Mimo Calculation

1. MIMO

2. Introduction
All radio communications systems, regardless of whether mobile radio networks like
3GPP UMTS or wireless radio networks like WLAN, must continually provide higher
data rates. In addition to conventional methods, such as introducing higher modulation
types or providing larger bandwidths, this is also being achieved by using multiple
antenna systems (Multiple Input, Multiple Output – MIMO). Multiple antenna solutions can
be used in order to increase the spectrum efficiency as well as the peak data rates.
Different approaches aim for different purposes, e.g. traditional beamforming and
transmitter diversity techniques increase the coverage and capacity. Spatial multiplexing,
a technique which requires multiple antennas at both transmitter and receiver, increases
the peak data rates and spectrum efficiency up to several hundred percent.

3. MIMO
Systems utilizing multiple transmit and multiple receive antennas are commonly known as multiple input multiple output
(MIMO) systems. This wireless networking technology greatly improves both the range and the capacity of a wireless
communication system. MIMO systems pose new challenges for digital signal processing given that the processing algorithms
are becoming more complex with multiple antennas at both ends of the communication channel.
Traditional wireless communication systems with one transmit and one receive antenna are denoted as single input single
output (SISO) systems, whereas systems with one transmit and multiple receive antennas are denoted as single input
multiple output (SIMO) systems, and systems with multiple transmit and one receive antenna are called multiple input single
output (MISO) systems. Conventional smart antenna systems have only a transmit side or only a receive side equipped with
multiple antennas, so they fall into one of last two categories. Usually, the base station has the antenna array, as there is
enough space and since it is cheaper to install multiple antennas at base stations than to install them in every mobile station.
Strictly speaking, only systems with multiple antennas at both ends can be classified as MIMO systems. Although it may
sometimes be noted that SIMO and MISO systems are referred as MIMO systems. In the terminology of smart antennas,
SIMO and MISO systems are also called antenna arrays

4. Discussion about MIMO
 Tx diversity in LTE.
 SU-MIMO and MU-MIMO.
 Spatial multiplexing in LTE.
 UE feedback (CSI, PMI, RI and CQI) in LTE.
 Open loop spatial multiplexing in LTE.
 Closed loop spatial multiplexing in LTE.

5. Conventional Radio System (SISO)
Conventional systems use one transmit and one receive antenna. In MIMO terminology, this is called Single Input,
Single Output (SISO)
SISO

6. According to Shannon, the capacity C of a radio channel is dependent on bandwidth B and the signal-to-
noise ratio S/N. The following applies to a SISO system:
Shannon-Hartley theorem for SISO

7. Multiple Antenna Systems
A MIMO system typically consists of m transmit and n receive antennas Figure below . By using the same channel,
every antenna receives not only the direct components intended for it, but also the indirect components intended for
the other antennas. A time-independent, narrowband channel is assumed. The direct connection from
antenna 1 to 1 is specified with h11, etc., while the indirect connection from antenna 1 to 2 is identified as cross
component h21, etc. From this is obtained transmission matrix H with the dimensions n x m.
General MIMO
The following transmission formula results from receive vector y, transmit vector x, and
noise n:

8. y = Hx + n .
Formula : MIMO transmission
Data to be transmitted is divided into independent data streams. The number of streams M is always less than or
equal to the number of antennas; in the case of asymmetrical (m E n) antenna constellations, it is always smaller or
equal the minimum number of antennas. For example, a 4x4 system could be used to transmit four or fewer streams,
while a 3x2 system could transmit two or fewer streams. Theoretically, the capacity C increases linearly with the
number of streams M.
Shannon-Hartley theorem for MIMO

9. Single layer vs. Multiple layers
The data rate only increases
logarithmically as a function of the SNR
(or SINR – Signal to Interference and
Noise Ratio), at a high SNR. This is
according to the Shannon theorem
rdata = BW x log2(1+SNR)
(max data rate rdata is equal to the
bandwidth, BW, multiplied by the base-
2 logarithm of the SNR plus 1).

10. The data rate only increases logarithmically as
a function of the SNR (or SINR – Signal to
Interference and Noise Ratio), at a high SNR.
This is according to the Shannon theorem
rdata = BW x log2(1+SNR)
(max data rate rdata is equal to the
bandwidth, BW, multiplied by the base-2
logarithm of the SNR plus 1).
On the other hand, at a low SNR, the max data
rate increases almost linearly. Therefore, it is
not efficient aiming only to obtain a high SNR.
It is more efficient to try to create several
“data pipes” with lower SNR (sharing SNR),
which will lead to a multiplication of the
maximum achievable data rate with up to the
channel rank rmax.. Without/With MIMO

11. A traditional way of sharing the SNR is actually by
spread spectrum techniques, e.g. CDMA, where
the transmission is multiplexed over a wider
bandwidth. Different configurations of multiple
antennas are shown in Figure1-3. These include
SISO (Single Input Single Output), MISO (Multiple
Input Single Output), SIMO (Single Input Single
Output) and of course, MIMO (Multiple Input
Multiple Output). The naming convention refers to
input/output of the radio channel. This means that
the transmitter antenna(s) correspond to input to
the radio channel and the receiver antenna(s)
reception correspond to the output of the radio
channelAntenna configurations

12. MIMO IN LTE
There are seven different transmission modes in LTE.
Switching between the modes is done by RRC
signaling.
 Mode 1 (”Single antenna port, port 1”)
o One antenna
o Can be used for classical beamforming without
precoding feedback
 Mode 2 (”Transmit Diversity”)
o SFBC (Alamouti)
o 2 or 4 tx antennas
 Mode 3 (”Open loop spatial multiplexing”)
o 2 or 4 tx antennas
o CQI and RI feedback
o Tx schemes:
 Tx diversity
 Large delay CDD
 Mode 4 (”Closed Loop spatial multiplexing”)
o 2 or 4 tx antennas
o CQI, PMI and RI feedback
o Tx schemes:
 Tx diversity
 CL SM
 Mode 5 (”Multi User MIMO”)
o Two UEs can be scheduled in the same RB
o Tx schemes:
 Tx diversity
 MU-MIMO
 Mode 6 (”Closed loop spatial multiplexing, single layer”)
o As mode 4, but with RI hardcoded to 1
o Tx schemes:
 Tx diversity
 CL SM
 Mode 7 (”Single antenna port, port 5”)
o Can be used for classical beamforming without
feedback.

13. Single User MIMO (SU-MIMO)
When the data rate is to be increased for a single UE, this is called Single User MIMO (SU-MIMO)
SU-MIMO

14. Multi User MIMO (MU-MIMO)
When the individual streams are assigned to various users, this is called Multi User MIMO (MU-MIMO). This
mode is particularly useful in the uplink because the complexity on the UE side can be kept at a minimum by
using only one transmit antenna. This is also called 'collaborative MIMO'.
MU-MIMO

15. Spatial Multiplexing
Spatial multiplexing is not intended to make the transmission more robust; rather it increases the data rate. To do
this, data is divided into separate streams; the streams are transmitted independently via separate antennas.
Because MIMO transmits via the same channel, transmissions using cross components not equal to 0 will
mutually influence one another.
MIMO 2x2 antenna configuration
If transmission matrix H is known, the cross components can be calculated on the receiver. In the open-loop method, the transmission includes special sections that are also
known to the receiver. The receiver can perform a channel estimation. In the closed-loop method, the receiver reports the channel status to the transmitter via a special
feedback channel. This makes it possible to respond to changing circumstances.

16. Mathematical Calculation of MIMO
2X2 MIMO Calculation
overall data transmission process can be as below. The red arrow and four blocks
(h11,h12,h21,h22) between the two antenna is to illustrate the possible data path between the
two Tx and two Rx antenna.

17. h11, h12,h21,h22 are special numbers (coefficient) to show how much of the data is going through
each of the possible path. The greater the value is, the larger portions of data is being transmitted
in that path. A matrix which is made up of these channel path coefficient is called "Channel
Information Matrix". The reciever and transmitter relationship is represented as follows.
The main idea behind MIMO is that, the sampled signals in
spatial domain at both the transmitter and receiver end are
combined so that they form effective multiple parallel spatial
data streams which increase the data rate. The occurrence of
diversity also improves the quality that is the bit-error rate
(BER) of the communication.

18. Suppose that the spectrum of a SISO communication channel is 1MHz and the signal-to-noise ratio is 24dB. Using Shannon
formula in equation
where C is the capacity,
B the bandwidth of the channel and the signal-to-noise ratio.
By definition
Therefore

19. Applying the inverse function for the log function, the exponential function base 10 to both sides is expressed
as
Hence the capacity is calculated as
However, if we increase the number of antennas at both transmits and receive end of the SISO system to 2 and apply the MIMO channel
capacity formula in equation to the 2x2 MIMO system, with the same channel bandwidth of 1MHz and signals-tonoise
ratio of 24dB.

20. Example 2
Where IM is a 2 x 2 identity matrix and Ps/N =.. (S/N) signal-to-noise ratio,
the capacity is calculated as

21. Applying the change of base formula,
Comparing the capacities of example 1 and 2 has proven that the capacity of the SISO channel can be
doubled or increased by a factor of 2 if the number of antennas at both transmitter and receiver end of the
SISO channel are increased to 2