a or b?

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Wireless LANs can provide network flexibility and make it easy to support a roving workforce, but pitfalls abound. For instance, you must decide which flavor of 802.11 technology to select. Not long after the original 802.11 specification was ratified in 1997, the 802.11 Working Group formed two Task Groups, 802.11a and 802.11b, to work on extensions to the PHY Layer of the 802.11 specification and to solve some of the shortcomings of that original specification. The resulting 802.11a and 11b specifications also were designed to work with the original 802.11's MAC sublayer. But that's where much of the resemblance between these two standards ends.

To help in your decision-making process, we will now consider some of the options, security concerns, and the pieces of the puzzle you'll need to consider when evaluating a WLAN deployment, at least as things stand at this writing.

Once 802.11b gear hit the marketplace in 1999, network managers chose it as their preferred WLAN standard, mainly because there were no significant contenders since manufacturers were slow to produce any quantity of 802.1 la gear. But by late 2001 everything changed as vendors released 802.11a access points and radio network interface cards. This change meant that anyone considering the deployment of a WLAN had another viable wireless technology to consider. Then in 2003 the manufacturers "jumped the gun" by releasing 802.11g gear in advance of a finalized set of specifications upon which to build that gear. Of course, now that 802.11g has been finalized expect also to find Wi-Fi certified 802.11g products all over the place.

Nonetheless, 802.11b is still the technology in current favor. And while some industry experts believe that 11a might be the anointed successor to 802.11b, others believe that since the 802.11g specification has been finalized, 11a may find itself out in the cold. So the decision on which specification to use when deploying a new WLAN can get a bit complicated.

Since 802.11g is spanking new and thus products built upon that standard do not have the experience behind them that only an installed base can provide, we will consider the major points of differentiation between 11a and 11b. However, there is an extensive discussion of the new specification in Chapter 6 and a discourse on the challenges of adding 802.11g to an existing 802.11b network in Chapter 10.

It's only through the examination of the main technical differences between 802.1 la and 802.11b specifications that it is possible formulate a choice between 802.11b (and its 802.11g extension) and 802.11a. (Some may even opt for adopting a mixed environment.)

In 802.11b's favor: unlike 802.11a, 11b's products were introduced into the marketplace in 1999. Next, 802.11b's throughput is adequate for many network scenarios. Since the technology has evolved through several generations and has been used in numerous real-world situations, it has had most of the kinks worked out and its networking gear has come down to near-commodity prices. Finally, almost all HotSpot technology is based on 802.11b.

As Fig. 7.1 indicates, products with the 802.1 la designation offer higher bandwidth and more channels than 802.11b products. But before you upgrade (or before you go wireless for the first time), there are some traps to be aware of.

 

802.11a

802.11b

Frequency :

UNII Band

ISM Band

Frequency Band:

5 GHz range (300MHz)

2.4 GHz range (83MHz)

Modulation:

OFDM

DSSS

Channel Bandwidth:

20MHz (8 usable channels) non overlapping channel

22MHz (3 channels) Overlapping channel : 14

Data rate:

54Mbps (Layer3 -> 36Mbps) -PHY rate: 6, 9, 12, 18, 24, 36, 48, 54Mbps

11Mbps (Layer3 -> 5Mbps) -PHY rate: 1, 2, 5.5, 11Mbps

Coverage:

indoor (30m) outdoor (100m)

indoor (50 m) outdoor (150m)

Max power:

EIRP 200mW, 1W, 4W

EIRP 1mW/MHz

AP simultaneous Users:

100+ users

20-30 users


Figure 7.1: Technical differences between 802.11a and 802.11b.

Note 

This analysis uses published information, published data and the system performance parameters readily available from the FCC, the IEEE and the International Telecommunications Union (ITU). It also tries to clear up some of the confusion that has been perpetuated through the information that's been available to date, much of which, in the author's opinion, misinforms about the actual performance and network capacity of both 11b and 11a technologies.

Everyone who compares these two technologies finds major points of differentiation, but when the two are examined more closely there is no clear "winner." They each have different operational criteria.

To assess the network capacity of a wireless LAN built upon each specification, you must first understand that these two standards have different physics and operational characteristics such as:

  • The possibility of interference-although the scale may tilt a bit in favor of 802.1 la there is little difference between the two.

  • Throughput-802.11a is much higher than 802.11b's throughput, but in many instances the throughput difference isn't that important because of the applications that will be run over the WLAN.

  • Decipherable Signal Range, i.e. achievable communication range between the AP and the station, and the corresponding service coverage area-802.11b wins this contest; but in some instances, such as an area that routinely hosts a multitude of wireless users, 802.11a would be more desirable than 802.11b.

Then you must consider the different value propositions that these standards offer. They touch on many different areas including:

  • Different end-user values by segments (e.g. corporate offices have different requirements than R&D departments).

  • Usage models (e.g. a large, but busy, corporate conference room has different networking requirements than a warehouse).

  • Applications (word processing has different bandwidth requirements than videoconferencing).

  • Existing WLAN equipment (e.g. is there an existing 802.11b network?).

Now let's examine the differences between these two technologies as they pertain to the average corporate network's needs.

Interference: There are two "givens" when considering the possibility of interference in the operation of an 802.11a or b WLAN. The first concern is the unlicensed bands that 11a and 11b use, and the interference that might exist between all of the different devices that use that spectrum. The second is that given the cost of licensed spectrum, free spectrum is, and always will be, very attractive. Slivers of frequency that may not now be overcrowded will, in the near future, become so. Therefore, the claim that a technology such as 802.11a utilizes "un-crowded spectrum" is not a relevant buying consideration. Both the 2.4 GHz and the 5 GHz bands are subject to overcrowding and interference, and are used by many devices outside the WLAN arena.

The 2.4 GHz band (2.400-2.4835) is used by, not only, 802.11 and 802.11b devices, but also another WLAN technology, HomeRF. In addition, this ISM band is also used by communication systems such as Bluetooth, proprietary cordless phones, and non-communication devices, e.g. microwaves and lighting devices.

The 5 GHz band (5.15-5.25 GHz, 5.25-5.35 GHz, and 5.725-5.825 GHz), which at the moment appears less crowded than the 2.4 GHz band, hosts an ever-increasing amount of traffic. In addition to 802.11a devices, communication systems such as satellite systems (mobile and earth exploration), short range wireless systems, radio location systems, and electronic news gathering systems use the 5 GHz frequencies. The main non-communication device utilizing the 5GHz band is radar.

Throughput: An important consideration when determining which WLAN technology to use is the amount of bandwidth, data rate, or throughput the technology provides to each network user, and how well that throughput can support the applications running on the network.

Note 

For our purposes, data rate is the amount of data that can be sent from one node on the wireless network to another, within a given timeframe-usually seconds, e.g. 11 Megabits per second or 11 Mbps. The difference between data rate and throughput is the measure of raw bits traveling from one node to another, in comparison to the bits representing the message content. This difference is determined by a number of factors including the latency inherent in the PHY components of the radio, the overhead and acknowledgement information that accompany every transmission, and pauses between transmissions.

To help put data rate and throughput numbers into perspective, consider this:

Technology

Data Rate

Actual Throughput

Shared Among Users?

Est. Time to Download 100 MB File (actual throughput)

56.6 Kbps Modem

56.6 Kbps

56.6 Kbps

No

4 hours

10/100 Ethernet

100 Mbps

100 Mbps

Yes

8 seconds

T-1 line

1.536 Mbps

1.536 Mbps

Yes

8 minutes 41 seconds

801.11b

11 Mbps

5-7 Mbps

Yes

2 minutes 8 seconds

802.11a

54 Mbps

31 Mbps

Yes

26 seconds

802.11b/g

54 Mbps

12 Mbps

Yes

1 minute 13 seconds

802.11g

54 Mbps

31 Mbps

Yes

26 seconds


Figure 7.2: Speed comparisons of various connectivity technologies.

As you know, 802.11b offers a maximum data rate of 11 Mbps, which translates into approximately 5 to 7 Mbps of actual throughput, while 802.11a offers a 54 Mbps data rate, or approximately 31 Mbps of actual throughput. But, keep in mind when considering throughput rate that:

  • It is shared among all network users who use it simultaneously.

  • The throughput is managed through a CSMA/CA (Carrier Sense Multiple Access/Collision Avoidance) technique modeled on its wired equivalent (i.e. Ethernet).

  • Most network traffic (wired and wireless) is bursty, and there are typically only a few users on the network at any one time, so all WLAN networks (whether using 11a or 11b technology) offer their users generally very good connectivity speeds.

  • An 802.11a network can easily support several simultaneous streaming media data streams and still have enough capacity to serve other end-users with high wireless data rates. Conversely, 802.11b networks are limited in the types of applications that they can host.

Decipherable Signal Range: One of the most fundamental and significant differences between communication systems operating at 2.4 and 5 GHz is the achievable communication range between the AP and its computing devices, and the corresponding coverage area-the decipherable signal range. As you shall learn, when comparing each specification's decipherable signal range, both 802.1 la and 802.11b wireless systems are governed by the same variables.

Without delving deeply into the theories of electromagnetic wave propagation, we will look at the propagation performance (refers to the movement of the transmission signal through the airways) in the ISM and U-NII bands. Here's what you need to understand about decipherable signal range.

Because the 802.11a carrier frequency is more than twice as high as the 802.11b carrier frequency, the electromagnetic propagation through the channel should theoretically attenuate the signal twice as much (6 dB according to the so-called Friss equation). While this holds true in an "open field" situation, in an indoor or campus environment, additional parameters must be considered, such as reflection, wall penetration, moving vehicles, how fast the channel changes, and so forth. Thus, while the laws of physics dictate that the range of free-space (i.e. open field) radio communications decreases with higher frequencies, indoor propagation differs from free space because of absorption and reflections. Moreover, power transmit levels and the type of modulation used also affect range. The result is that it is very difficult to arrive at a generic formula to accurately describe such propagation.

Note 

The Friss equation gives the free space power received by an antenna. This equation helps in finding out the received signal strength at the receiver side when there is an unobstructed line of sight path between the transmitter and receiver. The function is of the form

  • Pr = PtGrGtλ^2/(16*π*π*d*d*L)

where Pr is the power of the signal at the receiver, Pt is the power of the signal at the transmitter, Gt is the transmitter antenna gain, Gr is the receiver antenna gain, d is the separation between the antenna and the receiver, λ is the wavelength and L is the system loss factor which is assumed to be 1 for practical purposes.

Various models, techniques and analyses have been created to give some insight into the propagation question, including:

  • The Motley-Keenan model (J.M. Keenan, A.J. Motley, "Radio Coverage in Buildings," British Telecom Technology Journal, Vol. 8, No. 1, January 1990, 19-24).

  • The Kamerman path loss model (A. Kamerman, "Coexistence between Bluetooth and IEEE 802.11 CCK Solutions to Avoid Mutual Interference" Lucent Technologies Bell Laboratories, Jan. 1999, also available as IEEE 802.11-00/162, July 2000).

  • Long-distance models (T. Rappaport, Wireless Communications, Prentice Hall, New Jersey, 1996).

  • Multi-breakpoint models (D. Akerberg, "Properties of a TDMA Picocellular Office Communication System," IEEE Globecom, December 1988, 1343-1349).

  • Sophisticated ray-tracing techniques (K. Pahlavan, A. Levesque, Wireless Information Networks, J. Wiley & Sons, Inc., New York, 1995).

Unfortunately, some of the indoor models suggest that a carrier frequency that is twice as high will attenuate the signal by 6 dB, whereas other models reach an entirely different conclusion. While there are many reasons for such contradictory conclusions, the primary explanation is that there are a number of variables that govern the decipherable signal range of every wireless system, whether 802.11-based or not. Some considerations are

  • RF power transmit level, the power at which the signal is transmitted.

  • Required ES/N0, the signal energy required to recover the transmitted symbol (the technical wireless term for the information contained in a message) compared to the environmental noise. (Because symbols are shorter at greater throughput levels, they require more energy in the symbol to recover it for the same error rate. This is one reason a WLAN system's throughput decreases as the distance between the AP and its computing devices grows.)

  • Environment, the physical characteristics of the radio's environmental surroundings affect the path loss.

  • Signal propagation, the physics of the radio spectrum and frequency in which the radio operates.

But the core difference between communication systems operating at 2.4 and 5 GHz is the achievable communication range between the AP and the computing device, and the corresponding service coverage area. Assuming common environments and system operating parameters, systems operating in the 2.4 GHz frequency band offer roughly double the range of those operating in the 5 GHz band, again holding power and throughput constant. This doubled range is explained by radio wave propagation physics, which dictate that, all other things being equal, a higher frequency signal will have a lesser range than a lower frequency signal. (Of course, this assumes a conservative 5 GHz path loss.)

Recently published papers based on varying models and techniques have compared the network capacity of 802.11a and 802.11b WLANs, but many reached contradictory conclusions. Here's why: one model can indicate that 802.11b networks offer superior performance to 802.1 la, but only under the assumption that all 802.1 la solutions transmit at 15 dBm, which isn't always the case. Another model can show clear network capacity advantages of 802.11a over 802.11b; however, the model is based upon a system that does not meet the full specifications of 802.11a, so the model does not provide a truly accurate representation of the full performance of optimized 802.11a systems.

Let's now assess the network capacity of wireless LANs by first looking at the network capacity offered by current 802.11a solutions and compare those to 802.11b solutions.

start sidebar
3COM TESTS 2.4 AND 5 GHZ PROPAGATION IN TYPICAL OFFICE ENVIRONMENT

The authors (Niels van Erven, Robert Yarbrough, and Lloyd Sarsoza) of a 3Com document entitled "2.4 and 5 GHz propagation measurements for WLAN," measured 2.4 and 5 GHz propagation in a common U.S. office environment. In other words, the test was conducted in a building with metal floor and metal roof, cubicle walls with metal sheets inside, and some drywall in the line-of-sight (LOS) path. In the case of a LOS path, where the Tx (transmit) and Rx (receiver) vertical polarized antennae were above the cubicles, the average path loss difference between 2.4 GHz (11b) and 5.2 GHz (11a) was around 7 dB. When the antennae had a non-LOS path (e.g., one antenna inside a cubicle), the difference was 2 to 3 dB.

The test results indicate that the more reflection there is in the signal's path, the less difference there is in propagation between the two frequencies. The test's results also suggest that with proper antenna positioning, 11b will have an additional link budget of about 6 to 7 dB compared to 11a. (However, for less optimal antenna positions, this difference is closer to 2 to 3 dB.)

It was also discovered that additional factors can play an important role in the actual range difference between 802.11b and 802.11a, e.g. the achievable Tx power (the transmit power of the radio) and Rx sensitivity (the receiver sensitivity of the radio), use of antenna diversity schemes, use of sophisticated time equalizers for 11b, etc. Current 802.11b implementations show a high level of optimization with respect to these parameters. (Note that for 802.11a, it is very difficult to get high Tx power with commercially available power amplifiers with linear performance to guarantee proper receiver sensitivity for the high bit rates.)

In another test, 3Com found that when 802.11b (running at 11 Mbps) and 802.11a (running at 6 Mbps) are compared, the data throughputs are similar. This is documented in a 3Com paper entitled "Comparing Performance of 802.11b and 802.1a Wireless Technologies," which states, "The available link budgets are also about the same." 3Com also found that the propagation is the only major difference. In fact, 3Com concluded, "In the best case, 802.11b can go roughly 50 to 70 percent farther than 802.11a. In the worst case the range is nearly the same." 3Com's overall conclusion based on its test was, "the high rate ranges of 802.11b are very similar to the 'low rate' ranges of 802.11a."

The importance of such tests is that they can help a network manager create a wireless network that can transition between 802.11b and 802.11a with respect to access point placement.

end sidebar

Measuring Performance

The primary industry-standard performance metrics used to define connectivity for a WLAN deployment include range, coverage and rate-weighted coverage.

  • Range is the greatest distance from an access point (AP) at which the minimum data rate can be demodulated with an acceptable packet error rate or probability of error per bit (commonly known as "bit error rate" or "BER"), where it is assumed that there are no co-channel or adjacent-channel radiators in the vicinity.

  • Coverage applies to moderate-size or large cellular deployments and is a measurement of the resulting cell size, or square meters per AP.

  • Rate-weighted coverage is the integral of the bit rate with respect to area covered (expressed as megabits/second times square meters).

Range, coverage, and rate-weighted coverage are strongly influenced by not only the physical environment, but also by transmit power, receiver sensitivity, noise and interference. By analyzing, understanding and managing such parameters, WLAN system designers can have a significant effect on the overall performance of the system.

Transmit (Tx) power: Refers to the transmit power of the radio. FCC regulatory standards set upper bounds on transmitted power for 802.11a systems operating in the United States. The limit in the 5.15 to 5.25 GHz band is +16.02 dBm. In the 5.25 to 5.35 GHz band it is +23.01 dBm. The maximum upper bound on transmit power for 802.11b transmissions is +30 dBm. (Other national regulatory agencies also have set limits.)

Receiver (Rx) sensitivity: Refers to the receiver's sensitivity to the radio. According to the IEEE, an 802.11b receiver should be able to detect a -76-dBm signal and demodulate it with a bit error rate of less than or equal to 10e-5 in the absence of adjacent-channel interference (ACI). If ACI is present, the receiver sensitivity figure is specified at -70 dBm. In comparison, Fig. 7.3 shows the minimum Rx sensitivity for various data rates with and without ACI for 802.11a.

click to expand
Figure 7.3: For bit error rates less than or equal to 1e-5, the 802.11a standard specifies minimum receiver sensitivity with and without adjacent-channel interference (ACI).

Noise and interference: Interference can dramatically affect the performance of any WLAN. In general, interference is either caused by radio devices operating in the same bands or by thermal noise, or both. Thermal noise is the only source of interference for a single AP. For multiple APs (i.e. multiple cells), however, there is also interference from adjacent channels and co-channels. The overall impact of such interference is heavily dependent upon the number of available frequency channels and cell deployment. Careful cell deployment and management of the number of available channels can mitigate its effects.

Bit error rate: A bit error rate of better than 10e-5 is considered acceptable in WLAN applications. By using standard graphs of BER vs. Eb/No (i.e. the bit error rate versus the ratio of Energy per Bit (Eb) to the Spectral Noise Density (No)) for the different modulation schemes, it's possible to then calculate the minimum required signal-to-noise ratio (S/N) values in decibels.

click to expand
Figure 7.4: For bit error rates less than or equal to 1e-5, there are defined minimum signal-to-noise ratios for 802.1b and 802.1a that will allow the required data rates to be met.

Physical environment: By using indoor "path-loss models," designers can quantify ambient impairments and achieve an understanding of how a system will operate when deployed. For instance, in an indoor environment, the signal power at the receiver SRx is related to the transmit power STx as shown in the following equation (Equation 1).

(1) Here, C = the speed of light (m/s), f(Hz) = the center frequency and N = the path-loss coefficient (dimensionless). The ITU recommends using N = 3.1 for 5-CHz and N = 3 for 2.4-GHz applications. click to expand

Range Comparisons

Some published analyses argue that 802.11b provides superior range when compared with 802.11a. However, those conclusions are based on an incorrect assumption that both 802.11b and 802.11a radiate at the same transmit power, which may not necessarily be the case. Optimized 802.11a solutions can transmit at +23 dBm as compared with practicable (meaning real-life devices) 802.11b effective isotropic-radiated-power (EIRP) values of +15 to +19 dBm.

Another possible error arises from choosing an incorrect path-loss coefficient (N). This error can lead to an assumption that 802.11b solutions have a range of 100 meters with +15-dBm EIRP. Using those numbers, we can calculate that the N used in the 802.11b calculations was approximately 2.535 (see Equation 2). This is less than the ITU's recommended figure of three.

(2) 

However, by using the EIRP values quoted from published papers, together with the ITU reference model and path-loss coefficient N = 3, the maximum theoretical range of an 802.11b network operating at the maximum EIRP of 30 dBm is 154 meters, declining significantly at an EIRP of +19 dBm to 66.4 meters, then to 48.4 meters at +15 dBm.

The same analysis also uses N = 3 in its 802.11a calculations, resulting in an 802.11a range calculation that appears to be very small next to that of 802.11b. However, as mentioned above, the ITU recommends N = 3.1 for 802.11a calculations. When those ITU-recommended figures are used, the range of 802.1 la improves, relative to 802.11b, giving 54 Mbps at a distance of 14 meters, down to 6 Mbps at 51 meters.

In addition, conventional 802.11a WLANs transmit at + 18-dBm EIRP, while an optimized solution can transmit at +23 dBm, thereby extending the range to 30 meters at 54 Mbps and 108 meters at 6 Mbps.

Note 

If you have a WLAN running at a full 11 or 56 Mbps (sending, receiving) and there is only one user connected, then that user will get the whole 11 or 56 Mbps; two or more simultaneous users must share that bandwidth. Note that this is not the number of users connected to the WLAN-you could have 50 WLAN users within range of the AP and if none of them are sending or receiving data then very little bandwidth will be utilized; they must be sending or receiving data at the same time to slow the resource down. Also, the further a WLAN user gets from the AP, or if there are physical structures in the way, the connection speed drops for "falls back." In the case of 11b APs, the speed falls back from 11 Mbps to 5.5 Mbps to 2 Mbps. A similar fall back occurs with 11a APs. Since there is also a certain amount of overhead required to process the data traversing the airwaves (e.g. encrypting, sending, receiving, and decrypting), an 11b WLAN's speed could top out at 5 or 6 Mbps and an 11a network's speed could be limited to less than 32 Mbps.

Interoperability

Interoperability provides the assurance of backward compatibility with existing equipment, as well as a future migration path to any new technology that might be purchased in the future. Thanks to IEEE and the Wi-Fi Alliance, interoperability is a non-issue. Without these two organizations and the participation of the wireless networking industry en mass, 802.11 technology would probably never have taken off. As long as you buy gear that carries the Wi-Fi Alliance's "Wi-Fi" brand, you are golden as far as interoperability is concerned. The vast majority of each specification's WLAN gear is capable of inter-operating with products from competing vendors, without the need of any special engineering support to make them work together. (Of course, 802.11b products can't interoperate with 802.11a products or vice versa.)

There are exceptions, of course, especially in the "Smart" AP arena because of the proprietary technology used to provided additional features and functionality such as Quality of Service, security, management, etc.

Global Spectrum Unification

Although both 802.11b and 802.11a have been on the books since September 1999, only 802.11b has been accepted globally. 802.1 la has run into 5 GHz band allocation and regulation disputes in several countries. Multi-national companies and international travelers must take these issues under consideration when considering which wireless technology to purchase. (802.11g also is expected to run into quite a few roadblocks on its way to global acceptance.) This means that only 802.11b devices comply with virtually all local regulatory standards, and thus 11b devices are the only devices that are legal to operate throughout most of the world.

Such global spectrum unification issues are not a problem for solutions contained within a single country. But if a multi-national company or international traveler opts for 802.11a (or 802.11g) for their wireless networking technology, they may be required to purchase different devices or maintain different networks in order to adhere to individual country's regulations.

click to expand
Figure 7.5: A general view of the 5 GHz worldwide spectrum allocation and authorized transmit power as of 4/01/02.

click to expand
Figure 7.6: The international regulatory standards to which all 802.11 devices must adhere.

For more information on Wi-Fi's regulatory restrictions see Appendix III: Regulatory Specifics re Wi-Fi.

The Cost Differential

Current list prices have 802.11a components at about 25% higher than 802.11b equipment. Furthermore, in the typical WLAN layout, 802.11a networks require many more access points than an 802.11b network. Thus, if costs are a concern, and your network isn't hosting bandwidth intensive applications such as large schematics or streaming media, you should probably look into 802.11b. However, 802.11a can provide a WLAN with enough capacity for growth-not only in the user base, but also in the inevitable bandwidth-hungry applications of the future.

Eventually, the price gap between 802.11a and 802.11b will shrink with economies of scale. In addition, many wireless chipset suppliers have announced dual-mode 802.11a/b chipsets, and wireless NIC vendors are releasing dual-mode NICs. Thus, similar to the 10/100Mbps Ethernet gear, single-priced, dual 802.11a/b gear should become commonplace, with one set of gear being used for both types of networks-802.11a and 802.11b.

Existing Installations

Because there is no provision for interoperability between 802.11a and 802.11b, it's often not cost-effective for companies with an existing 802.11b WLAN to migrate to 802.11a. Also, some industry experts feel that since 802.11g has been finalized, for those that need to upgrade an 11b WLAN, 11g will be the better upgrade path. In such an instance, 802.11b vendors will provide a simple firmware upgrade so that 802.11b gear can become 802.11g gear. But remember that 802.11g is still limited by many of the same issues plaguing 802.11b, e.g. three nonoverlapping channels and frequency interference.



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Going Wi-Fi. A Practical Guide to Planning and Building an 802.11 Network
Going Wi-Fi: A Practical Guide to Planning and Building an 802.11 Network
ISBN: 1578203015
EAN: 2147483647
Year: 2003
Pages: 273

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