paper 2013 multiple input multiple output system

7/30/2019 Paper 2013 Multiple Input Multiple Output System

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IEEE Antennas and Propagation Magazine, Vol. 55, No. 1, February 2013 253

Multiple-Input Multiple-Output SystemCapacity: Antenna and Propagation Aspects

Hakan nanolu

Qualcomm Technologies, Inc.90 Central Street, Boxborough, MA, 01719, USA

E-mail: [email protected]

Abstract

This tutorial aims to review some of the system and measurement work done at Qualcomm related to multiple-input-multiple-output (MIMO) systems around the 2000-2005 timeframe. During the same period, Qualcomm was activelyinvolved in the development of the MIMO technology adopted by IEEE 802.11n. In this tutorial, we show the spectralefciency and physical-layer (PHY) data rates that can be reached with Qualcomms MIMO technology using practical8 x 8 and 16 x 16 antenna arrays mounted on a laptop. The results are based on measurements performed inQualcomms New England ofces. We show that very high data rates can be achieved for an ofce deployment. Theresults were compared with the simulated results obtained with IEEE802.11n MIMO channel models, and a good matchwas observed with channel model E.

Keywords: Wireless communication systems; SISO; MIMO; IEEE 802.11n; system capacity; channel modeling; indoor channel modeling; correlation; cross-correlation; OFDM; WLAN; modulation; fading; signal; noise; SNR; slot antennas

1. Introduction

T he paper published in 1998 by G. J. Foschini and M. J.Gans [1] showed the potential for a signi cant increase inwireless channel capacity when multiple-input multiple-output(MIMO) techniques are employed in a radio propagation envi-ronment rich with scatter. The theoretical results indicated thatthe channel capacity increases proportionally with the number of transmitting and receiving antennas. The theoretical

boundaries of a wireless communication system using MIMOtechniques published in [1] showed that one can achieve n times more bits/cycle throughput than Shannons classicalformula for each 3 dB increase in signal-to-noise ratio (SNR),

where n is the number of antenna elements at both the trans-mitter and the receiver. Although the theoretical capacity lim itsof MIMO systems were studied in [1] for Rayleigh-fadingchannels, the paper did not elaborate on the possible losses dueto channel and antenna correlation.

In [2], Espax and Boutros simulated capacity and outage probability in a at-fading channel with antenna correlation.In their study, they concluded that the presence of signi cantantenna correlation can result in substantial capacity reduc tionswhen compared to the independent and identically dis tributed(iid) case. They also explained that decreased capacity resultedfrom a reduced set of viable spatial modes, and they suggested

new power-allocation techniques to recover some of the losses.

Similar studies can be found in [3-11].

Many measurements were performed to understand the propagation channel and capacity that can be achieved inrealistic deployments. Spatial-correlation properties of a pico-cell environment were measured in [12]. The spatial correla tionmatrix and Doppler power spectrum were derived from themeasurements for a 4 4 antenna array. The measure mentsconcluded that 0.4 separation between the elements of theantenna array was suf cient to minimize correlation. Astochastic MIMO radio-channel model and its experimentalvalidation were also presented in [13] for a 4 4 antenna array.The measurement results presented in [13] were utilized inIEEE 802.11n channel modeling that is covered in this tuto rial.The MIMO capacity for an indoor of ce environment wasmeasured in [14], with 4 4 antenna arrays of 2 and 4 antenna spacings at both transmitter and receiver. Themeasurement results in [14] showed that the 2 case had aslightly higher capacity than the 4 case. The impact of theantenna correlation on the MIMO channel capacity was alsoanalyzed in [15-17].

MIMO has also been an interesting topic for the IEEE Antennas and Propagation Magazine . The propagation andantenna aspects of MIMO systems were covered in [18-24].


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254 IEEE Antennas and Propagation Magazine, Vol. 55, No. 1, February 2013

The promising theoretical and measured capacity gainsafforded using MIMO were the main motivations for the work started in Qualcomms New England of ce (QNE) in 2001.The initial focus was to understand the capacity offered byMIMO systems for wide-area networks (WANs). The focuseventually shifted to small-cell indoor deployments, speci -cally targeting those outlined by the IEEE 802.11n standardeffort. The team performed indoor channel measurements usingan in-house-developed channel sounder that we will describein detail here. The channel sounder was utilized to measurethe MIMO channel, and to provide data to enable the channelcapacity to be estimated for several deployment sce narios using

practical antenna arrays. Qualcomm submitted a proposal for anOFDM-based MIMO transmitter/receiver spa tial-multiplexingtechnique to the 802.11n standards body. An end-to-endcommunication-system prototype, using FPGAs and discreteRF components, was developed based on the proposal. TheMIMO spatial-processing techniques, array-calibration, andrate-adaptation algorithms were all validated using the real-time prototype. In parallel with the prototype development,simulations were also performed to benchmark the performanceof the proposed techniques for the 802.11n MIMO channel

models. Details of these channel models are summarized in thistutorial, and a comparison of system throughput achieved onthe measured channels is provided. In addition, the capacity of 8 8 and 16 16 antenna arrays was measured for an of cedeployment, with printed slot-antenna arrays mounted on the

back of a laptop screen. Different polarization elements werecombined to explore the impact of polarization diversity onsystem performance.

2. MIMO System Capacity

If the signal and noise are independent, and the receivedsignal is the sum of the transmitted signal and the noise, thenthe rate of transmission, R , was given in [25] as

( ) ( ) R H y H n= , (1)

i.e., the entropy of the received signal, ( ) H y , less the entropyof the noise, ( ) H n . The channel capacity is

( ) ( )( )

max P x

C H y H n= . (2)

In wireless communication systems, the channel noise is treatedas an additive white Gaussian noise (AWGN) process. Thetransmitted signals are limited to an average power, P . Thereceived signals then have an average power of P N + , where N is the average noise power. The maximum entropy for thereceived signals occurs when they also form a white-noiseensemble, since this is the greatest possible entropy for a power P N + , and can be obtained by a suitable choice of the ensembleof transmitted signals, namely if they form a white-noiseensemble of power P .

The entropy of the received ensemble is then

( ) ( )2log 2 H y W e P N = + , (3)

where W is the information bandwidth, and the noise entropy is

( ) [ ]2log 2 H n W eN = . (4)

The channel capacity is

( ) ( ) 2log P N

C H y H n W N

+ = = (5)

2log 1 P

W N

= +

.

The channel SNR, P N in Equation (5), can also be written as

2 P

H N

= , (6)

where the normalized channel power-transfer characteristic is2 H , and is the average SNR. Using Equations (5) and (6),

the well-known standard formula for the Shannon capac ity asgiven in [26] is expressed in bits per second (bps):

( )22[bps] log 1C W H = + . (7)The capacity formula given in Equation (7) is for a single-inputsingle-output (SISO) channel. In a at-fading SISO channel, H is one-dimensional, and is expressed as a com plex scalar.

The channel capacity can also be normalized to the infor-mation bandwidth, W , and rewritten as

[ ] ( )22 bps Hz log 1 N C H = + . (8)The bandwidth-normalized channel capacity is equivalent tofrequency spectral ef ciency.

It is evident from Equation (7) that the capacity of a com-munication channel with additive white noise can be increasedeither by adding more information bandwidth, or by improvingthe average SNR, . The achievable capacity in wirelesscommunication systems is typically limited by practi cal limitsimposed on the usable bandwidth and transmitting power levels. Given these constraints, it is still possible to increasecapacity by exploiting the spatial structure of the communicationlink through the use of antenna arrays at both the transmitter and/or receiver. Additional spatial channels will increase thedimensionality of the channel response, H , given inEquation (8), from one-dimensional SISO to ( )min n m-dimensional MIMO.


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The capacity limits of wireless communication systems ina fading environment when using multiple antennas (MIMO)were studied by G. J. Foschini and M. J. Gans in [1]. InFoschinis paper, receiving diversity and transmitting diversity,which are special cases of MIMO antenna systems, were also

presented. In this tutorial, we will also cover the specialdiversity cases of MIMO antenna systems when the matrixchannel elements of H are Rayleigh. The Rayleigh channelmodel for an R T n n channel matrix, H , has normalindependent and identically distributed, complex, zero-mean,and unit variance entries x :

( ), ,1 2ij I ij Q ij H x jx= + . (9)

The SISO channel can be obtained by substituting 1i j= = inEquation (9). The normalized channel power-transfer charac-teristic for the SISO channel is then

( )2 2 212ij I Q H x x= + . (10)

Here, I x and Q x are independent, standard normal randomvariables. It can be shown that the sum of squares of k nor malrandom variables is distributed according to the chi-squareddistribution with k degrees of freedom, which is usu ally denoted

as 2k . The SISO channel spectral ef ciency is therefore

2 _ 2 2log 1 N SISOC = + . (11)

The spectral ef ciency for receiving diversity is obtained for Rn n= and 1T n = as

2 _ 2 2log 1 N RxDiv nC = + . (12)

The spectral ef ciency for transmitting diversity is obtained for 1 Rn = and T n n= as

( ) 2 _ 2 2log 1 N TxDiv nC n = + . (13)

The Rayleigh fading channel spectral ef ciency is shown inFigure 1 for 4 4, 8 8, and 16 16 MIMO antenna systemsfor 21 dB average received SNR. We also show the spectral

ef ciency of the 1 1 (SISO), 1 8 (transmit diversity), 8 1(receive diversity) for the same average SNR on the same g-ure, for comparison. The spectral ef ciencies of 4 4, 8 8,and 16 16 antenna systems are approximately 7, 14, and 29times more than for a 1 1 antenna system for 21 dB averagereceive SNR at the 95th percentile.

The same gure shows a small spectral-ef ciency gain for 1 8 transmitting and 8 1 receiving diversity con gura tions,compared to the 1 1, no-diversity case. It is obvious that thehigh ef ciency can only be achieved with increased antennason both the transmitter and receiver.

2.1 Qualcomm MIMO/OFDM System Designfor IEEE 802.11n

The promising capacity gures outlined above were themain motivation behind the MIMO work initiated at Qualcomm.

Based on the high theoretical MIMO capacity in aRayleigh channel, we proposed an orthogonal frequency-divi-sion-multiplexing- (OFDM) based MIMO system designed to802.11n standards. The discussion here assumes perfectknowledge of the channel at both the access point (AP) and user terminal (UT). The measurements taken in the QNE of cesshowed that the uplink and downlink channels were reciprocalin a time-division-duplex (TDD) 20 MHz deploy ment. Thetechnique that assumes perfect knowledge of the channel at thetransmitter will be referred to as full channel-state information(FCSI) in the remainder of the tutorial. The spatial multiplexingmodes are based on eigenvalue decompo sition of the channel.For the 802.11 OFDM waveform, this decomposition is

performed for each of the 48 data transmis sion subbands out of 64 total OFDM tones, where four tones are dedicated to pilottransmission, and the remaining 12 tones serve as frequencyguard bands, such that the set L of OFDM tone indices is

{ }1,....,6,8,....,20,22,....,26 L = . Let ( ) H be the MIMOchannel matrix that gives the coupling between the four transmitting and four receiving antennas for subband index :

( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )

1,1 1,2 1,3 1,4

2,1 2,2 2,3 2,4

3,1 3,2 3,3 3,4

4,1 4,2 4,3 4,4

h h h h

h h h h

h h h h

h h h h

H =( ) , (14)

Figure 1. The cumulative distribution of Rayleigh-fadedchannel spectral efciency for an average received SNR of 21 dB: blue dashed, 1 1; red dashed, 1 8; green dashed,8 1; blue solid, 4 4; red solid, 8 8; green solid, 16 16

(number of receiving antennas number of transmittingantennas).


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where ( ),i jh is the coupling between the jth transmitting andthe ith receiving antenna at subband , L .

One can compute the eigenvalue decomposition of the

channel correlation matrix, ( ) ( ) H H H , as follows:

( ) ( ) ( ) ( ) ( )= H H H H V V , (15)

where ( )V is the matrix the columns of which are eigenvec-tors of ( ) ( ) H H H ; ( ) is a diagonal matrix of the eigen-values of ( ) ( ) H H H for subband , the diagonal elementsof which are ( )i , 0 3i ; and H A denotes the conjugatetranspose of matrix A . ( )V is also a matrix of righteigenvectors in the singular-value decomposition of ( ) H ,given by ( ) ( ) ( ) ( )= H H U V , where ( ) is a diagonalmatrix containing the singular values of ( ) H , which are thesquare roots of the diagonal elements of ( ) , the eigenvaluesof ( ) ( ) H H H . The columns of ( )U are left eigenvectorsof ( ) H , and are also eigenvectors of ( ) ( ) H H H .

The eigenvalues are then ranked in order for each sub-

band, so that ( ) ( ) ( ) ( )0 1 2 3 . Let n denotethe vector containing the nth ranked eigenvalues for all 48subbands, L ( 0 3n ):

( ) ( ) ( )26 ,..., ( 22),..., 22 ,..., 26n n n n n = . (16)

Assume the receiver noise variance, 2 , is constant across theoperating band, and is known by the transmitter and receiver.

Dividing the eigenvalues by 2 yields the effective SNR asso-ciated with each eigenmode.

A narrowband at-fading MIMO system is modeled as

y = Hx + n , (17)

where y and x are the receiving and transmitting vectors,respectively, and H and n are the channel matrix and thenoise vector, respectively. The transmitting vector, x , for a4 4 MIMO system is

= x Vx . (18)

Here, x is a 41 vector of four independent baseband com plexdata streams. Equation (18) can be expanded as

11 12 13 141 1

21 22 23 242 2

31 32 33 343 3

41 42 43 444 4

v v v v x x

v v v v x x

v v v v x x

v v v v x x

=

. (19)

In Equation (19), 1 x , 2 x , 3 x , and 4 x are the symbols trans-mitted from the rst, second, third, and fourth antennas,respectively. Substituting Equation (18) into Equation (17), onecan observe the received vector as follows:

( ) ( ) ( ) ( ) ( ) ( )= + H y U V V x n . (20)

Since the eigenvector steering matrix is orthonormal, thereceived vector per subband is

( ) ( ) ( ) ( )= + y U x n . (21)

The transmitted data 1 x , 2 x , 3 x , and 4 x , are recovered on the

receiving end by multiplying the received vector by ( ) H U :

( ) ( ) ( ) ( ) ( ) ( ) ( )= + H H H U y U U x U n (22)

( ) ( ) ( )= + H x U n .

If the channel estimates at the receiver do not match the chan nelestimate used to compute the eigenvector steering matrix, V , atthe transmitter, there will be crosstalk (i.e., inter-streaminterference) between the eigenmodes, which degrades thereceived SNR on each of the modes. In time-division duplexsystems, this mismatch is caused when the uplink and downlink

channels are not reciprocal, i.e., H UpLink DownLink H H . In practice, factors that impact channel reciprocity includedifferences in the amplitudes and phases of the RF transmitter and receiver chains over the information bandwidth. Wedeveloped a calibration algorithm that effec tively removesthese imbalances and restores the channel capacity.

The details of the spatial processing technique describedabove can be found in [27-29].

In the next section, we will summarize the MIMO/OFDMsystem architecture based on transmitting and receiving spatial

processing, and provide details about the array-calibration procedure.

2.2 QNE MIMO/OFDM System Architecture

Qualcomm proposed the OFDM-based MIMO WLANmodem architecture shown in Figure 2 to the IEEE 802.11nstandards body. The key attributes of Qualcomms approachcan be summarized as follows:

Fully backward compatible with IEEE 802.11a,g

20 MHz bandwidth

Enhanced throughput and range for legacy stations


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Scalable MIMO architecture supporting up to four Tx/Rxantennas

Extended modulation and coding data rates.

The modulation schemes employed are backwardcompati ble with 802.11b,a,g. Additional code rates are intro-duced to provide additional spectral ef ciency, including theuse of 256 QAM. All modulation formats are coupled to spe-ci c code rates, as indicated in Table 1. The SNR ranges givenin the table are to maintain 1% or better frame error rate (FER).

The proposed spatial-processing technique relies on theeigenmode computations at both the access point and user terminal to derive spatial-multiplexing processing vectorsused on the forward and reverse links. However, in order tominimize spatial-mode crosstalk, the access point (AP) anduser terminal (UT) transmitting- and receiving-chain gain/

phase differences must be measured and compensated for ina calibration procedure, so that the channel on the forwardlink can be translated to reverse-link steering vectors with anassumption of reciprocal channels in the forward and reverse

links [30].

The user terminal and access point make channel esti-mates on the transmitted 48 tones during the eight-symbols-long MIMO portion of the frame, as shown in Figure 3. Theuser terminal transmits the calibration tones and saves the cur-rent measured values of the forward-link channel matrices. Theaccess point uses the calibration tones to make an esti mate of the reverse channel, r H , for each calibration tone. Once theuser terminal receives the reverse-channel r H matri ces, itcomputes the access-point and user-terminal cor rection factorsusing the saved forward-channel matrices. We assume that the

reverse- and forward-channel matrices are reciprocal, i.e.,T r f H H = , so that we have

( )T r UT f AP H K H K = , (23)

where UT K is a diagonal UT UT N N matrix the nonzero ele-ments of which give the ratio of the transmitting and receivingcomplex gains for each of the user-terminal ports, and AP K isthe similar diagonal matrix for the access point. Let UT and

AP denote the vectors that are the diagonal elements of the

UT K and AP K , respectively. The calibration technique deter-mines these adjustment vectors given measurements of theforward and reverse channels. The correction matrix, C , isthen given as follows:

11 12 13 14

21 22 23 24

31 32 33 34

41 42 43 44

T r

f

c c c c

c c c c H C

c c c c H c c c c

= =

. (24)

Figure 2. A generic block diagram of Qualcomms 802.11n modem proposal.

Table 1. The modulation and co de rate SNR boundaries.

SNR Range[dB]

[ ]

Code Rate ModulationSpectral

Efciency(bps/Hz)

0 1/2 BPSK 0.5

0 3.25 < 1/2 QPSK 1.0

3.25 6.0 < 3/4 QPSK 1.5

6.0 9.5 < 1/2 16QAM 2.0

9.5 11.2 < 5/8 16QAM 2.5

11.2 12.5 < 3/4 16QAM 3.0

12.5 16 < 7/12 64QAM 3.5

16 17 < 2/3 64QAM 4.0

17 18.5 < 3/4 64QAM 4.5

18.5 20 < 5/6 64QAM 5.0

20 24 < 3/4 256QAM 6.0

24 > 7/8 256QAM 7.0


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Figure 3. The frame structure for 8 8 channel sounding.

Figure 4. The cluster geometry of the IEEE 802.11TGnchannel model.

The access-point adjustment vector is the mean of the nor-malized rows of C , where the normalization consists of scal ingeach row such that the rst element is unity. The normal ized

row is therefore { }1 , 1,...,i ij i AP b c c j N = = , and the mean, AP , is the sum of the rows ib divided by UT N . The user-

terminal adjustment factors are then the means of the normalizedcolumns of C , where the jth column is normal ized by the ithelement of AP is the sum of these columns ib divided by

AP N .

An alternative calibration technique can also be found in[31].

3. IEEE 802.11 Indoor Channel Model

A set of indoor MIMO WLAN channel models were proposed by the IEEE 802.11 TGn channel-model task group[32]. The developed models are based on the cluster modelof Saleh and Valenzuela, given in [33]. The proposed channelmodels in the standards aim to cover the propagation envi-ronment from benign to challenging deployment scenarios,such that the performance of MIMO spatial-processing tech-niques and algorithms could be benchmarked. Although themodels do not address each individual deployment, in prac tice,a given deployment environment is expected to fall into oneof the channel-model categories that is covered by the channelmodels in the standard. The cluster-model geometry is shown inFigure 4. Figure 5. The two-antenna correlation model.

The channel response between the mth transmitting andnth receiving antennas is

( )( )

( )( )

2

1 1

, ,

m nkl kl j r r K L

nm kl kl m nk l kl kl

eh t a t

r r

+

= ==

+

( ) ( )mn mnTx kl Rx kl G G . (25)

Here, the kl a is the complex amplitude of the ray departing themth transmitting antenna with angle kl , re ected by the l thobject of the k th cluster and reaching the nth receiving antennawith arrival angle kl ; is the wavelength; and is the path-

loss factor. The ( )mnTx kl G and ( )mn Rx kl G are the transmittingand receiving antenna gains at the given angles. The channelresponse given in Equation (25) can be written as

( ) ( ) ( ), , ,h t h t h = , (26)

where t is time, and and are angle dependencies.


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We will derive the correlation between two receivingantennas separated far enough from a transmitter, as depicted inFigure 5, assuming that the channel doesnt vary in time, i.e.,

kl a is not a function of time.

Let ( )1 s t and ( )2 s t be the time-domain signals at tworeceiving antennas in Figure 5. If the two signals are comingfrom the same transmitter, the received signals can be written asfollows:

( ) ( )1 jkr e

s t a t r

= ,

(27)

( ) ( )( )

( )2

jk r r e s t b t

r r

+=

+.

If ( ) p , the power azimuth spectrum (PAS) is the probabil itydistribution function of the angle of arrival, , at the receiver,then the correlation between the two receiving antennas is

( ) ( ) ( ){ } ( )*1 2d s t s t p d

= . (28)

If the transmitting and receiving antennas are separated, i.e.,r r , this can be simpli ed as

( ) ( ) ( )( )

( )2 sin*

d j

d a t b t e p d

= . (29)

If ( ) p is uniformly distributed, then the above simpli esfurther to

( ) 0J 2d

d

= . (30)

If ( ) p is a truncated distribution for multiple clusters, thecorrelation in Equation (28) can be written as

( ) ( ) ( ){ } ( )0,

0,

*1 2

1

k k

k k

K

k d E s t s t P d

+

=

= . (31)

Equation (31) shows the cross correlation between the wavesimpinging on two antenna elements. It has been shown thatthe correlation coef cient, which is a function of the distance

between the antenna elements, depends on the power azimuthspectrum and on the radiation patterns of the antenna ele-ments. In the following study, we will assume an omnidirec-tional radiation pattern. This was shown in [34] to be the

best t to measured results in urban and rural areas. Thetruncated Laplacian power azimuth spectrum con ned within( 0 0 0 0, + ) is given as

( ) 0,,,1 ,

2exp

2

c N k L k L

L k k L k

Q P

=

=

( ) ( ){ }0, 0,k k k k + (32)

where ( ) is the step function, L is the standard devia tion,and c N is the number of clusters. The constant , L k Q are

derived such that ( ) L P ful lls the requirement of a probabil-ity distribution function, that is,

( ) ,,1

21 exp 1

c N k

L L k L k k

P d Q

=

= =

.(33)

After calculating , L k Q satisfying the condition given in Equa-

tion (33), the complex- eld cross-correlation function de nedin Equation (31) for a generic angular distribution function,

( ) P , for the Laplacian distribution, is given by

( ) ( ) xx XY R D jR D = + , (34)

where 2 D d = . The real and imaginary parts of the complex- eld cross-correlation functions are

( ) ( ) ( ), 2, 0 21 , 1 2

,

JJ 4

2 2(2 )

c N L k m xx L

k L k m

L k

Q D R D D

m

= == +

+

( ) ( )0, ,cos 2 ,

k m L k k m T , (35)

( ),, ,

22, exp k m L k k

L k L k T

= +

( ) ( ),

22 sin 2 cos 2k k

L k m m m

(36)

( ) ( ), 2 1, 21 , 0 2

,

J4

2 2(2 1)

c N L k m xy L

k L k m

L k

Q D R D

m

+

= ==

+ +

( ) ( )0, ,cos 2 1 ,k m L k k m E + , (37)

( ),, ,

22, exp k m L k k

L k L k E

=

( ) ( ) ( ),

22 1 sin 2 1 cos 2 1k k

L k m m m

+ + + +

.

(38)


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The combined correlation matrix can be generated from . .i i d H 1 Rx Tx N N matrix where its entries are independent and

identically distributed random variables:

{ }1/2 1/2. . . .Combined Tx Rx i i d TxRx i i d H R R H R H = = . (39)

Here, is the Kronecker product of the transmitter andreceiver correlation matrices. The MIMO channel transmittingand receiving correlation matrices and the Kronecker productare given by the following for 2 2 antenna arrays:

12

21

1

1

Tx

Tx Tx R

=

,

(40)

12

21

1

1

Rx

Rx Rx R

=

,

12 12 12 12

21 12 21 12

21 21 12 12

21 21 21 21

1

11

1

Rx Tx Tx Rx

Rx Tx Rx Tx

TxRx Tx Tx Rx Rx

Tx Rx Tx Rx

H

=

. (41)

The possible channel con gurations and cross correlations between two transmitting and two receiving antennas are shownin Figure 6. In this gure, ijh are the channel responses for

1, 2i = , and 1, 2 j = counts for the transmitting and receivingantennas. The cross correlations between the transmitting and

receiving antennas are depicted in the gure with Txij and Rxij

, which can be calculated from Equa tion (31).

The combined channel responses can be formulated interms of independent and identically distributed variables andthe cross correlation between the antennas as

12 12 12 1211 1

12 21 12 21 12 2

21 321 21 12 12

22 421 21 21 21

1

1

1

1

Rx Tx Tx Rx

Rx Tx Rx Tx

Tx Tx Rx Rx

Tx Rx Tx Rx

h x

h x

h x

h x

=

.

(42)

An example of an 802.11 TGn indoor MIMO channel model isshown in Table 2. The details of the other channel models, A,B, C, D, and F, are given in [32]. The correlation and channelmatrices given from Equations (31) to (40) were cal culated for each tap de ned in the table. The table also de nes the number of clusters, the taps in each cluster, and their angle of arrival(AoA), angle of departure (AoD), transmitting angle spread(TxAS), and receiving angle spread (RxAS).

The properties of the other TGn channel models are sum-marized in Table 3.

Figure 6. The 2 2 cross-correlation and channel model.

The fading characteristics of the indoor channels are verydifferent from the outdoor mobile channels. In indoor wirelesssystems, the transmitter and receiver are stationary, and peo ple

are moving in between them. In outdoor mobile systems, theuser terminal is often moving, which generates much higher Doppler frequency shifts. As a result, a new function, ( )S f ,has to be de ned for indoor environments in order to t theDoppler power-spectrum measurements. The ( )S f can beexpressed as

( ) 21

1d

S f f

A f

=

+

. (43)

Here, A is a constant used to de ne ( )0.1S f at a given fre-quency, d f , being the Doppler spread. The Doppler spread, d f , is de ned as

0d f

= , (44)

where 0 is the environmental speed, and is the wave length,de ned by

c

c

f = . (45)

Here, c is the speed of light, and c f is the carrier frequency.Doppler frequency shifts in indoor environments have beenobserved in the range up to approximately 6 Hz at a 5.25 GHzcenter frequency, and up to approximately 3 Hz at a 2.4 GHzcenter frequency. The measured Doppler power spectrum for asingle-delay tap, together with the bell shaped tting functionas de ned in Equation (41), are shown in Figure 7.

Alternative channel models, based on ray-tracing andhybrid techniques, can be found in [35] and [36].


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T a b

l e 2 . I E E E 8 0 2 . 1 1 T G n

C h a n n e l m o d e l

E .

T a p

I n d e x

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

1 8

E x c e s s

D e l a y

[ n s ]

0

1 0

2 0

3 0

5 0

8 0

1 1 0

1 4 0

1 8 0

2 3 0

2 8 0

3 3 0

3 8 0

4 3 0

4 9 0

5 6 0

6 4 0

7 3 0

P o w e r

[ d B ]

2

. 6

3

. 0

3

. 5

3

. 9

4

. 5

5

. 6

6

. 9

8

. 2

9

. 8

1 1

. 7

1 3 . 9

1 6

. 1

1 8

. 3

2 0

. 5

2 2

. 9

A o A

[ ]

1 6 3

. 7

1 6 3

. 7

1 6 3

. 7

1 6 3

. 7

1 6 3

. 7

1 6 3

. 7

1

6 3

. 7

1 6 3

. 7

1 6 3

. 7

1 6 3

. 7

1 6 3 . 7

1 6 3

. 7

1 6 3

. 7

1 6 3

. 7

1 6 3

. 7

A S [ ]

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

3 5

. 8

A o D

[ ]

1 0 5

. 6

1 0 5

. 6

1 0 5

. 6

1 0 5

. 6

1 0 5

. 6

1 0 5

. 6

1

0 5

. 6

1 0 5

. 6

1 0 5

. 6

1 0 5

. 6

1 0 5 . 6

1 0 5

. 6

1 0 5

. 6

1 0 5

. 6

1 0 5

. 6

A S [ ]

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

3 6

. 1

P o w e r

[ d B ]

1

. 8

3

. 2

4

. 5

5

. 8

7

. 1

9

. 9

1 0 . 3

1 4

. 3

1 4

. 7

1 8

. 7

1 9

. 9

2 2

. 4

A o A

[ ]

2 5 1

. 8

2 5 1

. 8

2

5 1

. 8

2 5 1

. 8

2 5 1

. 8

2 5 1

. 8

2 5 1 . 8

2 5 1

. 8

2 5 1

. 8

2 5 1

. 8

2 5 1

. 8

2 5 1

. 8

A S [ ]

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

4 1

. 6

A o D

[ ]

2 9 3

. 1

2 9 3

. 1

2

9 3

. 1

2 9 3

. 1

2 9 3

. 1

2 9 3

. 1

2 9 3 . 1

2 9 3

. 1

2 9 3

. 1

2 9 3

. 1

2 9 3

. 1

2 9 3

. 1

A S [ ]

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

4 2

. 5

P o w e r

[ d B ]

7

. 9

9

. 6

1 4 . 2

1 3

. 8

1 8

. 6

1 8

. 1

2 2

. 8

A o A

[ ]

8 0

. 0

8 0

. 0

8 0

. 0

8 0

. 0

8 0

. 0

8 0

. 0

8 0

. 0

A S [ ]

3 7

. 4

3 7

. 4

3 7

. 4

3 7

. 4

3 7

. 4

3 7

. 4

3 7

. 4

A o D

[ ]

6 1

. 9

6 1

. 9

6 1

. 9

6 1

. 9

6 1

. 9

6 1

. 9

6 1

. 9

A S [ ]

3 8

. 0

3 8

. 0

3 8

. 0

3 8

. 0

3 8

. 0

3 8

. 0

3 8

. 0

P o w e r

[ d B ]

2 0

. 6

2 0

. 5

2 0

. 7

2 4

. 6

2 0

. 6

A o A

[ ]

1 8 2

. 0

1 8 2

. 0

1 8 2

. 0

1 8 2

. 0

1 8 2

. 0

A S [ ]

4 0

. 3

4 0

. 3

4 0

. 3

4 0

. 3

4 0

. 3

A o D

[ ]

2 7 5

. 7

2 7 5

. 7

2 7 5

. 7

2 7 5

. 7

2 7 5

. 7

A S [ ]

3 8

. 7

3 8

. 7

3 8

. 7

3 8

. 7

3 8

. 7


11/22


Table 3. A summary of the TGn channel models.

Channel A B C D E Frms Delay Spread [nsec] Single Tap 15 30 50 100 150

Number of Taps 1 9 14 18 18 18Power Delay Pro le Window [nsec] Single Tap 80 200 390 730 1050

Number of Clusters 1 2 2 3 4 6

Figure 7. The measured Doppler power spectrum of a sin gledelay tap, together with the bell- shaped tting func tion.

4. Antenna and Propagation Measurements

The main goal of the measurement campaign was toevalu ate the achievable data rates in an of ce deployment with

practical antenna arrays, using the spatial processing describedin Section 2.1. We also aimed to understand the capacityincrease with the larger antenna array and mixed-polarized slotradiators.

The antenna measurement platform (AMP) was a chan nelsounder that was built by Qualcomm to measure the MIMOchannel for up to 16 16 antenna con gurations in twodimensions. The two tables on which the measurement antennaswere installed as they are shown in Figure 8 were controlled

by two stepping motors. The stepping motors could move them perpendicularly to each other. The antenna meas urement

platform was used to collect statistical data samples of theMIMO channel over approximately 7 at 5.17 GHz. The platform could operate in both the 5 GHz and 2 GHz bands.

The antenna measurement unit (AMU) of the channelsounder was connected with an RS-232 cable to the xed-location channel-sounding chassis. This was comprised of anRF chassis with four transceivers, an FPGA board, and a lap topthat ran software that controlled the measurement plat form. Thesetup is depicted in Figure 9.

The mobile channel-sounder chassis was comprised of the same RF chassis and FPGA board, and is referred to below

Figure 8. The antenna measurement unit (AMU) of theMIMO channel sounder.

Figure 9. A block diagram of the antenna measurementplatform.

as the mobile unit (MU). This was the channel-sounder chas-sis that was moved to different locations during the channel-measurement campaign. The antenna measurement unit andmobile unit communicated over the air (OTA) during eachchannel measurement to control the mobility platform, initiatechannel sounding, etc.

Initiation of the channel sounder and control of theantenna measurement unit was performed from the mobile-unit terminal via an over-the-air (OTA) time-division duplexlink. The time-division duplex OFDM packets transmitted


12/22


periodically between the antenna measurement unit and themobile unit ware 1 ms in duration, and consist of 222 OFDMsymbols, each containing 64 tones in 20 MHz with 312.5 kHzsubcarrier spacing. The operational frequency of the channelsounder was set to 5.17 GHz.

The antenna arrays were located on the top of the mov-able platform for the antenna measurement units side of thelink, and on top of the RF chassis for the mobile units side of the link. Figures 8 and 10 show the antenna measurement unitand mobile unit terminals as con gured for this measurementcampaign.

In order to obtain accurate channel measurements, theantenna measurement unit and mobile unit terminals had to belocked to each other in time and frequency. In this setup, themobile unit acquired the antenna measurement units soundingsignal at the beginning of each measurement run (i.e., at eachlocation), and a phase-locked loop kept the two ends of the link locked. The frequency stability was maintained by an OCXOwith 0.01 ppm stability, installed as a reference clock at bothends of the link. Although timing between the mobile unit and

the antenna measurement unit was locked, the sam pling timefrom frame to frame moved less than a sample period, as thechannel changed at a slow pace. The variation in sampling timeof the frames caused phase-slope differences between channelestimates derived from adjacent frames. During processing of the channel measurements, a very small phase-slope differencefrom frame to frame was observed, and corrected with respectto the rst frame at each location.

The channel-sounder chassis utilized here was capable of simultaneous measurement of a 4 4 MIMO channel. An RFswitch box, shown in Figures 11 and 12, was used to extendthe measurements to cover 8 8 and 16 16 antenna-arraycon gurations through time multiplexing of the four trans-ceivers. The 8 8 channel measurements interpolated frommultiple 4 4 channel measurements shared in time with RFswitching can be expressed as

4 4 4 48 8

4 4 4 4

A B x x

x C D x x

H H H

H H

=

, (46)

where 4 4 A D x H are 4 4 channel matrices derived from sequen-

tial 4 4 channel measurements taken at different closelyspaced time slots. The 4-to-8 and 4-to-16 switch box built for the higher-dimension MIMO channel measurements is shownin Figure 12. The number of antenna ports was selected toenable 16 16 channel measurements; the 8 8 channelmeasurement covered here utilized only half of the 16 ports of the switch box.

The switch box used four Chelton Control Systems SI-14-03028 RF switches, which had 3.8 dB loss, 70 dB isola tion, anda 100 ns switching speed. The operational frequency range was2-18 GHz. The control signals for the RF switches come fromthe FPGA board.

Figure 10. The mobile unit (MU) of the MIMO channelsounder.

Fig ure 12. The hardware of the RF switch box.

Figure 11. The 16 16 RF switch box, with 16 slot-radiat ingantennas.


13/22


As part of the measurement campaign, two eight-elementdual-polarized slot-radiated antenna array con gurations, tunedat 5.18 GHz, were designed. The operational frequen cies thatwere selected fell into the operational bands of the antennameasurement platform (AMP) that was used for channelmeasurements. We designed two different array con gurations:in one con guration, we used all cross-polarized () antennas asdepicted in Figure 13 (left side); in the other con guration, wemixed cross-polarized with 45-rotated crosses (+), as depictedin Figure 13 (right side). These antenna arrays were named the8-array and 8-array, respec tively.

The different array con gurations enabled us to accessthe impact their design had on channel capacity. The con gu-ration given in Figure 13 (right) had more gain than the con-

guration with all crosses, which would have been expected toresult in greater capacity. The higher capacity for the 8-arraycon guration may have been due to the use of mixed cross-

polarized () and rotated-cross (+) elements.

In both array con gurations, the co-located element pairswere separated by 2 from each other in the x and y direc-

tions. The 8-array board size was 2-7/8 in in the x direction,and 2-5/16 in in the y direction. The 8-array board size was3-3/4 in in the x direction and 2-5/16 in in the y direction. How-ever, these arrays could possibly have been made smaller bymoving the elements slightly closer together, and/or byremoving additional board material.

The antennas were printed on 32 mil thick Rogers-4003material ( 3.55r = ). We designed the antennas with Zelands

IE3D Method of Moments (MoM) simulation tool. The designles were exported to the Power PCB layout tool, and the

remaining layout work such as connectors, transmission lines,

etc. were nished using this layout software package.Figures 14 and 15 show the fabricated antenna arrays (8 and8-arrays) after modi cation.

Figures 16 and 17 show the measured (and simulated)return losses of the 8 and 8-arrays, respectively. It could beseen that the resonance frequency of the 8-antenna arrayclosely matched the predicted resonance from the simulations.The differences between the measured and simulated reso nancefrequencies of the 8-antenna array may have been due to the

proximity of the slot radiators to the board edge, which causeda fringing effect.

The channel measurement campaign was comprised of moving the mobile unit chassis to various locations, whilehaving the antenna measurement unit xed at a single loca tion.At each location, 500 samples of the forward ( AMU MU )and reverse ( MU AMU ) channels were consecutivelycaptured. Additionally, samples of the forward and reversenoise oors were captured, making sure that all transmittedsignals were disabled to prevent transmitter sig nals fromcontaminating the noise- oor measurement at the receiver.

Each sample, which was a time-division duplex frame,consisted of 222 OFDM symbols, 10 symbols of which were

Fig ure 13. Dual-Polarized slot-radiating antennas: 8-array(left), 8-array (right).

Figu re 14. The fabricated 8 slot-radiating antenna array.

Figur e 15. The fabricated 8-slot-radiating antenna array.

the SISO preamble, eight symbols were the MIMO preamble(for channel sounding), 12 symbols were control channels, andthe remaining 192 symbols were the data eld, as depicted inFigure 3. Within the 192-symbol data eld, each symbol had 48data subcarriers spaced 312.5 kHz apart, which were used for channel sounding.

Because of the large amount of data collected at eachlocation and for each frame, and given the limited speed of theUSB interface between the laptop running the channel-sounder

program, the frame period (i.e., the channel sample period) was~40 ms. This large frame period implied that Doppler shiftsabove ~12.5 Hz could not be unambiguously resolved. To


14/22


Figur e 16. The measured and simulated return losses of the 8 slot-radiating antenna array (solid: simulated, dashed:measured).


15/22


Figure 17. The measured and simulated return losses of the 8-slot-radiating antenna array (solid: simulated, dashed:measured).


16/22


compensate for this, the velocity of the antenna-measurement platform in the x and y directions was limited to 2 cm/s.

In order to facilitate 8 8 channel measurement, the dataeld of 1 ms long was used for channel sounding. The dataeld consisted of 192 OFDM symbols (each 4 s in duration),

which were partitioned into eight symbol sub-frames followed by a one-symbol gap to allow for RF switching between thevarious sets of antennas. Each sub-frame constituted a 4 4channel estimate. Four sub-frames (i.e., one block), as shown inFigure 3, yielded an 8 8 channel estimate. The frame structureused for the measurements reported here yielded ve blocks,which allowed us to collect more data samples for statisticaldata analysis.

The 8 8 channel estimates derived from the time-multi- plexed sets of four 4 4 channel estimates were processedto nd the spatial correlation, eigenvalues, channel capacity,estimated PHY rate, and Tx-Rx pair impulse response.

The antenna measurement platform 4 4 channelsounder utilized a space-time Hadamard matrix to code the

transmitted signals, thus enabling all 16 channel estimates to be simultaneously extracted at the receiver, while yielding anadditional processing gain. As a result, each channel estimateencompassed four symbol periods.

The average noise power utilized in the computation of the SNRs was derived from the noise measurement by aver-aging the noise power over all the receivers, all 48 info-tones,all 192 symbols (per frame), and ve noise measurementframes, to get one average noise power per location. Thecomplex spatial correlation was calculated per tone across theframes (time samples) for each location. For receiver correla-tion, the samples for each reference transmitter port wereappended to generate a larger sample pool; the same wasdone for transmitter correlation with the reference receiver

ports. The magnitude squared of the complex correlation wasthen averaged across the tones and locations to generate the8 8 receiver and transmitter correlation matrices for both theantenna measurement unit and mobile unit. The resulting cor-relation matrices were representative of the correlation in theof ce. The measurement locations within the of ce are shownin Figure 18. A range of locations for the mobile unit wasarbitrarily selected far and near from the antenna measurementunit to provide a larger sampling of possible channels (LOS,

NLOS, high SNR, low SNR). Additionally, the orientation

of the mobile unit antenna array was varied relative to theantenna measurement unit array for different locations. At eachlocation, the VGA/AGC were manually adjusted to achieve the

best SNR.

The 8 8 antenna array used in the measurement wasinstalled at the back left corner of a mockup laptop screen, asis shown in Figure 19a. In 16 16 cases, another eight-ele mentarray was mounted on the right corner of the back of the screen,as shown in Figure 19b.

Figure 18. The ofce measurement locations.

Figure 19a. An 8 8 antenna installation on a laptop.

Figure 19b. A 16 16 antenna installation on a laptop.


17/22


The eigenvalues of H H H were found using the MATLAB eig() function per sample, per tone, and per block. Theresulting eight eigenvalues were sorted (largest to small est),and scaled to normalize the total eigenvalue power, with thescaling given by

1

ii N

k k

N

=

=

. (47)

Here, the i are the eigenvalues of H H H , the i are the

scaled eigenvalues, and N is the normalized power (number of transmitters), which in this case was eight. The scaledeigenvalues were subsequently scaled by the average linear SNR over the 8 8 MIMO channel for the spectral ef ciencycalculation, as in Equation (48):

( )mod

21

log 1es N

N i avg i

C SNR =

= + . (48)

The spectral ef ciency was individually calculated for eachlocation, frame, and block, but also for all the locations groupedtogether and using an assumed xed SNR, which effectivelyentailed removal of the path loss and examination of spectralef ciency with purely the channel variation. For the former,the spectral ef ciency per tone for each sample was averagedto get a single spectral-ef ciency value per sample, which wasthen used to nd the spectral ef ciency cumulative distributionfunction (CDF). The latter calculation was done for differentassumed SNR values, allowing the spectral ef ciency as afunction of SNR curve to be com puted.

An estimate of the achievable MIMO PHY data rate wascalculated using a simple SNR-to-rate mapping, as shownin Table 1, by use of the measured eigenvalue SNRs. Theachievable PHY data rate of the 8 8 MIMO channel wasfound by summing up the attainable spectral ef ciency on eachindividual eigenmode for each channel sample and aver agingthem across the sub-tones, and then multiplying the averagedspectral ef ciency by the total information band width.

We found the PHY data rate for 20 MHz (using 48 datatones from the 802.11n speci cation) and 40 MHz bandwidths(using 108 data tones from the 802.11n speci cation). For example, at measurement location 1 of the 8 8 measurement,

the spectral ef ciency for the 8 and 8 antenna arrays were17.6 bps/Hz and 22.4 bps/Hz, from Table 4. For 20 MHz, thetotal information bandwidth was 48312.5 KHz = 15 MHz. Thetotal PHY rate in 20 MHz bandwidth of the 8 antenna arraywas therefore calculated as 1517.6 = 264 Mbps at 18.2 dBaverage receiving SNR.

The eigenvalues of the 8 8 channel estimates werecalculated for every frame and tone at each location. Subse-quently, the eigenmode SNR cumulative distribution functionsat each location and the cumulative distribution functions of the normalized eigenvalues across all the locations were found.

The former related directly to the channel capacity at a givenlocation, while the latter showed the channel variation acrossall the locations where measurements were taken.

A sample gure, showing the normalized ranked eigen-value power in time (frame index) for all the modes and for asingle tone at location 22, is given in Figure 20. It could be seenthat the strongest (i.e., principal) eigenmode was very stable,whereas the least-signi cant mode had large relative variation.

Figure 21 shows the cumulative distribution functions of all the normalized eigenvalues over all the measurement loca-tions when taken as one sample pool. This gave the distribu-tion of the eigenvalues after removing the effects of path-lossand transmitter/receiver frequency response due to the chan-nel-sounder transceiver lters. The solid lines and dashed linesin the gure show the normalized eigenvalue distribution atthe antenna measurement unit and the mobile unit, respec-tively. The measured distributions at the antenna measurementunit and the mobile unit corresponded to the downlink anduplink directions in a time-division duplex system. The meas-urement results showed that the eigenvalue distribution in the

uplink and downlink directions was very close for the strong-est eigenvalue, which implied channel reciprocity. However,the difference between the uplink and downlink eigenvalueincreased for lower eigenvalues as the power and the SNR gotlower, as depicted in Figure 20.

A comparison of the measured and simulated 8 8 spec-tral ef ciency using TGn channel models B, C, D, and E [32]is given in Figure 22. It could be seen that the channel modelmost closely matching the measured channel in terms of capacity was channel model E. However, it must be noted that the simulated results assumed a uniform linear array (ULA),whereas the measurements were for a two-dimensional slotted array, thus making the results not directly comparable. It could

be seen from Figure 18 that there was no line of sight (LOS) between the antenna measurement unit and the mobile unit inmany measurement locations. The building had brick outer walls, and inner walls of drywall hung on metal studs. The sizeof the of ce was 125 ft 50 ft, with 10.5 ft ceilings.

The spectral ef ciency given a xed SNR was examined by taking all the normalized eigenvalues from all the loca-tions. This enabled the spectral ef ciency as a function of theSNR to be plotted and compared with the 8 8 independentand identically distributed and correlated (using the measured

spatial correlation magnitude, in this case from the antennameasurement unit) independent and identically distributedchannel spectral ef ciencies, as shown in Figure 23. It could

be seen in Figure 23 that the spectral ef ciencies measured atthe antenna measurement unit and mobile unit were very close,and that they fell below the 8 8 independent and identicallydistributed spectral ef ciency curve by ~7 b/s/Hz at 25 dB SNR.This was expected, as the measured eigenvalue distributions atthe antenna measurement unit and the mobile unit were alsovery close, as depicted in Figure 21. The spec tral ef ciencycurve of the correlated independent and identi cally distributedchannel, using the antenna-measurement-unit measured spatial


18/22


Table 4. The measured SNR, spectral efciency, and PHY rate at each measurement locationfor the 8 and 8-arrays.

LocationRSS 8 (8)

[dBm]SNR 8 (8)

[dB]

N C Spectral

Efciency8 (8)

[b/s/Hz]

PHY Ratein 20 MHz

8 (8)[Mbps]

PHY Ratein 40 MHz

8 (8)[Mbps]

1 69.34 (65.38) 18.20 (22.24) 17.6 (22.4) 264 (336) 594 (756)

2 74.54 (72.30) 18.53 (20.93) 18.0 (22.4) 270 (336) 608 (756)3 76.17 (74.35) 16.83 (18.90) 15.2 (19.2) 228 (288) 513 (648)4 63.77 (63.52) 23.79 (23.99) 23.6 (26.4) 354 (396) 796 (891)5 60.57 (57.69) 26.87 (25.92) 27.2 (26.4) 408 (396) 918 (891)6 70.96 (70.51) 22.06 (22.71) 23.6 (25.6) 354 (384) 796 (864)7 71.40 (69.91) 21.73 (23.23) 22.4 (25.2) 336 (378) 756 (850)8 77.65 (75.99) 15.57 (17.50) 14.0 (17.2) 210 (258) 472 (580)9 64.71 (63.75) 23.06 (23.30) 24.0 (27.2) 360 (408) 810 (918)

10 64.39 (63.49) 26.91 (27.68) 24.4 (28.0) 366 (420) 823 (945)11 50.60 (49.74) 25.21 (26.75) 23.2 (26.8) 348 (402) 783 (904)12 79.22 (77.26) 14.66 (16.32) 13.2 (16.2) 198 (243) 445 (546)13 68.10 (64.02) 25.59 (23.45) 24.0 (21.6) 360 (324) 810 (729)

14 80.21 (77.6) 13.46 (15.77) 12.4 (15.4) 186 (231) 418 (519)15 63.45 (62.81) 27.83 (28.31) 28.0 (30.0) 420 (450) 945 (1012)16 65.43 (64.34) 22.12 (26.78) 22.8 (30.8) 342 (462) 769 (1039)17 75.43 (73.03) 18.15 (20.11) 17.2 (20.4) 258 (306) 580 (688)18 76.84 (73.35) 15.08 (20.14) 13.6 (20.8) 204 (312) 459 (702)19 69.34 (69.82) 22.28 (23.50) 16.8 (21.2)) 252 (318) 567 (715)20 76.11 (76.32) 17.73 (16.90) 16.8 (16.8) 252 (252) 567 (567)21 69.23 (67.57) 24.05 (23.53) 25.6 (24.8) 384 (372) 864 (837)22 61.01 (60.50) 30.05 (27.30) 32.8 (29.2) 492 (438) 1107 (985)23 66.60 (66.39) 26.60 (21.37) 28.8 (23.6) 432 (354) 972 (796)24 57.58 (57.16) 26.15 (26.37) 27.6 (29.6) 414 (444) 931 (999)

25 72.18 (69.65) 21.13 (23.43) 22.0 (26.4) 330 (396) 742 (891)Mean 62.19 (61.17) 23.84 (23.99) 21.39 (23.74) 321 (356) 722 (801)

Figure 21. T he normalized eigenvalue cumulative distribu-tion functions across all the locations: solid, AMU (antennameasurement unit); dashed, MU (mobile unit).

Figure 20. Some sample normalized eigenvalues in time(frame index) for a single tone.


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Table 5. The measured SNR, spectral efciency, and PHY rate at eachmeasurement location for the 16-arrays.

LocationRSS

[dBm]SNR [dB]

N C SpectralEfciency[b/s/Hz]

PHY Ratein 20 MHz

[Mbps]

PHY Ratein 40 MHz

[Gbps]

1 67.00 25.95 54.8 822 1.852 73.95 19.05 38.0 570 1.283 74.55 18.71 35.6 534 1.20

4 62.91 28.30 59.2 888 2.05 61.33 26.31 55.6 834 1.886 68.59 24.42 53.2 798 1.807 70.37 22.57 45.8 687 1.558 75.68 17.25 34.0 510 1.159 62.82 24.65 54.0 810 1.82

10 64.73 26.31 50.0 750 1.6911 79.30 13.93 24.4 366 0.82412 78.32 15.02 26.0 390 0.87813 65.76 25.05 43.2 648 1.4614 75.45 17.93 34.4 516 1.1615 63.16 24.22 48.8 732 1.6516 65.74 25.35 55.6 834 1.8817 77.50 15.90 27.8 417 0.9418 79.09 14.30 24.8 372 0.8419 70.72 22.60 36.4 546 1.2320 71.54 21.84 41.6 624 1.4021 76.78 16.70 30.8 462 1.0422 58.56 24.62 50.0 750 1.6923 65.10 25.91 56.4 846 1.9024 57.17 26.23 56.0 840 1.8925 70.68 22.70 47.6 714 1.61

Mean 65.16 23.55 43.36 650.4 1.46

Figure 22. T he measured and simulated (using the TGnchannel models) 8 8 spectral efciency as a function of theeigenvalue SNR.

Figure 23. The 8 8 spectral efciency as a function of theeigenvalue SNR (the 4 4 independent and identically dis-tributed spectral efciency is shown for reference).


20/22


correlation magnitude, was very close to the measured spectralef ciency. The 4 4 independent and identically distributedspectral ef ciency curve is given as a reference.

The average received signal strength (RSS), SNRs, spec-tral ef ciencies, and physical layer throughputs for 20 MHzand 40 MHz bandwidths are given at each measurement loca-tion in Table 4. The transmitted power levels of the antennameasurement unit and the mobile unit were 11 dBm per antenna. The numbers in parentheses show the measurementresults for the 8-element array with combined and +radiators. The numbers without parentheses show the meas-urement results for radiators only. One interesting obser-vation from the table was that although the received SNRs for 8 and 8-element arrays were very close at the locations 4, 6, 9,and 24, the measured spectral ef ciencies at the same loca tionswith the 8-element array were at least 2 b/s/Hz larger than the8-element array spectral ef ciency. We can con clude from thisobservation that the 8-element array had lower correlation thanthe 8-element array.

The same measurement results are summarized in Table 5for 16 slot radiators.

The measured spectral ef ciency at each location is compared between 8 8 and 16 16 antenna arrays in Figure 24.The gure showed that the spectral ef ciency of the 16 16antenna array was twice the spectral ef ciency of the 8 8antenna array at high SNRs. The ef ciency difference betweenthe two antenna arrays decreased with SNR. At 0 dB SNR,the capacities achieved using the two arrays were very close.The bene t of increased antenna array size was there fore moreapparent at high SNRs. It is important to note that the PHYrates given in the 20 MHz column of Table 4 and Table 5 were

measured ef ciency numbers, as the antenna measurement platform measurement bandwidth (BW) was 20 MHz. However,the rates given in 40 MHz were calculated by multiplyingthe average spectral ef ciency numbers by the information

bandwidth of 108 tones.

5. Conclusions and Future Trends

The 8 8 and 16 16 measurements performed withcross-polarized slot radiators showed that very high data ratescan be achieved for an indoor of ce deployment with propa-gation characteristics that are close to 802.11n TGn channelmodel E, when a full channel-state-information spatial-proc-essing technique and the modulation, coding, and SNR map-

ping given in Table 1 are employed. The antenna arrays util izedin the measurements could be incorporated into the back of alaptop or a tablet computer.

MIMO technologies are commercially deployed todayas wireless communication systems, such as with the Wi-Fi(WLAN), UMTS (3G), and LTE (4G) standards. In 802.11n

products, MIMO architectures increased the data rate from54 Mbit/s (802.11a/g) to 600 Mbit/s with the use of four spa tialstreams. In UMTS, the peak data rates with 2 2 MIMO were28 Mbps, 42 Mbps, 84 Mbps, and 168 Mbps, respec tively. InLTE, MIMO-enabled data rates reached 300 Mbps with a 4 4con guration.

In todays wireless networks, small-cell deployment isneeded for additional capacity, which is being driven by theincreasing demand placed on networks by smart phones. It isexpected that the demand for mobile data services will grow1000 times by year 2016. The high demand for mobile datacan be met with small-cell deployment and interference-man-agement techniques. Clearly, MIMO will play an importantrole in the small-cell high-capacity deployments. The increasedinterference level in small-cell deployments can be better managed by the use of MIMO and beamforming tech niques.

Massive MIMO is another important technique for high-capacity deployments. Massive MIMO deployment willrequire a signi cantly increased number of antennas in two-dimensional spaces. Antenna correlation and mutual interfer-ence will be critical to successful massive MIMO deploy ments.

MIMO techniques will continue to deliver increasedthroughput with advanced developments in silicon technologyand nano technologies. Carbon-nanotube antennas (CNA)look very promising for future MIMO systems. Although car-

bon-nanotube antennas have low ef ciency today, researchis being undertaken to improve the ef ciency. In the future,car bon-nanotube antennas can be embedded on the back of mobile devices to form MIMO antenna arrays. Antenna spac-ing, correlation, and capacity aspects of MIMO systems arevery critical in delivering the peak throughputs, especially for increased antenna-array sizes. The improvements to antenna-array size and form factors are critical to the success of future

broadband wireless systems using MIMO techniques.

Figure 24. A comparis on of the spectral efciencies as afunction of the eigenvalue SNR for the 8 8 and 16 16 arrays.


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6. Acknowledgements

The author greatly appreciates the very extensive andthoughtful review of the manuscript that was done by J. RodWalton, John Ketchum, and Steve Howard in QNE. He wouldalso like to thank to Leon Metraud, whose help with themeasurements was very valuable.

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Introducing the Author

Hakan Inanoglu is a Principal Engineer in QualcommInc., USA. He received his BS (1987) and PhD (1998) fromIstanbul Technical University, and his MS (1991) from Mid dleEast Technical University of Ankara. He has been with Aselsan(1987-1991), NortelNetas (1992-1996) in Turkey, and withOmnipoint (1996-1999) and Siemens-Opuswave (1999-2001)in the USA. Since 2001, he has been with Qual comm in the

New England of ce (QNE).

He has 25 years of experience in the communications

and wireless industry, from system design to standardization.He has worked on GSM, DECT, IS-661, CDMA, WCDMA,LTE, Wi-Fi, and 60 GHz wireless systems. He has hands-onexperience on various elds of wireless communication sys-tems, such as radio propagation, cell planning, RF design,antenna design, communication system design, radio systems,digital signal processing, and network protocols. Dr. Inanogluhas published several papers and contributed to a book chap ter.He has several patents ( ve granted, nine US active). He was anAdjunct Professor at the University of Massachusetts Lowell,and taught the graduate-level Antenna Theory and Designcourse in the Fall 2011 semester.

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