ELEC E7210: Communication Theory. Lecture 11: MIMO Systems and Space-time Communications

Transcription

1 ELEC E7210: Communication Theory Lecture 11: MIMO Systems and Space-time Communications

2 Overview of the last lecture MIMO systems -parallel decomposition; - beamforming; - MIMO channel capacity

3 MIMO Key building block for next generation. Are able to increase significantly data rates Both Tx and Rx diversity are exploited more reliable communications Multi-antenna signals can be jointly processed/combined increase of the system integrity or/and throughput

4 MIMO Significant increase of both the system capacity and spectral efficiency; capacity of wireless link increases linearly with increasing N min N t, N r Data rate can be increased by spatial multiplexing without consuming more frequency resources and without increasing the total transmit power Dramatic reduction of the effects of fading due to the increased diversity (especially is beneficial when the different channels fade independently)

5 MIMO CHANNEL Condition Number is defined as a ratio of the maximum and minimum eigenvalues of the MIMO channel matrix HH*. Large capacity gains from spatial multiplexing operation in MIMO wireless systems is possible when the statistical distributions of condition numbers have mostly low values. LOS conditions often create undesirable MIMO matrix conditions (i.e., high condition numbers) that can be mitigated using dual-polarized antennas.

6 Space-time coding (1) The multipath wireless channel is capable of enormous capacities, provided that the multipath scattering is sufficiently rich and is properly exploited through the use of an appropriate processing architecture Closed-loop MIMO and open-loop MIMO Transmission schemes that do not require CSI at the Tx may exploit the spatial dimension by introducing coding on the spatial domain: S-T coding X n L Codewords are matrices i block length

7 Space-time coding (2) Increases redundancy over space and time, as each antenna transmits a differently encoded fully redundant version of the same signal. The ML detector is optimal ST codes were originally developed in the form of STTCs; multidimensional Viterbi algorithm for decoding. STTCs can provide diversity equal to n and coding gain depending on the complexity of the code without loss in bandwidth efficiency.

8 Space-time coding (3) STBCs offer the same diversity as STTCs, combines all the copies of the received signal in an optimal way. STBCs are often preferred over STTCs, as their decoding is simpler. Alamouti STBCs for 2 Tx antennas in 3G standards STC assume perfect CSI at the receiver. Unitary and differential space-time coding has been proposed, which does not require CSI [Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading, IEEE Trans. Info. Theory, vol. 46, no. 2, Mar. 2000, pp ].

9 Space-Time Processing (1) The optimal decoding complexity is exponential in the number of antennas. Some of the approaches treat the transmission from each antenna as an independent user using conventional scalar codes in conjunction with multiuser detection techniques at the Rx (layered ST codes).

10 Space-Time Processing (2) Layered ST architectures exploit the spatial multiplexing gain by sending independently encoded data streams in diagonal layers (D- BLAST) or in horizontal layers (V-BLAST)

11 Space-time processing (3) D-BLAST - a diagonally layered coding structure in which code blocks are dispersed across diagonals in space-time.

12 Space-time processing (4)

13 Space-time processing (5) redundancy between the substreams is introduced through the use of specialized inter-substream block coding. In an independent Rayleigh scattering environment, this algorithm leads to theoretical rates which grow linearly with the number of antennas (number of Tx antennas = number of Rx antennas ), and the rates approach 90% of Shannon capacity. - Implementation complexity

14 Space-time processing (6) V-BLAST The encoding process is a demultiplex operation followed by independent bit-to-symbol mapping of each substream no inter-substream coding (conventional coding of the individual substreams may be applied). No explicit orthogonalization of the transmitted signals is imposed by the transmit structure at all. Instead, the propagation environment itself is exploited to achieve the signal decorrelation necessary to separate the cochannel signals.

15 Space-time processing (7) Block-diagram

16 Space-time processing (8) The received signal y Hx N The Rx must demultiplex the spatial channels: ZF (matrix inversion and the poor performance if the channel matrix is ill conditioned); MMSE; ML Symbol cancellation: interference from already-detected components of x is subtracted out from the received signal vector a modified received vector in which fewer interferers are present ( ~ DFE)

17 MIMO Rx (1) The ML detection is optimal Solving is impractical and exhaustive for high transmission rates, and the complexity grows exponentially with the number of antennas A solution: SD yˆ argmin y Hx SD solves this problem by searching for the closest point among all lattice points y that lie inside a sphere centered around the received vector and of radius d The algorithm runs recursively until all lattice points inside the sphere are found x X 2

18 MIMO Rx (2)

19 Diversity versus multiplexing (a fundamental tradeoff in multiple antenna channels) Multiple antennas can be used to increase diversity to combat channel fading. By sending signals carrying the same information through different paths, multiple independently faded replicas of the data symbol can be obtained at the Rx more reliable reception is achieved.

20 Diversity versus multiplexing (2) A slow Rayleigh fading environment with 1 transmit and m receive antennas, the transmitted signal passes through m different propagation paths If the fading is independent across antenna pairs, a maximal diversity gain (advantage) of m can be achieved: the average m error probability can be made to decay like 1/ SNR at high SNR, in contrast to 1/ SNR for the single antenna fading channel.

21 Diversity versus multiplexing (3) In MIMO systems, the underlying idea is still averaging over multiple path gains (fading coefficients) to increase the reliability. In a system with n transmit and m receive antennas, assuming the path gains between individual antenna pairs are i.i.d. Rayleigh faded, the maximal diversity gain is mn, which is the total number of fading gains that one can average over.

22 Diversity versus multiplexing (4) A MIMO channel can be beneficial through increasing the degrees of freedom available for communication. If, e.g., the path gains between individual Tx-Rx antenna pairs fade independently, the channel matrix is well-conditioned with high probability, then multiple parallel spatial channels are created by transmitting independent information in parallel through the spatial channels, the data rate can be increased, i.e. spatial multiplexing (e.g. BLAST scheme exploits this phenomenon)

23 Diversity versus multiplexing (5) A MIMO system can provide two types of gains: diversity gain and spatial multiplexing gain. Most of current research focuses on designing schemes to extract either maximal diversity gain or maximal spatial multiplexing gain. There are also schemes, which switch between the two modes, depending on the instantaneous channel condition Maximizing one type of gain may not necessarily maximize the other. For example, the coding structure from the orthogonal designs [V. Tarokh et al, Space-time block code from orthogonal designs, IEEE Trans. Inform. Theory, vol. 45, pp , July 1999.], while achieving the full diversity gain, reduces the achievable spatial multiplexing gain. Each of the two design goals addresses only one aspect of the problem, a concrete design depends on the application

24 Diversity versus multiplexing (6) It has been proven [L. Zheng D. Tse: Diversity and Multiplexing: A Fundamental Tradeoff in Multiple Antenna Channels ] that given a MIMO channel, both gains can be simultaneously obtained, but there is a fundamental tradeoff between how much of each type of gain any coding scheme can extract: higher spatial multiplexing gain comes at the price of sacrificing diversity. lim SNR log P e ( SNR) d log SNR lim SNR R(SNR) logsnr r

25 Diversity versus multiplexing (7) The i.i.d. Rayleigh flat fading channel. Consider a slow fading environment in which the channel gain is random but remains constant for a duration of L symbols. If L n m 1, the optimal diversity gain d * r achievable by any coding scheme of block length L and multiplexing gain r (r integer) is precisely d * r n r m r

26 Diversity versus multiplexing (8) May be interpreted as : out of the total resource of n Tx and m Rx antennas, it is as though r Tx and r Rx antennas were used for multiplexing and the remaining (n-r ) Tx and (m-r )Rx antennas provided the diversity. By adding 1 Tx and 1 Rx antenna, the spatial multiplexing gain can be increased by one while maintaining the same diversity level. The optimal tradeoff does not depend on L as long as L ; n m 1 no more diversity gain can be extracted by coding over block lengths greater than n m 1 than using a block length equal to n m 1

27 Diversity versus multiplexing (8)

28 Diversity versus multiplexing (9) R. W. Health et al, Switching between diversity and multiplexing in MIMO systems, IEEE Trans. Commun., June 2005.

29 MIMO Rx (3): FS channels Similarly to SISO, MIMO channels can be frequency selective Necessity of the equalizer

30 Frequency-selective MIMO channels Equalization over both space and time Complexity MIMO eq. problem SISO eq. problem MIMO+multicarrier modulation (MIMO-OFDM)

31 MIMO OFDM (1) OFDM is chosen over a single-carrier solution due to : lower complexity of equalizers for high delay spread channels or high data rates; efficient implementation over IDFT and DFT high flexibility in adaptive systems

32 MIMO OFDM (2) - At the receiver, FFT reduces the channel response into a multiplicative constant on a tone-by-tone basis. -With MIMO, the channel response becomes a matrix. Since each tone can be equalized independently, the complexity of space-time equalizers is avoided. - Multipath remains an advantage for a MIMO-OFDM system since frequency selectivity caused by multipath improves the rank distribution of the channel matrices across frequency tones, thereby increasing capacity

33 Space-time coding for MIMO-OFDM (3) Achievement of this full diversity requires that the information symbols be carefully spread over the tones as well as over Tx antennas. A space-frequency code (a space time-frequency code) is a strategy for mapping information symbols to antennas and tones as a means for extracting both spatial and frequency diversity.

34 Space-time coding for MIMO-OFDM (4) Space-frequency codes based directly on space time codes (with time reinterpreted as frequency) have been proposed but they fail to exploit the frequency diversity of a frequency-selective fading MIMO channel. A method for transforming any full-diversity space time code into a full-diversity space-frequency code has recently been proposed. W. Su et al, Full-rate full-diversity space-frequency codes with optimum coding advantage, IEEE Trans. Inform. Theory, Jan The design of space-frequency and space time-frequency codes an active research area.

35 Space-time coding for MIMO-OFDM (5) A. Multicarrier Delay Diversity Modulation Delay diversity was the first transmit diversity approach for flatfading MIMO channels. Multiple transmit antennas send delayed copies of same signal, and MLSE or DFE is used at the receiver to estimate the transmitted sequence.

36 Space-time coding for MIMO-OFDM (6)

37 Space-time coding for MIMO-OFDM (7) B. Closed-Loop MIMO-OFDM A closed-loop MIMO transmitter has knowledge of the channel, allowing it to perform an optimal form of pre-compensation A closed-loop MIMO-OFDM system can use beamforming on a tone-by-tone basis to transform a frequency-selecting MIMO channel into a collection of M parallel subchannels M min N t, N r

38 Space-time coding for MIMO-OFDM (8)