Waveform Design for the Massive MIMO Downlink Erik G. Larsson May 27, 2014 Div. of Communication Systems Dept. of Electrical Engineering (ISY) Link¨ oping University Link¨ oping, Sweden www.commsys.isy.liu.se MM YS
Conventional Multiuser MIMO Precoding 1/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
A Unique Feature of the Massive MIMO Downlink ◮ M − K unused degrees of freedom ◮ Channel nullspace: dim ( null ( H T )) = M − K ! ◮ Exploit nullspace for hardware-friendly waveform shaping: y = H T x + w = H T ( x + z ) + w if z ∈ null ( H T ) ◮ Per-antenna constant envelope or low-PAR multiuser precoding 2/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
“Discrete-Time Constant Envelope” (DTCE) Precoding ℋ mf y 1 [ n ] psf P A User 1 { u 1 [ n ]} psf P A Precoder mf y k [ n ] { u k [ n ]} User k { u K [ n ]} psf mf y K [ n ] P A Channel ℋ User K ⇒ Not phase modulation! Not equal gain combining! ⇒ Not constant modulus beamforming! ⇒ Requires extra emitted power but allows for reduced PA backoff. Worth it? 3/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Discrete-Time Constant-Envelope (DTCE) Precoding Algorithm � M L − 1 P � � h k,m [ l ] e jθ m [ n − l ] + w k [ n ] ◮ Channel model: y k [ n ] = M m =1 l =0 �� M � � L − 1 √ √ l =0 h k,m [ l ] e jθ m [ n − l ] √ √ m =1 = P E k u k [ n ] + P √ − E k u k [ n ] + w k [ n ] M � �� � “interference” J k [ n ] ◮ Find { θ m [ n ] } via: N K � � | J k [ n ] | 2 . min { θ m [ n ] } n =1 k =1 ◮ Capacity lower bound, for u k [ n ] Gaussian with unit energy � � PE k PE k R k = E log 2 � log 2 � � 1 /N PJ k + 1 � � � P · E [ J k J H k | H ] + I � ◮ For fixed P , select { E k } that maximize � k R k 4/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Extra Power Cost of DTCE at R = 2 bpcu/terminal, M = 80 , K = 10 0 L = 1, DTCE L = 4, DTCE 1 Required power [dB] L = 1, 4, Coop. lower bound 2 3 4 5 0 20 40 60 Window length 5/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
DTCE in Discrete vs. Continuous Time, RRC with β = 0 . 3 0.15 0.15 PAR: 3.95 dB 0.1 0.1 Quadrature Amplitude Quadrature Amplitude 0.05 0.05 0 0 − 0.05 − 0.05 − 0.1 − 0.1 − 0.1 − 0.05 0 0.05 0.1 0.15 − 0.1 − 0.05 0 0.05 0.1 0.15 Inphase Amplitude Inphase Amplitude (a) Discrete time (b) Cont. time 6/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Peak-to-Average Ratios, RRC with β = 0 . 3 SC TR-MRP 4-QAM OFDM MRP 7/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Amplitude Transfer Characteristics 8/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Amplifier Distortion ◮ Transfer function (complex baseband) y ( t ) = g ( | x ( t ) | ) e j arg x ( t )+ j Φ( | x ( t ) | ) . x ( t ) �→ ◮ Example: Rapp Model (class B) | x | /x max g ( | x | ) = α · (1 + ( | x | /x max ) 2 p ) 1 / (2 p ) Φ( | x | ) = 0 ◮ In-band distortion: with y =desired, ˜ y =actually received complex sample, y | 2 ] NMSE = E [ | y − λ ˜ λ ˜ y = LMMSE est. of y , E [ | y | 2 ] Empirical observation: the error ( y − λ ˜ y ) is independent of y ⇒ in-band distortion effectively yields an extra noise term ◮ Out-of-band distortion: Measured in terms of � f 0 + B/ 2 max f 0 , | f 0 | >B f 0 − B/ 2 S x ( f ) d f ACLR = � B/ 2 − B/ 2 S x ( f ) d f 9/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
In-Band Distortion, Example, M = 100 2 1.5 Quadrature Amplitude 1 0.5 0 − 0.5 − 1 − 1.5 − 2 − 2 − 1.5 − 1 − 0.5 0 0.5 1 1.5 2 Inphase Amplitude 10/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Out-of-Band Distortion, Example 10 0 PA operation at 10 1dB compression 20 MRP PSD [dB] 30 40 DTCE 50 10 dB back-off 60 70 0 0.5 1 1.5 2 Normalized Frequency, symbol rate = 1 11/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Amplifier Power Efficiency ◮ For class B PA: E [ | x ( t ) | 2 ] η = π | y max | · E [ | x ( t ) | ] ∼ P out 1 η ≤ π 4 · √ P in = √ 4 ≈ 78% , b ◮ Increased back-off ( b ) ⇒ reduced η ◮ Max efficiency requires constant-envelope in continuous time (CPM) 12/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Basic Tradeoff Radiated power to achieve rate R DTCE Δ P MRP ZF R-ZF 4 dB 10 dB PAR (cont. time) � � 1 + M P ⇒ For MRP: R k � max η log 2 , P = η · P cons. K P + D k +1 � � 1 + M − K P ⇒ For ZF: R k � max η log 2 , P = η · P cons. K D k +1 � � P ⇒ For R-ZF: R k � max η log 2 1 + G · , P = η · P cons. P J k + D k +1 � � P E k ⇒ For DTCE: R k � max E k ,η log 2 , P = η · P cons. P J k + D k +1 13/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
In-Band Distortion versus Efficiency MRP and ZF 14/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Out-Band Distortion versus Efficiency 10 20 30 1.8 dB 2.2 dB ACLR [dB] 40 LTE 5.2 dB 50 10 dB 60 70 14 dB MRP and ZF DTCE 80 20 dB 90 0 10 20 30 40 50 60 70 80 Efficiency η [%] 15/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Amplifier Power Consumption—at the Optimal Operating Point 0 10 20 30 40 50 60 70 80 90 16/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Amplifier Power Consumption—at the Optimal Operating Point 0 50 100 150 200 17/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Conclusions and Future Work ◮ Low-PAR precoding is ◮ not likely to yield substantial net power savings, but ◮ may greatly simplify the RF design ◮ Massive MIMO vision: High-End Performance with Low-End Devices ◮ Base stations built from handset technology! ◮ Class-B, or similar, amplifiers—operating at (near) saturation ◮ Using new low-PAR or CE waveforms ◮ Per-antenna output power on the order of 20-50 mW ◮ Ongoing work/unresolved issues ◮ Tightness of capacity bounds ◮ Per-antenna continuous-time constant envelope (CPM-like) modulation ◮ Imperfect CSI@TX 18/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
This talk was based on joint work with my colleagues ◦ Christopher Moll´ en (LiU, Sweden) ◦ Thomas Eriksson (Chalmers, Sweden) ◦ Saif K. Mohammed (IIT, Dehli) Thank You 19/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Backup Slides 20/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
Complexity of ZF and DTCE For a block of N symbols ◮ Zero-forcing requires ∼ O ( NK 2 M ) operations: ◮ N pseudo inverses, each ∼ O ( K 2 M ) , ◮ N matrix-vector multiplications, each ∼ O ( KM ) and ◮ (1 + K ) M Fourier transforms (each transmit signal and each channel impulse response). ◮ Discrete-time constant-envelope precoding requires ∼ O ( NKML ) operations. ◮ summation of KL complex terms in each iteration ◮ κNM iterations needed, where κ ≈ 5 21/19 Erik G. Larsson Communication Systems Waveform Design for the Massive MIMO Downlink Link¨ oping University
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