Multiple Input Multiple Output

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Multiple Input Multiple Output
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MIMO

• MIMO is introduced fairly recently.
• Will be used in 802.11n. 802.11n will be OFDM
  over MIMO.
• The basic idea is simple having multiple
  transmitting antennas and multiple receiving
  antennas.

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MIMO

• First, having multiple receiving antennas means
  that you can pick up more energy.
• Also, when one antenna is having trouble
  receiving signal, others are unlikely to be
  having the same problem. That is why commercial
  APs sometimes have multiple antennas also. It
  compares the received signal strength from
  different antennas and use the strongest one to
  decode the data. Called antenna diversity.
• As long as the antennas are sufficiently apart
  from each other, the signals are likely
  experiencing different fading. The space needs to
  be half of the carrier wavelength. If we are
  using 2.4GHz, the wavelength is about 10cm.

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MIMO

• Having multiple transmitting antennas does not
  necessarily mean that you can send more energy,
  because the transmitting energy is determined by
  other issues, such as your battery.
• However, it does mean that you can have multiple
  paths between the sender and the receiver. With
  nt transmitting and nr receiving antennas, you
  have nt times nr paths that can be assumed to be
  independent. If one path is in trouble, i.e.,
  there is someone in the blocking position right
  now, other paths are unlikely to be in the same
  situation at the same time. Much better than
  depending everything on only one path!
• Also, what makes MIMO possible is that the
  receiver antennas can operate in the linear range
  such that the received signal is the ADDITON of
  signals from multiple transmitting antennas.
• So, based on these high-level intuitions, MIMO is
  likely able to improve the performance. But how
  exactly?

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SIMO

• Single Input Multiple Output.
• Consider one transmitting antenna and two
  receiving antennas.
• Assume flat-fading, meaning that there is no
  multi-path, i.e., the received sample is relevant
  only to the current data symbol. We write it as
  ynxn wn.
• We can make this assumption because of OFDM.

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SIMO

• With two receiving antennas, we will receive
• that is, from the waveform received at each
  antenna, we can take a sample, and call it y1 and
  y2, respectively. Both samples are excited by x,
  but they are from different paths, therefore
  their channel coefficients (i.e., h1, h2) are
  different. One important thing to remember is
  that the noise from both antennas are usually
  assumed to be following the same distribution and
  have the same power and are independent from each
  other.

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SIMO Receiver

• For the simplest receiver, lets just add y1 with
  y2 and make a decision.
• Is this the optimal one?
• What if h110 while h21 (yes, this is
  possible!)? Remember that the noises are the same
  (random but following the same distribution) at
  both channels). Assume the data is 1 (BPSK), and
  this moment, the noises at both channels are -6.
  So, we will get (10(-6)) (1(-6)) -1, and we
  will think the sender sent 0!
• What is the problem? If we only use the strong
  channel we wont make the wrong decision!

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SIMO receiver

• The problem is that we are treating the
  information from a good channel and a weak
  channel in the same way.
• The information from the strong channel is more
  valuable than the weak channel.
• The optimal -- Maximum Ratio Combining (Section
  3.2.1 in the Tse book). We should weight the
  samples from the antennas according to the
  channel strength

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MISO

• Now consider the case when the sender has
  multiple antennas and the receiver has only one
  antenna.
• The sender has a power budget the total
  transmitting power cannot exceed a threshold.
• Assume that all antennas are sending the same
  data symbol at any time, so the receiver will
  receive
• where a1 and a2 represent the power allocated
  for antenna 1 and antenna 2, respectively.

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MISO

• The problem is to maximize the magnitude of the
  received signal x(h1a1h2a2) subject to the
  constraint that
• Any ideas?

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MISO

• Still maximum ratio combining. Define Lagrange
• Take the partial derivative of L over a1 and a2
• Means that a1 and a2 should be proportional to h1
  and h2.
• But this requires the sender knows the channel
  not always the case.

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The Altamonte Scheme

• The key is that the transmitting antennas are NOT
  restricted to sending the same data symbols at
  the same time.
• The Altamonte Scheme (Tse book Section 3.3.2).
  Consider two data symbols to be sent in two
  consecutive symbol times, u1 and u2 . At time 1,
  ant1 transmits u1 and ant2 transmits u2. At time
  2, ant1 transmits u2 and ant2 transmits u1.

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The Altamonte Scheme

• (These two formulas are from the Tse book.) So,
• Rearrange it, we have

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The Altamonte Scheme

• So, we have
• Note that
• that is, the two vectors are orthogonal to each
  other. So, to recover u1 and u2, we can multiply
• with the conjugate of either of the vectors.

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The Altamonte Scheme

• So, the magnitude of the received signal is
  proportional to , even when the transmitter
  is not aware of the channel coefficient at all.
• If the transmitter simply sends the same symbol
  over two antennas at the same power, the received
  signal is proportional to h1 h2 , and depends
  on the phase, they may cancel each other out!

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2 by 2 MIMO

• Now consider we have two transmitting antennas
  and two receiving antennas.
• A simple scheme called V-BLAST Send
  independent data symbols over the transmitting
  antennas as well as over time.

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MIMO

• MIMO receiver. Will receive two samples per time
  slot. hij the channel coefficient from Tx ant j
  to Rx ant i.
• How to decode the data?

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MIMO receiver

• The simplest receiver just do a matrix inversion
• This is NOT the optimal decoder! The maximum
  likelihood decoder is better.