The Multiple Input Multiple Output Computer Science Essay

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1Gnetworks (NMT,CNets,AMPS,TACS)are considered to be the first analog cellular systems, which started early 1980s. There were radio telephone systems even before that. 1G networks were conceived and designed purely for voice calls with almost no consideration of data services (with the possible exception of built-in modems in some headsets).

2G Wireless Standards:

2G networks (GSM, CDMAOne, D-AMPS) are the first digital cellular systems launched early 1990s, offering improved sound quality, better security and higher total capacity. GSM supports circuit-switched data (CSD), allowing users to place dial-up data calls digitally, so that the network's switching station receives actual ones and zeroes rather than the screech of an analog modem.

2.5G networks (GPRS, CDMA2000 1x) are the enhanced versions of 2G networks with theoretical data rates up to about 144kbit/s. GPRS offered the first always-on data service.

Name of the standard

Data rate





10 Kbps

~50 Kbps

~200 Kbps

Family of 2G/2.5G wireless communication standards:

GSM - Global System for Mobile Communication

CDMA - Code Division for Multiple Access

GPRS _ General Packet Radio Service

EDGE _ Enhanced Data for GSM Evolution

3G Wireless Standards:

3G networks (UMTS FDD and TDD, CDMA2000 1x EVDO, CDMA2000 3x, TD-SCDMA, Arib WCDMA, EDGE, IMT-2000 DECT) are newer cellular networks that have data rates of 384kbit/s and more. The UN's International Telecommunications Union IMT-2000 standard requires stationary speeds of 2Mbps and mobile speeds of 384kbps for a "true" 3G. Disadvantages

- Low coverage thus having bottle necks because of the need to have more base stations

- High Prices for 3g Devices

-Confusion was what standard to use WCDMA or CDMA2000

Name of the standard

Data rate


CDMA 2000




384 Kbps

5-30 Mbps

Family of 3G/3.5G wireless standards:

WCDMA - Wideband Code Division for Multiple Access

UMTS - Universal Mobile Telecommunication Standard

HSDPA - High Speed Downlink Packet Access

HSUPA - High Speed Uplink Packet Access

1XEVDO - Evolution Data Optimized

4G Wireless Standards:

4G technology is mainly a marketing buzzword at the moment. The ITI has taken ownership of 4G, bundling into a specification known as IMT-Advanced. The document calls for 4G technologies to deliver downlink speeds of 1Gbps when stationary and 100Mbps when mobile, roughly 500-fold and 250-fold increase over IMT-2000 respectively. Unfortunately, those specs are so aggressive that no commercialized standard currently meets them.

Historically, Long-Term Evolution (LTE), the standard generally accepted to succeed both CDMA2000 and GSM, have been marketed and labeled as "4G technologies," but that's only partially true: they both make use of a newer, extremely efficient multiplexing scheme (OFDMA, as opposed to the older CDMA or TDMA), however, LTE at around 100Mbps theoretical speed.

Practical, real-world commercial network LTE range between 30Mbps. Even though the speed of  LTE is well short of IMT-Advanced's standard, they're different than 3G networks and carriers around the world refer to them as "4G". Updates to these standards -- LTE-Advanced, respectively -- will increase throughput, but neither has been finalized yet

Name of the standard

Data rate




100-200 Mbps

Family of 4G wireless standards:

LTE - Long Term Evolution

WiMAX - World wide Interoperability for Microwave Access



MIMO systems are special class of wireless systems which have "multiple" antennas at the transmitter and receiver.

As there are multiple antennas(links) MIMO systems can be employed for DIVERSITY gain.

MIMO can increase the data rate by transmitting several information streams in "parallel".

Taking the space and multiplexing different data streams across it i.e., the space between the transmitter and receiver and multiplexing parallel information is known as "SPATIAL MULTIPLEXING".

MIMO is the key aspect of 3G and 4G systems.

Schematic representation of spatial multiplexing


In a MIMO system transmitting multiple independent information system to the transmitter and receiver is a very unique aspect and big advantage of MIMO multiple input and output of a MIMO system .This is possible through multi dimensional signal processing.

Description :

In MIMO we have 't' transmitting antennas ,so we are transmitting 't' symbols from the t transmit antennas.


X1, X2 ………….. Xt are transmit antenna's

Y1, Y2 …………... Yt are receive antenna's


hr1,h r2 are known as channel matrix

Each entry of this channel matrix is a flat fading channel coefficient.

Y1= h 11 X1 + h12X2+. . . . . . . . + h1t Xt

X1, X2 .. . . . . . Xt interfere at receive antenna 1

Y2= h21 X1 + h 22 X2+ . . . . . . . . . + h2t Xt

X1, X2. . . . . . Xt interfere at receive antenna 2

hij is the channel coefficient between the i th receive antenna and j th transmit antenna.


total of rt channel coefficent

MIMO channel matrix


r x t dimensional MIMO channel matrix

MIMO system model:





Special case:

t = 1 --------- Single Input Multiple Output( SIMO) system.



Hence, Receive diversity system is also termed as SIMO,

r = 1 . . . . Multiple Input Single Output(MISO) system.



T transmitter antennas and 1 single antenna's channel maintenance is row vector .This is known as Transmit diversity system or MISO system.

r = t = 1 Single Input Single

Y= hX +n Single Output(SISO) 1 transmit

antenna and receive antenna systems



r dimensional vector

power of each noise component at each receive antenna is

E(|ni|2)=C:\Users\Dileep\Pictures\m17.PNG n2

Assume E(ni nj *) = 0

Multidimensional covariance matrix



nr* - conjugate

| n1 | 2 are C:\Users\Dileep\Pictures\m17.PNG 2

n1 nr* are 0


Isotropic noise


Spatio- temporally white noise : noise is uncorrelated across antennas and time.

Rn = E( n n * ) = C:\Users\Dileep\Pictures\m17.PNG n2 I

MIMO Receiver:

Linear Receiver :

Y= Hx + n

H-1 y = x + H-1 n

In general case we can compute H-1 because of 2 reasons

1.Inverse only exists if r = t.

2.Even for square matrix inverse need not exist.

It defines the generalized inverse r ≥ t


When r ≥ t we have more equations(measurements)than unknowns (are t), because equations are r unknowns are t. Hence, there might not be an exact solution.

If the number of equation is less than the number of unknown then we can have possibility of infinite solutions. If the number of equation is more than the number of unknown's then we can have the possibility of non existing solution.

Amongst all possible transmit vector x , choose the minimum error vector

error || y - H x||2

y is least-square solution or measurement.

x is unknown.

Hence choosing x such that y-x measurement error is minimized.

Vector differentiation:

Let us consider the function f( x )

C:\Users\Dileep\Pictures\18.PNG = how to differentiate d C:\Users\Dileep\Pictures\18.PNG = ?





= c1 X1 + c2X2+. . . . . . . . +ct Xt



Now Let us consider







MIMO is a key component of next-generation wireless technologies and provides the bulk of LTE's peak throughput gains when compared with older technologies. However, MIMO gains can only be realized on a fully optimized network. MIMO optimization requires a different approach to traditional network optimization, with assessment of multipath conditions playing a key role in determining the potential throughput provided by a MIMO-enabled LTE network. Optimizing an LTE network for MIMO therefore requires a new set of scanning receiver parameters, including multipath CINR measurements, CN, and CQI for all key MIMO modes. PCTEL's See Gull Scanning Receivers provide high-quality data for all of these MIMO parameters, enabling network operators to construct an accurate picture of MIMO LTE networks.

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