Space Time Codes

2 Attenuation in Wireless Channels Path loss: Signals attenuate due to distance Shadowing loss : absorption of radio waves by scattering structures Fading loss :constructive and destructive interference of multiple reflected radio wave paths Channel parameters: coherence time, coherence bandwidth If symbol period>coherence time, the channel is time selective If symbol period< channel delay spread, the channel is frequency selective

3 Diversity techniques Powerful technique that provides wireless link improvement at relatively low cost. Unlike equalization, diversity requires no training overhead.

4 …Principle of diversity Receiving the same information bearing signal over 2 or more fading channels. Eg. If we space 2 antennas at 0.5 m, one may receive a null while the other receives a strong signal. By selecting the best signal at all times, a receiver can mitigate or reduce small-scale fading. This concept is Antenna Diversity.

5 Types of diversity Space Diversity Transmission using multiple transmit/receive antennas Either at the mobile or base station. At base station, separation on order of several tens of wavelength are required. Polarization Diversity Orthogonal Polarization to exploit diversity High art of space diversity is avoided.

6 …Types of diversity Frequency Diversity : More than one carrier frequency is used Multiple frequency channels separated by at least the coherence bandwidth Time Diversity : Information is sent at time spacings Greater than the coherence time of channel, so that multiple repetitions can be resolved

7 Spatial diversity Single-input, single-output (SISO) channel No spatial diversity Single-input, multiple-output (SIMO) channel Receive diversity Multiple-input, single-output (MISO) channel Transmit diversity Multiple-input, multiple-output (MIMO) channel Combined transmit and receive diversity

8 Spatial diversity (cont’d) Selection combining (SC) h1h1 h2h2 y x Monitor SNR Select branch

9 Spatial diversity (cont’d) Switched diversity Switch-and-stay combining (SSC) Switch-and-examine combining (SEC) h1h1 h2h2 x Comparator Channel estimator switching threshold

10 Spatial diversity (cont’d) Maximum ratio combining (MRC) Combining all the signals in a co-phased and weighted manner so as to have the highest achievable SNR at the receiver at all times. h1h1 h2h2 h1*h1* h2*h2*  y x

11 Spatial diversity (cont’d) Equal Gain Combining (EQC) Combining all the signals in a co-phased manner with unity weights for all signals so as to improve achievable SNR at the receiver at all times. h1h1 h2h2 h1*h1* h2*h2*  y x

12 Diversity Improvement Consider a fading channel (Rayleigh) Input s(t) Output r(t) Input-output relation r (t) =  (t) e -j  (t) s (t) + n (t) Average value of signal to noise ratio ___ SNR =  = (E b / N o )  2 (t) Channel

13 Diversity improvement in MRC Assumptions: The voltage signal γ i from each of the M diversity branches are co-phased to provide coherent voltage addition and are individually weighted to provide optimal SNR. Each branch has gain G i Each branch has same average noise power N

14 Resulting signal envelope applied to the detector is Assuming that all amplifiers have additive noise at their input and that the noise is uncorrelated between different amplifiers. Diversity improvement in MRC

15 Which results in a SNR applied to the detector γ M Using Chebychev’s inequality γ M is maximized when Diversity improvement in MRC

16 The Maximized value is The received signal envelope for a fading mobile radio signal can be modeled from two independent Gaussian random variables T c and T s each having zero mean and equal variance σ 2. Diversity improvement in MRC

17 Diversity improvement in MRC Hence γ M is a chi-square distribution of 2M Gaussian random variable with variance The resulting pdf for γ M is

18 The probability that γ M is less than some SNR threshold γ is Diversity improvement in MRC Hence the mean SNR is

19 Maximizing diversity with Space-Time Codes Space–Time Trellis Codes (STTC) often better performance at the cost of increased complexity Complex decoding (vector version of the Viterbi algorithm) —increases exponentially with the transmission rate Full diversity. Coding gain Space–Time Block Codes (STBC) Simple maximum–likelihood (ML) decoding based on linear processing Full diversity. Minimal or no coding gain

20 Scope of MIMO MIMO channels offer multiplexing gain, diversity gain, power gain (array gain) and a co–channel interference cancellation gain Tradeoff between diversity gain and multiplexing gain: Careful balancing between those gains is required Space-Time Coding: Space-Time block codes (STBC) and Space-Time Trellis Codes Easy to combine with error control codes MIMO systems offer a solution choice for future generation wireless networks Distributed MIMO: Cooperative wireless networks