CHAPTER 8 MIMO Xijun Wang

WEEKLY READING

1. Goldsmith, “Wireless Communications”, Chapters10

2. Tse, “Fundamentals of Wireless Communication”,Chapter 7-10

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MIMO TRANSCEIVER

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MIMO TRANSCEIVER

n Encoding¨ Mapping one data stream to one or more spatial data

streams.¨ Assumes no CSIT and focuses on enhancing reliability

through diversity.

n Precoding¨ Mapping the spatial data streams to the transmit

antennas.¨ Exploits the channel information available at the

transmitter and focuses on enhancing system performance.

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ENCODING STRUCTURE

n Spatial multiplexing

n Space–time (ST) coding

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SPATIAL MULTIPLEXING

n Vertical encoding Bell Labs Layered Space Time (BLAST) architecture

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the data stream is demultiplexedinto Mt independent streams

achieve at most a diversity order of Mr

transmite the independent codewords on separate antennas

SPATIAL MULTIPLEXING

n Diagonal encoding Bell Labs Layered Space Time (BLAST) architecture

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the data stream is first horizontally encoded

the codeword symbols are rotated across antennas

SPATIAL MULTIPLEXING

n D-BLAST

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a codeword is spread over all Mt antennas

achieve the full MtMr diversity gain

SPACE-TIME CODING

n Space–time coding (STC) scheme¨ introduce temporal and spatial correlation into the

signals transmitted from different antennas ¨ without increasing the total transmitted power or the

transmission bandwidth.

n A diversity gain that results from multiple paths between the base-station and the user terminal

n A coding gain that results from how symbols are correlated across transmit antennas

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SPACE–TIME CODE DESIGN CRITERIA

n Pairwise error probability ¨ the probability that an erroneous codeword e is

mistaken for the transmitted codeword x.

¨ q denotes the rank of A(x,e).¨ 𝜆n are the eigenvalues of the matrix A(x,e).¨

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SPACE–TIME CODE DESIGN CRITERIA

n Rank criterion¨ In order to achieve maximum diversity Mt Mr , the

matrix B(x,e) has to be full rank for any codewords x, e. ¨ If the minimum rank of B(x,e) over all pairs of distinct

codewords is q, then a diversity order of qMr is achieved.

n Determinant criterion. ¨ For a given diversity order target of q, maximize

over all pairs of distinct codewords.

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SPACE–TIME TRELLIS CODES (STTC)

n The space–time trellis encoder maps the information bit stream into Mt streams of symbols (each belonging in a size-2b signal constellation) that are transmitted simultaneously.

n The total transmitted power is divided equally among the Mt transmit antennas.

n The decoding complexity of STTC (measured by the number of trellis states at the decoder) increases exponentially as a function of the diversity level and the transmission rate

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EIGHT-STATE 8PSK STTC WITH TWO ANTENNAS

13Tx1

Tx2

EIGHT-STATE 4PSK STTC WITH TWO ANTENNAS

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Input: 0 1 2 3 2 1State:0

SPACE–TIME BLOCK CODES (STBC)

n Alamouti’s codes¨ First, it achieves full-diversity at full transmission rate for

any (real or complex) signal constellation. ¨ Second, it does not require CSI at the transmitter (i.e.

open-loop). ¨ Third, maximum-likelihood decoding involves only linear

processing at the receiver (due to the orthogonal code structure).

n Extensions¨ full-rate orthogonal designs exist for all real

constellations for two, four, and eight transmit antennas only,

¨ for all complex constellations they exist only for two transmit antennas (the Alamouti scheme).

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LINEAR PRECODING STRUCTURE

n A linear precoder functions as an input shaper and a beamformer with one or multiple beams with per-beam power allocation.

n Consider the singular value decomposition of the precoder matrix F

¨ orthogonal beam directions (patterns) are the left singular vectors UF

¨ the beam power loadings are the squared singular values D2

¨ The right singular vectors VF , termed the input shaping matrix

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LINEAR PRECODING STRUCTURE

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LINEAR PRECODING STRUCTURE

n A precoder therefore has two effects¨ decoupling the input signal into orthogonal spatial

modes in the form of eigen-beams¨ allocating power over these beams, based on the CSIT.

n If the precoded orthogonal spatial modes match the channel eigen-directions, there will be no interference among signals sent on these modes, creating parallel channels and allowing transmission of independent signal streams.

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LINEAR PRECODING STRUCTURE

n For orthogonal eigen-beams, if the beams all have equal power, the radiation pattern of the transmit antenna array is isotropic.

n If the beam powers are different, however, the overall transmit radiation pattern will have a specific shape.

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RECEIVER ARCHITECTURES

n joint ML decoding of the data streams ¨ the complexity grows exponentially with the number of

data streams.

n use linear operations to convert the problem of joint decoding of the data streams into one of individual decoding of the data streams

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LINEAR DECORRELATOR

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if there are more data streams than the dimension of the received signal (i.e., nt > nr), then the decorrelator operation will not be successful

remove this inter-stream interference is to project the received signal y onto the subspace orthogonal to the one spanned by the vectors

the decorrelator for the kth stream is the kth column of the pseudoinverse H† of the matrix H

SUCCESSIVE CANCELLATION

n the result of one of the filters could be used to aid the operation of the others.

n once a data stream is successfully recovered, we can subtract it off from the received vector and reduce the burden on the receivers of the remaining data streams.

n error propagation: an error in decoding the kth data stream means that the subtracted signal is incorrect and this error propagates to all the streams further down, k +1, . . . , nt .

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DECORRELATOR-SIC

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DECORRELATOR-SIC

n At high SNR, for i.i.d. Rayleigh fading, the basic decorrelator bank achieves the full degrees of freedom in the channel.

n Successive cancellation does not provide additional degrees of freedom.

n There is a power gain: by decoding and subtracting instead of linear nulling, the effective SNR at each stage is improved.

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MMSE RECEIVER

n decorrelator¨ completely eliminating inter-stream interference ¨ without any regard to how much energy of the stream

of interest is lost in this process

n matched filtering ¨ preserving as much energy content of the stream of

interest as possible ¨ at the cost of possibly facing high inter-stream

interference

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MMSE RECEIVER

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MMSE RECEIVER

n At high SNR¨ the inter-stream interference is dominant over the

additive Gaussian noise and the decorrelator performs well.

n At low SNR ¨ the inter-stream interference is not as much of an issue

and receive beamforming (matched filter) is the superior strategy.

¨ In fact, the bank of matched filters achieves capacity at low SNR

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MMSE RECEIVER

n Linear MMSE receiver

n Low SNR

n High SNR

n Output SINR

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MMSE RECEIVER

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MMSE-SIC

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MMSE-SIC

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The bank of linear MMSE receivers with successive cancellation and equal power allocation achieves the capacity of the i.i.d. Rayleigh fading channel.