Revision of Lecture Twenty-Eight

ELEC64 Advanced Wireless Communications Networks and Systems Revision of Lecture Twenty-Eight MIMO classification: roughly three classes create diversity, increase throughput, support multi-users Some classification also includes beamforming Single-user fractional-spaced receiver Baseband continuous-time model, discrete-time multirate model, discrete-time multichannel model SDMA induced MIMOs Adaptive beamforming assisted receiver, and transmit beamforming This lecture carries on MIMO A, B, C 38

ELEC64 Advanced Wireless Communications Networks and Systems SDMA Systems Previous lecture considers flat MIMO, we now considers frequency-selective MIMO, requiring space-time processing SDMA induced MIMO system: Assume one transmit antenna and L receiver antennas supporting M users No specific antenna array structure is assumed, so it is most generic Channels are frequency selective, and CIR connecting user m and lth receiver antenna is c l,m = [c 0,l,m c,l,m c nc,l,m] T user user user M Tx Tx Tx Symbol-rate received signal samples x l (k) for l L are given by s (k) s (k) s (k) M n (k) n (k) n (k) L x (k) x (k) x (k) L Multiuser Detector y (k) y (k) y (k) M s ^ (k d) s ^ (k d) s ^ M(k d) x l (k) = M m= n C i=0 c i,l,m s m (k i) n l (k) = x l (k) n l (k) n l (k) is complex-valued AWGN with E[ n l (k) ] = σ n, x l(k) is noise-free part of lth receive antenna s output, s m (k) is kth transmitted symbol of user m (assuming BPSK for simplicity) 38

ELEC64 Advanced Wireless Communications Networks and Systems Multiuser supporting capability Multiuser Detection in SDMA Systems CDMA: each user is separated by a unique user-specific spreading code SDMA: each user is associated with a unique user-specific CIR encountered at receiver antennas Unique user-specific CIR plays role of user-specific CDMA signature Owing to non-orthogonal nature of CIRs, effective multiuser detection is required for separating users A bank of M space-time equalisers forms MUD, whose soft outputs are L y m (k) = l= n F i=0 x (k) x (k) x (k) L w * 0,,m w * w*,,m n,,m * * 0,L,m,L,m w* w* 0,,m,,m w* n,,m w w w i,l,m x l(k i), m M w F F * n,l,m F w l,m = [w 0,l,m w,l,m w nf,l,m] T is mth user detector s equaliser weight vector associated with lth receive antenna, STE has order n F and decision delay d y (k) m 383

ELEC64 Advanced Wireless Communications Networks and Systems System Model Define n F (n F n C ) CIR matrix associated with user m and lth receive antenna C l,m = 6 4 c 0,l,m c,l,m c nc,l,m 0 0 0 c 0,l,m c,l,m c nc,l,m.. 0 0 0 c 0,l,m c,l,m c nc,l,m 3 7 5 Introduce overall system CIR convolution matrix C = 6 4 C, C, C,M C, C, C,M... C L, C L, C L,M 3 7 5 Then received signal vector x(k) = [x (k) x (k) x L (k)] T can be expressed by x(k) = C s(k) n(k) = x(k) n(k) where x l (k) = [x l (k) x l (k ) x l (k n F )] T for l L, n(k) = [n (k) n (k) n L (k)] T with n l (k) = [n l (k) n l (k ) n l (k n F )] T, and s(k) = [s T (k) st (k) st M (k)]t with s m (k) = [s m (k) s m (k ) s m (k n F n C )] T 384

ELEC64 Advanced Wireless Communications Networks and Systems Space-Time Equalisation Output of mth STE detector can be written as y m (k) = L w H l,m x l(k) = w H m x(k) l= where w m = [w T,m wt,m wt L,m ]T With y R m(k) = Re[y m (k)], M user detectors decisions are defined by ŝ m (k d) = sgn (y R m(k)), m M Minimum mean square error solution is defined by closed-form w (MMSE)m = C C H σ n I C (m )(nf n C )(d) for m M, where I denotes Ln F Ln F identity matrix and C i the ith column of C Adaptive implementation using LMS algorithm where ǫ(k) = s m (k d) y m (k) w m (k ) = w m (k) µx(k)ǫ (k) 385

ELEC64 Advanced Wireless Communications Networks and Systems Bit Error Rate of Space-Time Equaliser Note transmitted symbol sequence s(k) {s (q), q N s }, where N s = M(n F n C ) Let the element of s (q) corresponding to desired symbol s m (k d) be s (q) m,d Noise-free part of mth detector input signal x(k) assumes values from signal set m = { x (q) = C s (q), q N s } m can be partitioned into two subsets, depending on the value of s m (k d), as follows (±) m = { x(q,±) m : s m (k d) = ±} Similarly, noise-free part of mth detector s output ȳ m (k) assumes values from the scalar set Y m = {ȳ (q) m = wh m x(q), q N s } Thus ȳ R m(k) = Re[ȳ m (k)] can only take the values from the set Y R m = {ȳ (q) Rm = Re[ȳ(q) m ], q N s} Y R m can be divided into the two subsets conditioned on the value of s m (k d) Y (±) Rm = {ȳ(q,±) Rm Y Rm : s m (k d) = ±} 386

ELEC64 Advanced Wireless Communications Networks and Systems Bit Error Rate of STE (continue) Conditional PDF of y R m(k) given s m (k d) = is a Gaussian mixture where ȳ (q,) Rm p m (y R ) = N sb N sb q= p πσ n wm Hw e m y R ȳ (q,) «Rm σ n wh m w m Y() Rm and N sb = N s / is the number of points in Y () Rm Thus BER of the mth detector associated with the detector s weight vector w m is given by P E (w m ) = N sb N sb q= Q g (q,) (w m ) where Q(u) = π Z u e v d v and g (q,) (w m ) = sgn(s(q) m,d )ȳ(q,) Rm p σ n w H m w m Note that BER is invariant to a positive scaling of w m Alternatively, the BER may be calculated based on the other subset Y ( ) Rm. 387

ELEC64 Advanced Wireless Communications Networks and Systems Minimum Bit Error Rate Solution MBER solution for the mth STE detector is defined as w (MBER)m = arg min wm No closed-form solution, but gradient of P E (w m ) is P E (w m ) P E (w m ) = N sb πσn p w H m w m N sb q= e ȳ (q,) «Rm σ n wh m w msgn s (q) ȳ(q,) Rm w m m,d wm Hw m x (q,)! Gradient optimisation can be applied to obtain a w (MBER)m Adaptive implementation using LBER algorithm w m (k ) = w m (k) µ sgn(s m(k d)) e y Rm (k) ρ n x(k) πρ n where µ is adaptive gain, and ρ n kernel width 388

ELEC64 Advanced Wireless Communications Networks and Systems Simulation Results: Stationary System CIRs of 3-user 4-antenna stationary system C l,m (z) m = m = m = 3 l = ( 0.5 j0.4) (0.7 j0.6)z ( 0. j0.) (0.7 j0.6)z ( 0.7 j0.9) (0.6 j0.4)z l = (0.5 j0.4) ( 0.8 j0.3)z ( 0.3 j0.5) ( 0.7 j0.9)z ( 0.6 j0.8) ( 0.6 j0.7)z l = 3 (0.4 j0.4) ( 0.7 j0.8)z ( 0. j0.) (0.7 j0.6)z (0.3 j0.5) (0.9 j0.)z l = 4 (0.5 j0.5) (0.6 j0.9)z ( 0.6 j0.4) (0.9 j0.4)z ( 0.6 j0.6) (0.8 j0.0)z CIR order n C =, STE order n F = 3 and decision delay d = BER comparison of MMSE/MBER and LMS/LBER for three users 0 - LMS() MMSE() LBER() MBER() 0 - LMS() MMSE() LBER() MBER() 0 - LMS(3) MMSE(3) LBER(3) MBER(3) log0(bit Error Rate) - -3-4 log0(bit Error Rate) - -3-4 log0(bit Error Rate) - -3-4 -5-5 -5-6 -5 0 5 0 5 SNR (db) -6-5 0 5 0 5 SNR (db) -6-6 -4-0 4 6 SNR (db) 389

ELEC64 Advanced Wireless Communications Networks and Systems Simulation Results: Fading System 3 users, 4 receive antennas, and Rayleigh fading channels with each of CIRs having n C = 3 taps Each channel tap has root mean power of 0.5 j 0.5 Normalised Doppler frequency for simulated system was 0 5, which for a carrier of 900 MHz and a symbol rate of 3 Msymbols/s corresponded to a user velocity of 0 m/s (36 km/h) STE order n F = 5 and decision delay d = Frame structure: 50 training symbols followed by 450 data symbols BER comparison of LMS/LBER for three users 0 0 LMS() LBER() 0 0 LMS() LBER() 0 0 LMS(3) LBER(3) 0 0 0 0 0 0 BER BER BER 0 3 0 3 0 3 0 4 0 4 0 4 0 5 5 0 5 0 5 Average SNR (db) 0 5 5 0 5 0 5 Average SNR (db) 0 5 5 0 5 0 5 Average SNR (db) 390

ELEC64 Advanced Wireless Communications Networks and Systems Diversity We now consider diversity gain aspect of MIMO Transmit diversity: assume Two transmit antennas, which are sufficiently apart One receive antenna Two channel estimates are available at transmitter Receive diversity: assume One transmit antenna Two receive antennas, which are sufficiently apart Two channel estimates are available at receiver channel estimate x ML detector x h * h * h n Transmit Diversity y h channel estimate n h channel estimate Receive Diversity h x y h ML detector h * * Transmit diversity order of two: two transmit signals are h x and h x, and receive signal is y = h h x h h x n = ` h h x n Receive diversity order of two: optimal combined signal of two receive signals is y = h `h x n h `h x n = ` h h x n n channel estimate 39

ELEC64 Advanced Wireless Communications Networks and Systems G Space-Time Block Code Alamouti s G space-time block code uses two transmitter antennas and one receiver antenna In time slot (one symbol period), two symbols (x,x ) are transmitted While in time slot, transformed (x,x ), i.e. ( x,x ), are transmitted Assume narrowband channels with channel, h = h e jα and channel, h = h e jα Antenna spacing is sufficiently large, e.g. 0 wavelengths, so two channels are independently faded Fading is sufficiently slow so during two time slots channels h, h are unchanged n n x x x * x h * Linear Combiner ~ x x~ Maximum Likelihood Detector h y =h x h x n y = h x * h x * n h h Time slot x^ Time slot ^x Channel Esimator 39

ELEC64 Advanced Wireless Communications Networks and Systems G STBC (continue) Received signals at two time slots are respectively y = h x h x n y = h x h x n Assume perfect channel estimate h,h, linear combiner s outputs are x = h y h y = ( h h )x h n h n x = h y h y = ( h h )x h n h n Maximum likelihood decoding involves minimising decision metric x ( h h )x for decoding x and minimising decision metric x ( h h )x for decoding x 393

ELEC64 Advanced Wireless Communications Networks and Systems Space-Time Block Codes Encoding: generic STBC is defined by n p transmission matrix 3 g g g p x, x, x,p G = 6 g g g p 7 4... 5 = 6 x, x, x,p 4... g n g n g np x n, x n, x n,p Each entry g ij = x i,j is a linear combination of k input symbols x, x, x k and their conjugates Number of rows n is equal to number of time slots, and number of columns is equal to number of transmit antennas During time slot i, encoded symbols x i,, x i,,, x i,p are transmitted simultaneously from transmit antennas,,, p, respectively Code rate is obviously R = k/n Assume L receiver antennas, and channel connecting jth transmit antenna and lth receiver antenna is h j,l, then received signal arriving at receiver l during time slot i is p y i,l = h j,l x i,j n j,l where n j,l is AWGN for j, l-th channel ML detector or suboptimal low-complexity detector can be employed j= 3 7 5 394

ELEC64 Advanced Wireless Communications Networks and Systems Space-Time Block Codes (continue) Decoding: assuming perfect channel estimate, maximum likelihood decoding decides in favour of specific entry x i,j, i n, j p, that minimises the decision metric n i= L l= yi,l p h j,l x i,j j= An alternative is maximum a posteriori probability decoding, for details see relevant reference STBC examples (transmit antennas p =, 3, 4) G =» x x x x, G 3 = 6 4 x x x 3 x x x 4 x 3 x 4 x x 4 x 3 x x x x 3 x x x 4 x 3 x 4 x x 4 x 3 x 3, G 4 = 7 6 5 4 x x x 3 x 4 x x x 4 x 3 x 3 x 4 x x x 4 x 3 x x x x x 3 x 4 x x x 4 x 3 x 3 x 4 x x x 4 x 3 x x 3 7 5 G has time slots n =, G 3 and G 4 have time slots n = 8 395

ELEC64 Advanced Wireless Communications Networks and Systems STBC Examples (continue) STBC examples (transmit antennas p = 3, 4) H 3 = 6 4 x x x 3 x x x 3 x 3 x 3 x x x x x 3 x 3 x x x x 3, H 4 = 7 5 6 4 x x x 3 x 3 x x x 3 x 3 x x x x x 3 x 3 x x x x x 3 x 3 x x x x x x x x 3 7 5 H 3 and H 4 have time slots n = 4 Parameters of space-time block codes space-time code rate number of number of number of block code R transmitters p input symbol k time slots n G G 3 / 3 4 8 G 4 / 4 4 8 H 3 3/4 3 3 4 H 4 3/4 4 3 4 396

ELEC64 Advanced Wireless Communications Networks and Systems Summary Multiuser capacity of SDMA systems Space-time equalisation assisted multiuser detection for SDMA systems MMSE design and MBER design, adaptive implementation Diversity order, and space-time block codes 397