MIMO Architecture for Wireless Communication
Intel
®
Centrino
®
Duo MobileTechnology
Intel
®
Technology Journal
Volume 10Issue 02Published, May15, 2006ISSN 1535864XDOI: 10.1535/itj.1002
More information, including current and past issues of Intel Technology Journal, can be found at:
http://developer.intel.com/technology/itj/index.htm
MIMO Architecture for Wireless Communication 157
MIMO Architecture for Wireless Communication
Ilan Hen, Mobility Group, Intel CorporationIndex words: Alamouti scheme, beamforming, capacity, error probability, fading, intersymbolinterference, LDPC codes, MIMO channels, MRC, OFDM
ABSTRACT
In this paper, we consider the use of multipleinputmultipleoutput (MIMO) architecture for wirelesscommunication systems. We show how by employingMIMO architecture
,
architecture in which transmissionand reception are carried out through multiple antennas,one can design a superior wireless communication systemwith respect to reliability, throughput, and powerconsumption.
INTRODUCTION
In recent years, wireless communication devices havebecome more and more popular. However, at the sametime, the design of faster, more reliable, and powerefficient wireless communication systems has becomeevermore difficult. Wireless channels, as opposed towireline channels, exhibit highly irregular amplitudebehavior due to what is known as
fading
. The fading,essentially caused by the reception of multiple reflectionsof the transmitted signal (illustrated in Figure 1), is a keyinherent problem of wireless channels, which,unfortunately, cannot be avoided. Fading causes thereceived signal power to change rapidly in time, makingthe task of information extraction from the received signala fairly complicated endeavor. Furthermore, once theinformation is extracted, its reliability, manifested througherror probability, is often poor.
In this paper, we demonstrate how by exploiting thespatial diversity, namely, using multiple antennas, one canimprove reliability, increase transmission throughput, andreduce transmission power. We also briefly discuss thebenefits of using MIMO architecture along withorthogonal frequency division multiplexing (OFDM)modulation, and lowdensity parity check (LDPC) coding.First, we consider the reliability issue. We present a basicmodel for the wireless singleinput singleoutput (SISO,single transmit antenna, single receive antenna) channel,and show how the corresponding error probability iscritically damaged by fading. We then consider the singleinput multipleoutput (SIMO, single transmit antenna,multiple receive antennas) channel and describe theconcept of maximal ratio combining (MRC) as a way toexploit the receive diversity offered by this type of channel. We calculate the error probability achieved bythe MRC, showing it to be much smaller than the onecorresponding to the SISO channel, in which no spatialdiversity exists. Next, we consider the multipleinputsingleoutput (MISO, multiple transmit antennas, singlereceive antenna) channel, and we present somemechanisms that exploit the transmit diversity offered bythis channel. Specifically, the beamforming technique andAlamouti’s [3] scheme are analyzed. Bringing togethertransmit and receive diversity, the MIMO channel isintroduced. The beamforming technique and Alamoutibased scheme are shown to achieve full diversity, i.e., theytake full advantage of both transmit and receive diversityprovided by the MIMO channel. We discuss theperformance of the aforementioned spatial diversitytechniques, and we draw some conclusions as to when oneshould be preferred over the other.
Figure 1: Wireless channel–fading problem due tomultiple reflections
Intel Technology Journal, Volume 10, Issue 2, 2006
MIMO Architecture for Wireless Communication 158
Improved reliability is not the only outcome of usingmultiple antennas. About ten years ago, a remarkabletheoretical result regarding the capacity of MIMOchannels [1] suggested that the transmission rate overwireless channels can be dramatically increased whenusing multiple antennas. It turns out that the ability totransmit and receive through multiple antennas does notonly reject fading; better yet, it actually harnesses thefading itself in favor of increased throughput. We presentthe capacity of wireless MIMO channels, showing it to begreater than that of the wireline SISO channel. Moreover,the capacity formula is used to demonstrate how one canreduce transmission power by using multiple antennasystems.Finally, we briefly explain how, in principal, integrationbetween MIMO architecture, OFDM modulation, andLDPC coding (essentially the basic building blocks for themost advanced wireless communication standards, e.g.,802.11n, 802.16), can give rise to a superior wirelesscommunication system.The outline of the paper is as follows. We first present abasic model for the wireless SISO channel. We thenconsider the MRC technique, the beamforming technique,and Alamouti’s scheme. After that, we present thecapacity of MIMO channels and then discuss the benefitsof using MIMO architecture along with OFDMmodulation and LDPC coding. We conclude with someremarks on the performance of MIMO architecture andhow the Intel
®
Centrino
®
mobile technology benefits byembracing it.
THE WIRELESS CHANNEL
In this section, we present a basic model for the wirelesschannel and show its performance to be inferior to that of the wireline channel.The traditional wireline channel is modeled by theequation
y x n
= +
(1.1)where
x
is the channel input.
x
is a complex number, referredto as
symbol
, representing two bits of information, i.e., itcan take up to four different values according to themapping (in general,
x
may be chosen to represent morethan two bits of information):
00 01 10 11
s ss ss ss s
x E j E x E j E x E j E x E j E
→ = − −→ = − +→ = −→ = +
(1.2)We assume that all the above possible realizations of
x
are equally probable.
n
is the channel noise, accounting for the thermal noiseinduced by different parts of the receiver.
n
is modeledas a zero mean, complex Gaussian random variable withvariance
2
σ
per dimension, i.e., the real part of
n
andthe imaginary part of
n
are zero mean, statisticallyindependent Gaussian random variables with variance
2
σ
. Note that
22
0()2
En E n E nn
σ
∗
== =
(1.3)“
E
” and “
∗
” denote statistical expectation and complexconjugate, respectively. The channel signaltonoiseratio(SNR) is given by
222
.
s
E x SNR E n E
σ
==
(1.4)The receiver observes the channel's output
y
and decideswhich symbol, out of the four possible ones, was sent. Thereceiver tries to produce decisions with the best possiblereliability. We measure reliability through errorprobability. Let
( )
ˆ
x y
be the receiver decision. The errorprobability, denoted here by
{ }
r
P
ε
, is the probabilitythat
( )
ˆ
x y
is different than
x
,
{ } ( )
{ }
ˆ
r r
P P x y x
ε
= ≠
. (1.5)What receiver should we be using in order to achieveminimal error probability? The optimal receiver [2]decides that symbol
x
was sent, if the Euclidian distancebetween
x
and
y
is the smallest among all possibledistances (total of four in our case). The optimal receiver,referred to as
the maximum likelihood (ML)
receiver,achieves error probability [2] satisfying
Intel Technology Journal, Volume 10, Issue 2, 2006
MIMO Architecture for Wireless Communication 159
{ }
exp2
r
SNRP
ε
⎧ ⎫
≤ −
⎨ ⎬⎩ ⎭
. (1.6)Throughout the paper, we provide upper bounds on theerror probability. However, these bounds are tight for themidtohigh SNR range [2], which is the interesting SNRrange when targeting reliable, highthroughputcommunication. As we can see, for the wireline channel,the error probability decreases exponentially fast with theSNR. Does this excellent behavior remain intact whentransmitting over wireless channels? Unfortunately, theanswer is no. The fading, as shown next, dramaticallyincreases the error probability.The wireless channel model is similar to the wirelinechannel model, but with the input amplitude modified toaccount for the fading. The wireless channel is modeledwith the equation
y hx n
= +
(1.7)where
h
represents the fading. We consider anenvironment in which there is no line of sight (NLOS)between the transmitter and the receiver. For this kind of environment,
h
is modeled as a zero mean, complexGaussian random variable with variance
0.5
perdimension. Suppose for a moment, that the fading
h
is afixed deterministic number rather than a random variable.In that case, the channel SNR would be given by
( )
222
E hx SNR h E nSNR h
==
(1.8)and, as for the wireline channel, the error probabilitysatisfies
{ }( )
2
exp2exp.2
r
SNR hP hh SNR
ε
⎧ ⎫
≤ −
⎨ ⎬⎩ ⎭⎧ ⎫⎪ ⎪
= −
⎨ ⎬⎪ ⎪⎩ ⎭
(1.9)Let
z h
=
(1.10)then
{ }
2
exp.2
r
z SNRP z
ε
⎧ ⎫
≤ −
⎨ ⎬⎩ ⎭
(1.11)The above result accounts for the error probability for agiven realization of the fading
h
. In order to obtain theerror probability
{ }
r
P
ε
we must average the conditionederror probability (1.11) with respect to the probability lowof
z
{ } { } ( )

r r
P P z f z dz
ε ε
=
∫
(1.12)
( )
f z
is the probability density function of
z
. Since
h
is Gaussian distributed,
z
is the squared root of thesquared sum of two independent Gaussian randomvariables, which means [2]
z
is
Rayleigh
distributed
{ } ( )
{ }
02
()2exp,0.
ar
P z a f d f
β β β β β β
≤ == − ≥
∫
(1.13)Averaging (1.11) with respect to the Rayleigh distributionwe have
{ }
{ }
220
exp2exp21.12
r
z SNRP z z dzSNR
ε
∞
⎧ ⎫
≤ − −
⎨ ⎬⎩ ⎭
=+
∫
(1.14)It should be clear now how severe the damage caused bythe fading is: instead of having an error probability thatdecreases exponentially fast with the SNR (1.6), we havean error probability which is only inversely proportionalto the SNR. In the next section, we show how by usingmultiple antennas the situation can be rectified to someextent.
MIMO SYSTEMS RELIABILITY
In this section, we consider various spatial diversitytechniques aimed at reducing the error probability.
Receive Diversity
Consider the SIMO channel depicted in Figure 2.
Figure 2: SIMO channel