 About MIMO
 Application
 U of A System
MIMO HISTORYMIMO, MultipleInput MultipleOutput signaling was a groundbreaking development pioneered by Jack Winters of Bell Laboratories in his 1984 article "Optimum Combining in Digital Mobile Radio with Cochannel Interference". Since then, many academics and engineers have made significant contributions to the understanding of MIMO systems. In 1996, radically novel approaches were invented to increase signaling efficiency over MIMO channels. Gregory G. Raleigh and V.K. Jones wrote a paper "Multivariate Modulation and Coding for Wireless Communication" arguing that multipath channels can have a multiplicative capacity effect if the multipathsignal propagation is used in an appropriate communications structure. In the same year, Foschini introduced the BLAST concept in his paper "Layered SpaceTime Architecture for Wireless Communication in a Fading Environment When Using MultiElement Antennas". BLAST is one of the most widely examined techniques today. In 1999, the Shannon capacity of an isotropic fading MIMO channel was calculated by I. Emre Telatar in his paper "Capacity of multiantenna Gaussian channels". He stated that the channel capacity increases with the number of antennas and is proportional to the minimum number of transmit or receive antennas. This basic information theoretic result drew widespread attention to MIMO communications. Meanwhile, engineering research of MIMO systems also progressed. In 1998, Bell Lab performed the first successful technology demonstration under laboratory conditions. One year later, in 1999, Gigabit Wireless Inc. and Stanford Univeristy successfully held the first outdoor prototype demonstration. And Iospan Wireless Inc. (formerly Gigabit Wireless Inc., acquired by Intel) produced the first commercial product in 2002. As one of the first, a 4x4 MIMO academic testbed started operation at University of Alberta in 2003.
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CHANNELSMIMO channels arise in wireless communications environment where multiple transmit and receive antennas are used (see Figure 1). MIMO channels work best in highly scattering transmission environment, where multiple multiple paths exist between transmitters and receivers.
Figure 1: MIMO Channels
A communications system for a MIMO channel aims at exploiting the multipath signal propagation to increase channel capacity. Under certain assumptions [1][2], the correlated partial channels created by the scattering environment can be accurately described by the matrix equation:
Typical assumptions are:
For engineering uses, the following block diagram is preferred: Figure 2: Channel Model
The following simple models are often used to study and model basic MIMO channels:
Figure 3: Keyhole Channels
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CAPACITYThe value of the channel gain matrix H is affect by the fading in the channel. Whether or not a transmitter knows the value of H is crucial in how the MIMO system is operated: 1. Transmitters have Channel Knowledge (Waterfilling Capacity). If the value of the MIMO channel gain H is known at both transmitter and receiver, we can decompose the matrix H via the singular value decomposition SVD space [1]: where U and V are unitary, i.e. UU+=VV+=I (if Nr<Nt) and N=min(Nr,Nt). The matrix D contains the singular values of H, which are the positive square roots of the eigenvalues of HH+ and H+H . Now the channel equation can be written in an equivalent form:
Here, if Nt>Nr only the first Nr signals of x will be received and the NtNrremaining channels will be nulled. This leads to the following parallel Gaussian channel model
Figure 1: Parallel Gaussian channels
The capacity of N parallel complex channels can be computed following as [2]:
2. Transmitters without Channel Knowledge (Symmetric Capacity) Channel knowledge is not always available at the transmitters, so the only choice we have is to distribute the energy uniformly over all component channels. This leads to the definition of the "Symmetric Capacity":
The above formula can be written in terms the matrix eigenvalues of H as
E. Biglieri and G. Taricco review closes form expressions of the above equation[3].The plot specific function tells us that the capacity C of the MIMO channel shows an almost linear increase with the number of receiving antenna or transmitting antennas for Nr=Nt. Figure 3: Capacity with Nr=Nt antennas
3. MIMO Channel Capacity via Random Matrix Theory In a large MIMO system,, , with fixed aspect ratio alpha=Nt/Nr, the capacity per antenna tends towards a constant. This is shown via random matrix theory. Assume H is random Gaussian matrix and
The eigenvalues of W are randomly distributed according to the MarcenkoPastur Law with marginal probability density.
An example of 1000 random matrices of size 20x 10 is shown below: Figure 4: Example of eigenvalues
For , the empirical eigenvalue distribution converges to . The capacity per dimension for the large Rayleigh MIMO channel is consequently given by
For Ricean MIMO channels, modeled as
where M is a lowrank "fixedgain channel" and alpha is Rice factor. The MarcenkoPastur law can still be applied, if . Then, as N approaches infinity, the empirical distribution of . And, in the limit, the capacity of the Ricean channel is given by (1) with adjusted SNR. Thus, the Ricean channel has an effective energy of loss of , since the lowrank average channel contributes nothing in the limit. The figures below compare the analytical eigenvalue distribution for a rank(W)=4/2 channel with those obtained by physical measurements:
Figure 5: Eigenvalue analytical distribution
Figure 6: Distribution of Squared Singular Values measured by the U of A testbed (see U of A system).
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VERIFICATIONIn order to verify the MIMO potential in realistic propagation environments, researchers conducted measurement studies. Both indoor and outdoor measurements show promising throughput gain. There are 3 typical models observed.
1. Transmitter / Receiver correlation Correlated channel path gains occur in the realworld environment. The widely used correlated model is given by
where Hw is an Nr x Nt matrix with independent entries, Rr and Rt denote Nr x Nr and Nt x Nt antenna correlation matrices at the transmitter and the receiver sides, respectively. Based on the correlation properties of the receiver array response vector, or the singular values of the channels response matrix H, MIMO channel can be classified as highrank or lowrank channels. Highrank MIMO channels occur when there is a rich scattering environment and when there is little correlation among the channel path gains. The capacity of this channel can then be approximated by
Lowrank MIMO channels occur under scatterfree or longdistance links, where there is strong correlation between the channel path gains. The capacity of the lowrank MIMO channel can be approximated as
Additionally, if the SNR is low, correlation in the channel has little effect on capacity. In this situation, the capacity will approach
2. Keyhole Channels In realistic propagation environments, rank deficiency of a channel matrix may severely reduce the performance of MIMO system because of keyhole effects. These describe special MIMO channels which are degraded from a capacity point of view, but provide diversity in fading environments. A rank=1 channel model for a keyhole channels is given by
Keyhole channels have low capacity even though path correlations are low.
3. Waveguide channels The waveguide channel uses guided wave theory to model propagation in waveguidelike environments such as hallways, corridor or streets. Considering negligible losses, the channel matrix can be presented by [11][12]:
where Z is an L x L diagonal matrix, L is the number of propagation modes, V is an Nr x L matrix containing the contribution of each mode to the signal received at each antenna and A represents the L x Nt excitation matrix. Figure 1 is an example of what happens in a narrow corridor. Radio waves striking the walls reach the receiver via many reflections. Such multireflected rays will be heavily attenuated at the receiver because of the power loss with each reflection. In addition, smaller θ will cause lower reflection coefficients which will cause the additionally attenuation with every reflection. These effects eliminate multipath wireless components and reduce the MIMO channel rank. Thus, channel capacity will decrease with the distance down the corridor.
The following results were calculated and measured with the U of A testbed.
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OTHER CHANNELS
1. Cable Channels A cable bundle consisting of a number of twisted pair copper cables acts as a MIMO transmission system, particularly at high frequencies. MIMO processing can greatly reduce the extent of the farend crosstalk (FExT). In a practical system, FExT works as an unwanted noise and reduces the capacity of the cable channel. In the channel matrix, the diagonal terms represent the channel gains and the offdiagonal elements represent FExT. In a practical system, it is not too difficult to have knowledge of the MIMO cable channels because the environment of cable lines is mostly fixed. Thus, singular value decomposition (SVD) processing can be performed. Experimental results based on physical measurements on a five pair cable show the capacity of the MIMO cable channels has a potential improvement compared to that of a conventional connection.[1] Capacities per pair of the MIMO cable channel increases 16 and 9 bits/sec/Hz at frequencies of 10,20MHz respectively.
2. MMF Optical Channels The multimode causes mode propagation in the fiber, which limits the bandwidth, i.e. the capacity of the fiber. This is called modal dispersion. MMF Optical MIMO systems exploit the modal dispersion to increase the capacity by MIMO processing.
Figure 2 illustrate a 2x 2 MMF optical channel. The system includes t lasers and r photodetectors. The channel matrix can be shown to be given by [4]: where Q is the number of modes in MMF, gijk is the channel gain of the kth mode from the jth transmitter to the ith receiver, wc is the carrier frequency, is the phase delay associated with the kth mode. Optical MIMO channels behave like a complex Gaussian channel model used for wireless MIMO systems.[2][4] When Nr=Nt, the bandwidth achievable equals Nrx BSISO in an ideal environment, using the same length and same total energy as a SISO optical channel. [3].
3. FreeSpace Optical (FSO) channels FreeSpace optical channels are used to build largecapacity links. It improves its performance in a similar way to the wireless RF MIMO system by means of spatial diversity. The system includes multiple laser transmitters and multiple photodetector receivers. The channel with intensity modulation and direct detection can be expressed as [7] where denotes convolution, r represents the photodetector (PD) responsivity, and h(t) represents the impulse response of the channel. The fading due to atmospheric turbulence is mitigated by MIMO processing and the channel capacity and SNR are increased. [5][7].
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TESTBEDThe HCDC Lab at the University of Alberta has developed a flexible 4 x 4 MIMO testbed that allows realtime characterization of MIMO wireless channel. It consists of an independent transmitter and receiver that operate in the 902928MHz Industry Scientific and Medical (ISM) band. The transmitter and receiver stations each consists of a GVA development board (manufactured by GV and Associates Inc.) for the baseband processing, It contains two xilinx VirtexE 2000 field programmable gate arrays (FPGAs), four 12bit Analog Devices AD9432 analogtodigital converters (ADCs) , and four 12bit Analog Devices AD9762 digitaltoanalog converters (DACs).
Figure 1 shows the MIMO transmitter. From left to right, it consists of a GVA290 board, inline filters, a fourchannel RF upconverter module (from SignalCraft Technologies Inc.), and a multiantenna structure. GVA 290 board creates 4 baseband signals, upconverts them to an intermediate frequency (IF) of 12.5MHz and then converts these IF digital signals to analog waveforms, The outputs of the GVAs are transmitted to the fourchannel RF upconverter module through inline lowpass filters with a cutoff frequency of 15MHz. The RF board then upconverts these four independent IF waveforms to the 902928MHz band for transmission over the air through the "multiantenna structure".
Figure 2 shows the MIMO receiver. From left to right, it consists of the same multiantenna structure as used by the transmitter, an RF downconverter board (manufactured by SignalCraft Technologies Inc.) with four independent receive paths, inline filters, and a GVA290 board. The four signals received from the antennas are amplified and downconverted from the ISM band down to an IF of 12.5 MHz by the RF module. The four received IF signals are then sampled by the ADCs of the GVA290 board. These sample streams are processed by the FPGAs at a clock rate of 50MHz. The measurements presented in Section Measurement and Result were obtained with this platform.

MEASUREMENT RESULTSNote: To calculate the channel capacity it is always a SNR=20 dB assumed. The SNR results in the tables below show that this assumtion was fulfilled!
1. Indoor Results 

1.1 Parkade P1 of ECERF Building, U of A Antenna Spacing: Lambda/2 (16cm)
Measurement Results: 





1.2 3rd Floor of ETLC Building, U of A Antenna Spacing: Lambda/2 (16cm)
Measurement Results: 





1.3 5th Floor of Civil Engineering Building, U of A Antenna Spacing: Lambda/2 (16cm)
Measurement Results: 




1.4 V Wing Basement, U of A Antenna Spacing: Lambda/2 (16cm) Measurement Results: 





1.5 2nd Floor of ECERF Building, U of A Antenna Spacing: Lambda/2 (16cm) Measurement Results: 





1.6 5th Floor of ECERF Building, U of A Antenna Spacing: Lambda/2 (16cm), Lambda/4 (8cm), Lambda(32cm) Measurement Results: 






1.7 Indoor Moving measurement 1.7.1 Parkade P1 of ECERF Building, U of A Environment: Office Environment, thin walls, people moving. Antenna Spacing: Lambda/2 (16 cm) The moving speed was about 1 meter per second (walking speed). The recording of the Hmatrices has been done with a Cfunction, which can record 250 Hmatrices per second. M1: The starting and end point is 5 meter away from Location 4 of the stationary measurement and 25 meter from Location 5. A complete turn of about 60 meters has taken 1 minute and 30 seconds where the velocity for this turn has been almost linear. M2: In contrast to M1 this measurement is done on the lower level of Parkade P1 where the starting and end point is 6 meter away from Location 3 of the stationary measurements.



Channel Capacity M1 Channel Capacity M2 
Power Plot M1 Power Plot M2




2. Outdoor Results 2.1 Quad, U of A Antenna Spacing: Lambda/2 (16cm) Measurement Result: 





2.2 Corbett Field, U of A Antenna Spacing: Lambda/2 (16cm), Lambda (32cm) Measurement Results: 






2.3 U of A Farm Antenna Spacing: Lambda/2 (16cm) Measurement Results: 




2.4 Hawrelak Park Antenna Spacing: Lambda/2 (16cm) Measurement Results: 




3. Indoor/Outdoor Results 1st Floor V Wing, U of A Antenna Spacing: Lambda/2 (16cm) Measurement Results: 



