Research Article Capacity of 60GHz Wireless...

Research ArticleCapacity of 60 GHz Wireless Communications Based on QAM

Jingjing Wang12 Na Li3 Wei Shi4 Yangyang Ma1 Xiulong Liang1 and Xinli Dong5

1 College of Information Science amp Technology Qingdao University of Science amp Technology Qingdao Shandong 266061 China2 State Key Laboratory of Millimeter Waves Southeast University Nanjing Jiangsu 210096 China3 School of Information and Communication Engineering Beijing University of Posts and TelecommunicationsBeijing 100876 China

4Department of Electrical Engineering Ocean University of China Qingdao Shandong 266100 China5 China United Network Communications Corporation Qingdao Branch Qingdao Shandong 266072 China

Correspondence should be addressed to Jingjing Wang kathy1003163com

Received 24 January 2014 Accepted 2 April 2014 Published 29 April 2014

Academic Editor Feng Gao

Copyright copy 2014 Jingjing Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

With apparent advantages of the several GHz license-free spectrums 10Wmaximum transmit power and so forth 60GHzwirelesscommunication technology has become the first choice for Gbps level short-range wireless communicationsThis paper researches60GHz wireless communications over the additive white Gaussian noise channel Channel capacity with quadrature amplitudemodulation (QAM) is investigated for the unlicensed 59ndash64GHz radio spectrum set aside by FCC Moreover the capacity withQAM is compared to that with phase shift keying (PSK) It is shown that QAM is capable of providing Gbps data rate andoutperforms PSK especially when the modulation order is large The results prove that QAM is an attractive scheme for 60GHzwireless communications

1 Introduction

The growth of wireless communications is spurred by theconsumer desire for untethered access to information andentertainmentWhile contemporary unlicensed systems sup-port light and moderate levels of wireless data traffic asseen in Bluetooth and wireless local area networks (WLANs)current technology is unable to supply data rates compa-rable to wired standards like gigabit Ethernet and High-Definition Multimedia Interface (HDMI) [1] An abundanceof unlicensed spectrum surrounding the 60GHz operatingfrequency has the ability to support these high-rate commu-nications

The 60GHz band is an excellent choice for high-speedInternet data and voice communications since it offersbenefits such as several GHz license-free spectrums 10Wmaximum transmit power virtually interference-free opera-tion high level of frequency reuse enabled and highly secureoperation [2] However the 60G wireless channel shows20 to 40 dB increased free space path loss and suffers from15 (up to 30) dBkm atmospheric absorption depending on

the atmospheric conditions Multipath effects except forindoor reflections are vastly reduced at 60G making non-line-of-sight (NLOS) communication very difficult [1 3]While the high path loss seems to be disadvantage at 60GHzit however confines the 60GHz operation to within a roomin an indoor environment Hence the effective interferencelevels for 60GHz are less severe than those systems locatedin the congested 2ndash25GHz and 5ndash58GHz regions [2] Theoxygen absorption also enables higher ldquofrequency reuserdquosince radiation from one particular 60GHz radio link isquickly reduced to a level that will not interfere with other60GHz links operating in the same geographic vicinity [3]Federal Communications Commission (FCC) set aside the59ndash64GHz frequency band for general unlicensed applica-tions [4] The effect of the antenna directionality to 60GHzchannel capacity is studied in [5] The throughput of wirelessmobile ad hoc networks with directional antennas at 60GHzunlicensed band is investigated in [6]The capacity analysis of60GHz wireless communications based on PSK modulationis given in [7 8] Quadrature amplitude modulation (QAM)is widely used for the high-speed data transmission [9ndash11]

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 815617 5 pageshttpdxdoiorg1011552014815617

2 Journal of Applied Mathematics

Compared with other digital modulation techniques like PSKor PAMQAMmodulation has better anti-noise performanceand could make full use of the bandwidth

In this paper we investigate the capacity of 60GHz wire-less communication system over AGWN channel under theFCC rulesThemajormodulationmethod used here is QAMand capacity comparison between QAM and PSK is also sim-ply illustrated The rest of the paper is organized as followsSection 2 presents the general used QAM constellations andmakes a comparison between two different constellations for8-QAM Section 3 calculates channel capacity over AWGNchannel in 60GHzwireless communication system Section 4conducts Monte Carlo simulations to illustrate the channelcapacity And Section 5 gives a conclusion

2 QAM Constellations

QAM can be viewed as combined amplitude and phasemodulation When the requirement of data transfer rateexceeds the upper limit 8-PSK can provide QAM is generallyused Because the QAM constellation points are much moredisperse than PSK constellation points and the distancesbetween the constellation points are much bigger with thesame ary So QAM modulation could provide a bettertransmission performance

QAM signal waveforms may be expressed as [10]

119878119898(119905) = 119860

119898119888119892 (119905) cos 2120587119891

119888119905 minus 119860119898119904119892 (119905) sin 2120587119891

119888119905 (1)

where 119860119898119888

and 119860119898119904

are the information-bearing signalamplitudes of the quadrature carriers and 119892(119905) is the signalpulse The vector representation of these waveforms is

119878119898= [119860119898119888radic

1

2

120576119892

119860119898119904radic

1

2

120576119892] (2)

where 120576119892is the energy of the basic signal pulse 119892(119905)

M-QAM constellations can be constructed in manydifferent ways and they have different capacity and errorcharacteristics Although rectangular circle and star signalconstellations are common in practice a certain kind of con-stellation can be designed to achieve the best communicationperformance under some specific premises [12 13]

Figures 1 and 2 present two 8-QAM constellationsFigure 1 is a rectangular 8-QAM constellation and Figure 2is a circular 8-QAM constellation

Assuming that the signal points are equally probable theaverage transmitted signal power is [4]

119875av =1

119872

119872

sum

119898=1

(119860

2

119898119888+ 119860

2

119898119904) =

119860

2

119872

119872

sum

119898=1

(119886

2

119898119888+ 119886

2

119898119904) (3)

where (119886119898119888 119886119898119904) are the coordinates of the signal points

normalized by 119860

(1 1)(minus1 1)

(minus1 1)(minus1 minus1)(3 minus1)(minus3 minus1)

(minus3 1) (3 1)

Figure 1 Rectangular 8-QAM constellation

(1 1)(minus1 1)

(minus1 minus1)(1 minus1)

(minus1 minus (3) 0)

(0 1 + (3))

(1 + (3) 0)

(0 minus1 minus (3))

sqrt

sqrt

sqrt

sqrt

Figure 2 Circle 8-QAM constellation

As can be seen from the above figures the minimumdistances between the constellation points for (119886) and (119887) arerespectively

119889119886= 2

radic

1

6

119889119887= 2radic

1

3 + radic3

(4)

Comparing both

Ratio =

119889119887

119889119886

= radic

6

3 + radic3

asymp 1126

RatiodB = 20 log (1126) asymp 103

(5)

Minimum distance of signal set shown in Figure 1 isapproximately 1 dB less than that shown in Figure 4 withthe same average transmitted power The more the distancebetween the constellations the less the chance of a constel-lation point getting decoded incorrectly Actually the secondsignal constellation is the optimal one for 8-QAM because ithas the largest minimum Euclidean distance between signalpoints for a given transmitted power At the same time asshown in Figure 5 signal set with the circle constellation for8-QAM provides a higher data rate

Rectangular QAM signal constellations have distinctadvantage of being easily generated and transmitted astwo PAM signals impressed on phase-quadrature carriersIn addition they are easily demodulated Although it is

Journal of Applied Mathematics 3

minus40 minus30 minus20 minus10 0 10 20 30 400

1

2

3

4

5

6

SNR per bit (dB)

C (b

psH

z)

4-QAM8-QAM16-QAM

32-QAM64-QAM

Figure 3 Channel capacity of 119872-ary QAM system over AGWNchannels

C (b

psH

z)

0 10 20 30 400

1

2

3

4

5

6

7

SNR per bit (dB)

8-PSK8-QAM16-PSK

16-QAM64-PSK64-QAM

minus20 minus10

Figure 4 Relations between capacities of 119872-ary PSK and QAMwith the same average power

generally a sub-optimal modulation scheme compared toother 119872-QAM constellations in the sense that they do notmaximally space the constellation points for a given energyFor 119872 ge 16 the minimum distance required to achievea given average transmitted power is only slightly smallerthan the minimum distance required for the optimal 119872-ary

C (b

psH

z)

0 2 4 6 8 100

1

05

15

2

25

3

SNR per bit (dB)

Rectangular 8-QAMCircular 8-QAM

minus10 minus8 minus6 minus4 minus2

Figure 5 Capacity comparison between two different 8-QAMsignal constellations

QAM signal constellation For these reasons rectangular119872-ary QAM signals are most frequently used in practice [10]And they are also adopted in this paper

3 Channel Capacity

In general the channel capacity is a function of the channelrealization transmitted signal power and noise For AWGNchannel the shannon capacity is normalized with respect tothe bandwidth and expressed in bps that is normalized withrespect to the bandwidth is

119862 = 119882log2(1 + SNR) (6)

where 119882 is the system band width and SNR is the receivesignal to noise ratio defined by 120576

1198871198730 where 120576

119887is the energy

per bit [9]The Shannon capacity predicts the channel capacity 119862

for an AWGN channel with continuous-valued inputs andoutputs However a channel employing multilevelphasemodulation for example PAM PSK or QAM modulationhas discrete-valued inputs and continuous-valued outputswhich impose an additional constraint on the capacity cal-culation [10]

We consider themodulation channels with discrete-input119883 and continuous-output 119884 which is defined as [7 9]

119884 = 119883 +119882 (7)

where 119882 is a zero-mean Gaussian random variable withvariance 120590

2 and 119883 = 119909119896 119896 = 0 119902 minus 1 For a given 119883

it follows that 119884 is Gaussian with mean 119909119896and variance 1205902

That is

119901(

119910

119909119896

) =

1

radic2120587120590

119890

minus(119910minus119909119896)221205902

(8)


The capacity of this channel in bits per channel use is themaximum average mutual information between the discreteinput 119883 = 119909

0 1199091 119909

119902minus1 and the output 119884 = minusinfininfin

That is

119862 = max119901(119909119894)

119902minus1

sum

119894=0

int

infin

minusinfin

119901 (119910 | 119909119894) 119901 (119909

119894) log2

119901 (119910 | 119909119894)

119901 (119910)

119889119910 (9)

where

119901 (119910) =

119902minus1

sum

119896=0

119901 (119910 | 119909119896) 119901 (119909

119896) (10)

Assuming an equal a priori probability real or complexsignal constellation that is 119901(119909

119894) = 1119902 the channel capacity

of an AWGN channel with 119902-ary modulation is then [10]

119862 = log2(119902) minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

sum

119902minus1

119894=0119901 (119910 | 119909

119894)

119901 (119910 | 119909119896)

= log2(119902)

minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

119902minus1

sum

119894=0

exp[minus1003816100381610038161003816

119909119896+ 119908 minus 119909

119894

1003816100381610038161003816

2

minus |119908|

2

2120590

2]

(11)

where E[sdot] is the expected value operator and119908 is the complexwhite Gaussian noise modeled as a Gaussian distributedrandom variable with zero mean and variance 1205902 in each realdimension Equation (11) is a universal formula applied to 119902-ary PAMPSKQAM and can be evaluated by Monte Carlosimulation With normalized signal energy the relationshipsbetween channel capacity and SNR can be evaluated by (11)

4 Experimental Results and Analysis

In this paper Monte Carlo simulations are conducted topresent the channel capacity of 60GHz over AWGN channelsunder FCC regulations

Figure 3 shows the normalized channel capacity for 119872-ary QAM system over AGWN channels It is shown that theachievable data rate is 842Gbps for a 60GHz with 5GHzbandwidth at a SNR of 0 dB for 8-QAM system And for16-QAM and 64-QAM the data rate can be 1114Gbps and1319Gbps Hence QAM has potential to support Gbps datatransmission in the 60GHz system

Figure 4 shows comparison of channel capacities for 119872-ary PSK andQAMsystemswith the same average transmittedpower It shows that the data rate for 119872-QAM is higherthan that for 119872-PSK especially when 119872 gt 8 For 16-QAMthe data rate can improve 68 at a SNR of 0 dB and for64-QAM the improvement can reach 141 That is to sayQAM can achieve a higher data rate even at a lower SNRWe can conclude from this figure that when119872 gt 8 capacityperformance of theQAMsystem is better than that of the PSKsystemThe superiority of QAM is obvious because it has thelargest minimum Euclidean distance between signal pointsfor a given transmitted power

Figure 5 demonstrates the difference among channelcapacities for different119872-QAM constellations It shows thatfor 8-QAM the circle constellation provides a higher datarate This confirms our analysis in Section 2 Moreover thecapacity advantage of QAM with circle constellation overthat with rectangular constellation is quite small whereasthe latter is much easier to implement in practice Hencerectangular QAMmodulation is more preferable for 60GHzwireless communications

5 Conclusions

PSK is the common used modulation for 60GHz currentlybecause of its advantages in bandwidth and SNR Howeverthe data rate for 119872-PSK is obviously lower than that of 119872-QAM with the same average transmitted power Moreoveras 119872 increases the distance between the adjacent phasesgradually decreases which reduces the noise tolerance andmakes it difficult to guarantee the error rate while QAM canimprove the noise tolerance and provide a lower error rate

For119872-QAM many different signal constellations can bedesigned and conducted fromwhichwe can select an optimalone to meet our specific requirements in 60GHz wirelesscommunication

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the referees and edi-tors for providing very helpful comments and suggestionsThis project was supported by Key Laboratory of Univer-sal Wireless Communications (Beijing University of Postsand Telecommunications) Ministry of Education China(no KFKT-2013102) National Natural Science Foundationof China (no 61304222) Natural Science Foundation ofShandong Province (no ZR2012FQ021) Shandong ProvinceHigher Educational Science and Technology Program (noJ12LN88) and Open Project of State Key Laboratory ofMillimeter Waves (no K201321)

References

[1] R C Daniels and R W Heath Jr ldquo60 GHz wireless communi-cations emerging requirements and design recommendationsrdquoIEEE Vehicular Technology Magazine vol 2 no 3 pp 41ndash502007

[2] P Cheolhee and T S Rappaport ldquoShort-range wireless com-munications for next-generation networks UWB 60 GHzmillimeter-wave wpan and ZigBeerdquo IEEE Wireless Communi-cations vol 14 no 4 pp 70ndash78 2007

[3] S K Yong and C-C Chong ldquoAn overview of multigigabitwireless through millimeter wave technology potentials andtechnical challengesrdquo Eurasip Journal on Wireless Communica-tions and Networking vol 2007 Article ID 78907 2007


[4] Federal Communications Commission Amendment of Parts 215 and 97 of the Commissionrsquos Rules To Permit Use of RadioFrequencies above 40 GHz For New Radio Applications 1995

[5] A Seyedi ldquoOn the capacity of wideband 60GHz channels withantenna directionalityrdquo in Proceedings of the 50th Annual IEEEGlobal Telecommunications Conference (GLOBECOM rsquo07) pp4532ndash4536 November 2007

[6] M Alimadadi A Mohammadi and M D Soltani ldquoThrough-put analysis of Ad-Hoc networks with directional antenna at60GHzrdquo Journal of ElectromagneticWaves and Applications vol28 no 2 pp 228ndash241 2014

[7] H Zhang andTAGulliver ldquoOn the capacity of 60GHzwirelesscommunicationsrdquo in Proceedings of the Canadian Conference onElectrical and Computer Engineering (CCECE rsquo09) pp 936ndash939May 2009

[8] J Wang H Zhang T Lv and G T Aaron ldquoCapacity of 60 GHzwireless communication systems over fading channelsrdquo Journalof Networks vol 7 no 1 pp 203ndash209 2012

[9] K ChrisThe Benefits of 60 GHz Unlicensed Wireless Communi-cations YDI Wireless Whitepaper 2002

[10] J G Proakis Digital Communications Publishing House ofElectronics Industry 2006

[11] H Zhang and T A Gulliver ldquoCapacity and error probabilityanalysis for orthogonal space-time block codes over fadingchannelsrdquo IEEE Transactions on Wireless Communications vol4 no 2 pp 808ndash819 2005

[12] G J Foschini R D Gitlin and S B Weinstein ldquoOptimizationof two-dimensional signal constellations in the presence ofGaussian noiserdquo IEEE Transactions on Communications vol 22no 1 pp 28ndash38 1974

[13] C-E W Sundberg W C Wong and R Steele ldquoLogarithmicPCMweighted QAM transmission over Gaussian and Rayleighfading channelsrdquo IEE Proceedings F Communications Radarand Signal Processing vol 134 no 6 pp 557ndash570 1987

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Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Compared with other digital modulation techniques like PSKor PAMQAMmodulation has better anti-noise performanceand could make full use of the bandwidth

In this paper we investigate the capacity of 60GHz wire-less communication system over AGWN channel under theFCC rulesThemajormodulationmethod used here is QAMand capacity comparison between QAM and PSK is also sim-ply illustrated The rest of the paper is organized as followsSection 2 presents the general used QAM constellations andmakes a comparison between two different constellations for8-QAM Section 3 calculates channel capacity over AWGNchannel in 60GHzwireless communication system Section 4conducts Monte Carlo simulations to illustrate the channelcapacity And Section 5 gives a conclusion

2 QAM Constellations

QAM can be viewed as combined amplitude and phasemodulation When the requirement of data transfer rateexceeds the upper limit 8-PSK can provide QAM is generallyused Because the QAM constellation points are much moredisperse than PSK constellation points and the distancesbetween the constellation points are much bigger with thesame ary So QAM modulation could provide a bettertransmission performance

QAM signal waveforms may be expressed as [10]

119878119898(119905) = 119860

119898119888119892 (119905) cos 2120587119891

119888119905 minus 119860119898119904119892 (119905) sin 2120587119891

119888119905 (1)

where 119860119898119888

and 119860119898119904

are the information-bearing signalamplitudes of the quadrature carriers and 119892(119905) is the signalpulse The vector representation of these waveforms is

119878119898= [119860119898119888radic

1

2

120576119892

119860119898119904radic

1

2

120576119892] (2)

where 120576119892is the energy of the basic signal pulse 119892(119905)

M-QAM constellations can be constructed in manydifferent ways and they have different capacity and errorcharacteristics Although rectangular circle and star signalconstellations are common in practice a certain kind of con-stellation can be designed to achieve the best communicationperformance under some specific premises [12 13]

Figures 1 and 2 present two 8-QAM constellationsFigure 1 is a rectangular 8-QAM constellation and Figure 2is a circular 8-QAM constellation

Assuming that the signal points are equally probable theaverage transmitted signal power is [4]

119875av =1

119872

119872

sum

119898=1

(119860

2

119898119888+ 119860

2

119898119904) =

119860

2

119872

119872

sum

119898=1

(119886

2

119898119888+ 119886

2

119898119904) (3)

where (119886119898119888 119886119898119904) are the coordinates of the signal points

normalized by 119860

(1 1)(minus1 1)

(minus1 1)(minus1 minus1)(3 minus1)(minus3 minus1)

(minus3 1) (3 1)

Figure 1 Rectangular 8-QAM constellation

(1 1)(minus1 1)

(minus1 minus1)(1 minus1)

(minus1 minus (3) 0)

(0 1 + (3))

(1 + (3) 0)

(0 minus1 minus (3))

sqrt

sqrt

sqrt

sqrt

Figure 2 Circle 8-QAM constellation

As can be seen from the above figures the minimumdistances between the constellation points for (119886) and (119887) arerespectively

119889119886= 2

radic

1

6

119889119887= 2radic

1

3 + radic3

(4)

Comparing both

Ratio =

119889119887

119889119886

= radic

6

3 + radic3

asymp 1126

RatiodB = 20 log (1126) asymp 103

(5)

Minimum distance of signal set shown in Figure 1 isapproximately 1 dB less than that shown in Figure 4 withthe same average transmitted power The more the distancebetween the constellations the less the chance of a constel-lation point getting decoded incorrectly Actually the secondsignal constellation is the optimal one for 8-QAM because ithas the largest minimum Euclidean distance between signalpoints for a given transmitted power At the same time asshown in Figure 5 signal set with the circle constellation for8-QAM provides a higher data rate

Rectangular QAM signal constellations have distinctadvantage of being easily generated and transmitted astwo PAM signals impressed on phase-quadrature carriersIn addition they are easily demodulated Although it is



1

2

3

4

5

6

SNR per bit (dB)

C (b

psH

z)

4-QAM8-QAM16-QAM

32-QAM64-QAM


C (b

psH

z)

0 10 20 30 400

1

2

3

4

5

6

7

SNR per bit (dB)

8-PSK8-QAM16-PSK

16-QAM64-PSK64-QAM

minus20 minus10



C (b

psH

z)

0 2 4 6 8 100

1

05

15

2

25

3

SNR per bit (dB)





3 Channel Capacity


119862 = 119882log2(1 + SNR) (6)


1198871198730 where 120576

119887is the energy




119884 = 119883 +119882 (7)




That is

119901(

119910

119909119896

) =

1

radic2120587120590

119890

minus(119910minus119909119896)221205902

(8)



0 1199091 119909


That is

119862 = max119901(119909119894)

119902minus1

sum

119894=0

int

infin

minusinfin

119901 (119910 | 119909119894) 119901 (119909

119894) log2

119901 (119910 | 119909119894)

119901 (119910)

119889119910 (9)

where

119901 (119910) =

119902minus1

sum

119896=0

119901 (119910 | 119909119896) 119901 (119909

119896) (10)




119862 = log2(119902) minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

sum

119902minus1

119894=0119901 (119910 | 119909

119894)

119901 (119910 | 119909119896)

= log2(119902)

minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

119902minus1

sum

119894=0

exp[minus1003816100381610038161003816

119909119896+ 119908 minus 119909

119894

1003816100381610038161003816

2

minus |119908|

2

2120590

2]

(11)







5 Conclusions





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1

2

3

4

5

6

SNR per bit (dB)

C (b

psH

z)

4-QAM8-QAM16-QAM

32-QAM64-QAM


C (b

psH

z)

0 10 20 30 400

1

2

3

4

5

6

7

SNR per bit (dB)

8-PSK8-QAM16-PSK

16-QAM64-PSK64-QAM

minus20 minus10



C (b

psH

z)

0 2 4 6 8 100

1

05

15

2

25

3

SNR per bit (dB)





3 Channel Capacity


119862 = 119882log2(1 + SNR) (6)


1198871198730 where 120576

119887is the energy




119884 = 119883 +119882 (7)




That is

119901(

119910

119909119896

) =

1

radic2120587120590

119890

minus(119910minus119909119896)221205902

(8)



0 1199091 119909


That is

119862 = max119901(119909119894)

119902minus1

sum

119894=0

int

infin

minusinfin

119901 (119910 | 119909119894) 119901 (119909

119894) log2

119901 (119910 | 119909119894)

119901 (119910)

119889119910 (9)

where

119901 (119910) =

119902minus1

sum

119896=0

119901 (119910 | 119909119896) 119901 (119909

119896) (10)




119862 = log2(119902) minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

sum

119902minus1

119894=0119901 (119910 | 119909

119894)

119901 (119910 | 119909119896)

= log2(119902)

minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

119902minus1

sum

119894=0

exp[minus1003816100381610038161003816

119909119896+ 119908 minus 119909

119894

1003816100381610038161003816

2

minus |119908|

2

2120590

2]

(11)







5 Conclusions





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0 1199091 119909


That is

119862 = max119901(119909119894)

119902minus1

sum

119894=0

int

infin

minusinfin

119901 (119910 | 119909119894) 119901 (119909

119894) log2

119901 (119910 | 119909119894)

119901 (119910)

119889119910 (9)

where

119901 (119910) =

119902minus1

sum

119896=0

119901 (119910 | 119909119896) 119901 (119909

119896) (10)




119862 = log2(119902) minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

sum

119902minus1

119894=0119901 (119910 | 119909

119894)

119901 (119910 | 119909119896)

= log2(119902)

minus

1

119902

119902minus1

sum

119896=0

E119910|119909119896

log2

119902minus1

sum

119894=0

exp[minus1003816100381610038161003816

119909119896+ 119908 minus 119909

119894

1003816100381610038161003816

2

minus |119908|

2

2120590

2]

(11)







5 Conclusions





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Capacity of 60GHz Wireless...

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