of multipath fades is to transmit from multiple locations in space and receive at multiple locations. This multiple-antenna transmit and receive technique yields multiplicative⁴ orders of diversity — hyper-diversity. Without diversity, the margins required to overcome multipath fading are prohibitively large.

Rayleigh statistics tell us that 10% of the time a signal is 10 dB below, or equivalently 1/10^th of its nominal level. To guarantee that a 10 dB fade can be overcome, 10 times more power needs to be sent from the transmitter (or equivalently 10 dB margins are required). Rayleigh statistics also tell us that 1% percent of the time a signal is 20 dB below, or equivalently 1/100^th of its nominal level. The consequences of slow Doppler are, once again, that when a signal on an antenna goes into a fade, it tends to stay there long enough to cause an outage. From this, one can deduce that without spatial diversity⁵, 99% availability would translate into requiring 100 times the transmit power. In like manner, 99.9% availability would require 30 dB or 1,000 times the transmit power without adequate diversity. This much extra power is rarely available, so the key to wireline availability in non-LOS operation is spatial diversity.

How are the required margins determined for a given availability? The simplest way is to look at the familiar bit error rate (BER) vs. SNR plots. Once again, the Doppler is very slow; therefore features such as interleaving yield no gain. It is also worth pointing out that some frequency diversity gain for orthogonal frequency division multiplexing (OFDM), code-division multiple access (CDMA) and adequately equalized single carrier systems may result from delay spread.

The mechanism behind frequency diversity gain comes from the fact that multiple reflections arriving at the receiver are not expected to simultaneously fade. Some technologies make it possible to coherently combine the multiple reflections. Certain CDMA variants use what is termed a “rake” to micro-adjust the receiver fingers in time to collect and combine the multipath components. CDMA “rake” receivers are quite complex and their complexity grows rapidly with receiver data rate/bandwidth. Thus, for broadband data rates, only simplified, sub-optimal, versions of “rake” receivers are commercially viable.

Equalizers are also used to provide ‘multipath diversity’. Their implementations, however can be quite complicated. True maximum likelihood (Viterbi) equalizers grow exponentially in complexity as the data bandwidth increases. Approximations such as zero forcing (ZF) and minimum mean square error (MMSE) introduce unwanted distortions into the signal, which degrade the overall receiver performance.

OFDM provides the simplest mechanism for extracting frequency diversity gain. Since OFDM breaks the broadband data stream into many orthogonal (consistent with the fast Fourier transform [FFT] size) lower data rate sub-carriers, the duration of each data symbol is lengthened. These “long” data symbols are much more resistant to multipath.

Another equivalent way to look at delay spread consequences is to work in the frequency domain. Delay spread has the effect of forming notches within the RF channel bandwidth. A channel coherence bandwidth is equal to 1/(rms_delay_spread). The amount of frequency diversity gain is related to the receiver RF bandwidth vis-à-vis the coherence bandwidth.

As a rule of thumb, it is generally assumed that a channel's frequency selective fades are correlated over a coherence bandwidth. In urban environments, the difference between signal paths is likely to be fractions of a mile. The time it takes a signal to travel one mile is around 5 μs. Assuming 0.1 mile root-mean-square (RMS) path length difference, we get around 500 ns of RMS delay spread. It is therefore reasonable to assume that RF channels less than 2 MHz (1/500 × 10^-9) in bandwidth will exhibit “flat” fading, and thus derive virtually no benefit from little frequency diversity. The following derivations assume flat fading conditions. All curves are for quadrature phase shift keying (QPSK) and do not include coding and antenna array gain.

Note: single-input, single-output (SISO) mobile phones (on the downlink) can operate in non-LOS because they use sophisticated vocoders, which tolerate orders of magnitude of more errors than TCP data. Mobile phones also do not have the wireline availability requirements of fixed wireless.

From Figure 6 we can deduce that a system with 2^nd-order diversity requires fade margins of around 15 dB⁶.

For a 2 × 3 multiple-input, multiple output (MIMO) system with 6^th-order diversity (see Figure 7), the required fade margins are around 5 dB⁷.

In order to get to the next level of precision, we need to look at what happens to the margins if the fade duration and frequency diversity components are included in the analysis.

The following simulations take into account the fade duration component (see Figure 8a, b) along with frequency diversity (see Figure 8b). Many different scenarios were looked at with the help of an in-house simulator. Subsequent plots are representative of the margins required under the following set of assumptions:

• Doppler = 0.001 Hz: Such low Doppler must be designed for because it will likely occur. Once again, in fixed wireless environments neither the receiver nor the transmitter is moving, so the sources of Doppler are autos, wind and other transitory phenomena. Note that a system must be designed to accommodate a wide range of possible Doppler spreads, from virtually no Doppler to tens of Hz.

• Flat fading is assumed in Figure 8a.

• IEEE 802.16a-6 (http://grouper.ieee.org/groups/802/16/meetings/mtg14/report.html) is the channel model that is assumed in Figure 8b. IEEE 802.16a-6 RMS delay spread is such that systems with RF bandwidths of greater than 500 kHz can start realizing some frequency diversity benefits.

The fade margin traces shown in the following plots are selected as a result of many simulations such that 99.9% link availability is guaranteed based on outages lasting less than 10 seconds.

Basically, figure 8 describes the particular fade margin traces are chosen such that 99.9 percent availability is guaranteed based on less than a 10 second outage.

In (8a) with flat fading assumed, a 2 × 3 MIMO enjoys a 23 dB multipath fade margin advantage over SISO and a 12 dB multipath fade margin advantage over 1 × 2.

In (8b)Frequency selective fading is assumed as per IEEE 802.16a-6; in this case 2 × 3 MIMO enjoys a 17 dB multipath fade margin advantage compared with SISO and a 10 dB multipath fade margin advantage compared with 1 × 2.

With parameters such as transmit powers, antenna gains and receiver RF bandwidths being equal, a 2 × 3 MIMO system has a 10 to 15 dB multipath fade margin advantage over 1 × 2 systems. Figure 9 illustrates how 15 dB smaller margins more than quadruple the coverage area. The slope of the dashed line is referred to as the path loss coefficient (γ = 4 is assumed in the figure. For γ = 4, 12 dB exactly doubles the radius, thereby quadrupling the coverage area. It also describes the 2 × 3 MIMO's 15 dB gains compared with a 1 × 2 system that more than double the cell radius, thereby quadrupling the area covered.

In addition to extending the service coverage, the mitigating of multipath fading also improves spectral efficiency and provides system capacity gain. Spectrum is always at a premium and so must be reused as many times as the system will allow. Cellular environments necessarily bring about spectrum reuse.

The mechanism behind capacity gains in systems with frequency reuse is demonstrated in figure 10. Note that the total allocated spectrum is subdivided into a number of subsets equal to the reuse factor, i.e. a reuse factor of seven results in seven subsets. One-seventh of the total spectrum is then assigned to each of the seven cells within a cluster. For reuse — 1 systems, the whole spectrum is available for every cell.

In Figure 10, the gray cells contain the same set of frequencies. Reuse of three results in 2.33…capacity multiplier compared to reuse of seven. Reuse one has three times the capacity of reuse three and seven times the capacity of reuse seven systems.

The mechanism for improving spectral efficiency by mitigating multipath fading is the following.

Spectral efficiency/reuse factor is related to the system carrier-to-interference (C/I) ratio. The C/I for a given reuse factor is determined by the ratio of signal of interest (SOI) path loss distance to the path loss distance of the interferors. The farthest point for the signal of interest is the cell radius, R. Interference comes from other cells using the same frequency and travels a distance, D. The designed for C/I is therefore related to the ratio of D to R.

In a hexagonal-shaped cellular system:

Another quantity that plays a role in calculating the C/I ratio is the propagation path loss slope coefficient γ, which is generally assumed to be around 4. So the green-field reuse C/I (no multipath fading or shadowing) is equal to:

where N is the number of interfering base stations seen by the customer premise equipment (CPE) on the downlink. The number of interfering base stations in view is related to the CPE antenna beamwidth and the reuse factor.

The following set of figures depicts the sources of co-channel interference in cellular environments. Note the SOI and the interference multipath fades are not correlated, so when the SOI is in a fade while the interferors are not, the C/I is drastically reduced.

It can be concluded, from Figure 11, that MIMO's multiple transmit and receive antennas combine to reduce the SOI multipath fading and provide array gain, thereby allowing a lower pre-processing C/I ratio. MIMO results in a more favorable frequency reuse and improved system spectral efficiency.

Multiple antennas at both the base station and the CPE can also be used to substantially reduce the co-channel interference present in all cellular systems with frequency reuse.

To mitigate the co-channel interference, multiple antennas are phased/combined such that notches are formed in the direction(s) of the inteferor(s), thus providing a gain in the C/I (see Figure 12). Tighter spectrum reuse is thus permitted. Note: One less notch can be formed than the number of CPE and/or base station antennas.

When a user is not close to the edge of a cell, enough power for successful communications becomes available even in the event of a multipath fade. In this case, MIMO's multiple antennas are used to send user data in parallel. Use of multiple antennas at both transmitter and receiver allows the opening of parallel spatial data pipes within the same RF channel. This MIMO mode of operation is termed Spatial multiplexing⁸.

Spatial multiplexing drastically increases user data rates, capacity and spectral efficiency. At the receiver, the signals from the multiple transmit antennas display distinct multipath profiles (or equivalently spatial signatures). These spatial signatures allow the CPE processing to aggregate the multiple parallel data streams. Minimum numbers of transmit or receive antennas serve as the data rate multiplier. For example, two transmit and three receive antennas would double (min^2,3) the data rate.

MIMO's flexible design is geared from the ground up for non-LOS, cellular operation and offers:

• Diversity gain — Spatial diversity through multiple antennas can be used to combat multipath fading, significantly improving link reliability and extending coverage. If both base station and CPE have multiple antennas, multiplicative diversity gain can be obtained at both the transmitter and the receiver.

• Spectral efficiency gain (Spatial multiplexing) — The use of multiple antennas at both the transmitter and the receiver allows opening of parallel spatial data pipes within the same RF channel. User data is then sent in parallel out of the multiple antennas. In this way, the data pipes provide an increase in user data rates proportional to the number of antennas.

• Array gain — Multiple antennas both base station and CPE coherently combine signals to increase the SNR and hence improve coverage.

• Interference suppression — Multiple antennas at both the base station and the CPE can be used to suppress co-channel interference and hence allow a reduction in the frequency reuse factor. The lower the frequency reuse factor, the more efficiently the spectrum is used. Efficient spectrum use significantly increases capacity.

Together, these features form a fundamental set necessary to enable mass deployment

The bit error rate (BER) curves and their derivations can be found in Haykin, “Digital Communications,” February 1988, John Wiley & Sons, ISBN: 0471629472

Sklar, “Digital Communications: Fundamentals & Applications,” 2nd Bk&cdr edition, January 2001, Prentice Hall PTR, ISBN: 0130847887

Proakis, “Digital Communications,” 4th edition, August 2000, McGraw-Hill Higher Education, ISBN: 0072321113

The green-field C/I derivations can be found in: Lee, “Mobile Cellular Telecommunications,” 2nd edition, 1995, McGraw-Hill, ISBN: 0070380899

1. Rician K-factor is defined as the ratio of the power in the specular (LOS) to the power in the diffuse (multipath) component. The higher the K-factor, the more LOS the link (A K-factor of infinity means the link is LOS, a K-factor of zero means the received signal contains no LOS component)

2. Delay spread results from a signal's multiple reflections arriving with disparate delays due to the different path lengths traveled in route from the transmitter to the receiver (~5 micro seconds for every “extra” mile traveled).

3. Margins are extra power necessary to overcome signal fades when they occur.

4. A 2 × 3 MIMO system creates 6^th order diversity

5. Spatial Diversity — Receive: A signal is simultaneously sampled and combined at multiple locations in space. Transmit: A signal is simultaneously launched out of multiple locations in space.

6. Margins are further reduced by up to 3 dB with the two receive-antenna array gain.

7. Margins are further reduced by up to 5 dB with the three receive-antenna array gain and the two transmit-antenna array gain.

8. MIMO link adaptation algorithms automatically and dynamically (in real-time) decide whether transmit diversity or spatial multiplexing should be used on a per subscriber basis.

Victor Shtrom, has been involved in the design and deployment of “smart” antenna technologies for wireless cellular voice and data systems for nearly a decade. Most recently, Dr. Shtrom was the senior technical marketing manager for Iospan Wireless. He was involved in the definition of the IEEE 802.16 standard and performed cost/benefit trade-offs for existing and emerging technologies. He has also held positions with ARGOSystems and Boeing. Dr. Shtrom holds a Ph.D. in communication theory and has authored numerous papers in the areas of blind equalization and smart antenna processing.

Dr. Jose Tellado is the director of PHY Design for Iospan. He joined Iospan in 1999 during its early start-up stages, and has since been directly involved in the development of the Company's MIMO-OFDM-enabled AirBurst^™ technology. Prior to joining Iospan, Dr. Tellado was a research assistant at the information systems laboratory at stanford university. There, he proposed new advanced methods for Multicarrier Modulation (DMT/OFDM).He has also consulted for apple computers advanced technology wireless group and globalstar in the areas of WLAN and LEO Satellite cellular system respectively. He received the M.S. and Ph.D. degrees in electrical engineering, with an emphasis on communication theory, from stanford university in 1994 and 1999, respectively. He has over 12 IEEE publications, 10 xDSL standard contributions and 10 pending patents.

Professor Arogyaswami Paulraj is the chairman and founder of Iospan Wireless and a professor of electrical engineering at Stanford University. He supervises the research group at Stanford that pioneered the area of space-time techniques in wireless communications systems. Prior to joining Stanford He was the chief scientist for Bharat Electronics, the director of the Center For Development of Advanced Computing, and director of the Center For Artificial Intelligence and Robotics (all in India). Previous to that, he led the development of military sonar systems for the Indian Navy. He holds a BE degree from Naval Engg. College, India and a Ph.D. form the Indian Institute of Technology, Delhi. He is a Fellow of the IEEE.

They can be contacted at vshtrom@yahoo.com, jtellado@iospanwireless.com and paulraj@leland.stanford.edu.