Reduced-Complexity Joint Frequency, Timing and Phase Recovery for PAM Based CPM Receivers Sayak Bose Department of Electrical Engineering and Computer Science University of Kansas, Lawrence, Kansas 1 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Overview • Introduction to Continuous Phase Modulation (CPM) related work • Motivation of research • Signal models and complexity reduction principle • Joint timing and phase error detector (TED & PED) • Effect of large frequency offsets on TED and PED • Performance analysis metrics and bounds • Simulation results • False lock recovery using reduced complexity detector configurations • Conclusions and future work 2 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Introduction to Continuous Phase Modulation (CPM) related work CPM Receivers CPM Receivers Laurent Laurent PAM- -Based CPM Based CPM PAM Decomposition of Decomposition of Conventional CPM Conventional CPM CPM CPM Symbol Symbol Carrier Phase Carrier Phase Carrier Carrier Symbol Symbol Carrier Phase Carrier Phase Carrier Carrier Timing Recovery Frequency Timing Recovery Frequency Timing Recovery Frequency Timing Recovery Frequency Recovery Recovery Colavope, Colavope , Recovery Recovery Recovery Recovery D’ D ’Andrea Andrea, , Recovery Recovery Perrins, , Raheli D’ ’Andrea Andrea, , Perrins Raheli D D’ ’Andrea Andrea, , Mengali,Morelli D’ ’Andrea Andrea, , D Mengali,Morelli D Bose,Green Bose,Green Mengali,Ginesi Mengali,Ginesi Mengali,Morelli Mengali,Morelli Mengali Mengali Conference papers: E. Perrins, S. Bose, and M. P. Wylie-Green, “Timing Recovery Based on the PAM Representation Joint Frequency, Joint Frequency, of CPM," IEEE Military Communications Conference (MILCOM02008), San Diego, CA, November Joint Timing & Joint Timing & Joint Timing & Joint Timing & Timing & Phase Timing & Phase 2008 Phase Recovery Phase Recovery Joint Frequency, Joint Frequency, Phase Recovery Phase Recovery Recovery Recovery Timing & Phase Timing & Phase E. Perrins, S. Bose, and M. P. Wylie-Green, "PAM-Based Timing Synchronization for ARTM Morelli, , Vitetta Vitetta Recovery Morelli Recovery Modulations," in Proceedings of the International Telemetering Conference, San Diego, CA, October 2008. 3 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Motivation of research Why CPM? – Power and bandwidth efficient. – Easy to use with low-cost PAs. Problems with CPM – Receiver complexity. – Receiver synchronization. – Motivation for using Pulse Amplitude Modulation (PAM) – Linearize CPM; first proposed for binary CPMs in the well-known paper by Laurent. – Reduce receiver complexity by discarding low-energy PAM pulses. – Recover symbol timing using simple algorithms. 4 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Conventional CPM signal model ⎧ ⎫ n ∑ α = π α − ⎨ ⎬ ( ; ) exp 2 ( ) s t A j h q t iT i ⎩ ⎭ = 0 i •f(t) is the frequency pulse, it has a finite duration of L symbol times and an area of 1/2. •q(t) is the time-integral of f(t) •h is the modulation index, it is typically a rational number • α n are drawn from an M-ary alphabet 5 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Conventional CPM signal model...contd. • The phase can be grouped into two terms since q(t) = 1/2 for t>LT: n ∑ φ α = π α − ( ; ) 2 ( ) t h q t iT i = i 0 − n n L ∑ ∑ = π α − + π α 2 ( ) h q t iT h i i = − + = 1 4 4 4 2 4 4 4 3 1 42 4 3 1 0 i n L i φ α φ ( t ; ) − n L n • Since the modulation indexes are rational numbers, h=k/p, we can describe the signal with a finite state machine: ( ) ( ) σ = α α α α ↔ σ = φ α α α L , , , , , ,..., , − − − − − + − 1 4 4 4 4 2 4 4 4 4 3 3 2 1 1 1 n n n n n n n L n L n n − 1 L states pM α n − L + 1 α n α n − 1 α n − 2 φ − L + … 1 n mod p φ n − L L − 1 elements k 6 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Pulse Amplitude Modulation (PAM) based CPM model • M-ary Single-h − 1 N E ∑∑ α = − s ( ; ) ( ) s t b g t iT , k i k s T = k 0 i s • PAM complexity reduction principle − = − = Number of PAM Components P ( L 1 ) and 2 ( 1 ) log N M P M 2 − { } N 1 E ∑ ∑ κ ⊆ − α = φ − j L s 0 , 1 , , 1 ( ; ) − ( ) ( ) N s t e b c g t iT i L k i k s T = 0 i k s - Subset the largest amplitude pulses to reduce the number of matched filters (MF) - Reduce number of trellis states in the detector 7 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
PAM based joint timing and phase error detector • Received signal model in AWGN channel − 1 N E ( ) ∑∑ θ = − τ − + j s ( ) ( ) r t e b g t iT w t , k i k s T = k 0 i s •Coherent detection - Symbol detection using the Viterbi algorithm (VA) - Decision-directed timing recovery - Decision-directed phase recovery • Noncoherent detection - Symbol detection using the Viterbi algorithm - Decision-directed timing recovery without explicit phase information Note: - Timing and phase recovery uses decisions from the receiver. - Symbol detection and signal recovery are based on maximum likelihood principle. 8 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
PAM based joint timing and phase error detector • Metric increment in VA for sequence detection { } − L 1 ~ ∑ 0 ~ − θ ≤ ≤ φ τ = j 0 Re ( , , ) 0 t L T y c e 0 s − ' i i i L = 0 i ∑ ~ ~ φ τ − θ = τ & j * & ( , , ) ( ) y c e b x • PAM-based TED is given by k , i − , i i i L k i ∈ k k TED − 1 L ∑ 0 ~ − θ φ τ = & j Re{ ( , , ) } 0 y c e where the TED increment − i i i L = i 0 ~ ∑ − θ φ τ = τ * j ( , , ) ( ) z c e b x • PAM-based PED is given by , − k i , i i i L k i ∈ k k PED − L 1 ∑ 0 ~ − θ φ τ = j Im{ ( , , ) } 0 where the PED increment z c e − i i i L = i 0 τ + + ( ) ∫ i D T − θ τ ≅ − τ − k s j ( ) ( ) ( ) x r t e g t iT dt MF bank filter output k , i k s τ + iT s ≤ ≤ + and 1 1 D k L 9 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Error detector implementation α ˆ { } [ m ] r MF bank n − Interpolator VA { ( )} g t ∈ κ k k ˆ c − τ n − ˆ [ ] D n D ϕ ˆ ˆ − θ − [ ] − j n D − − e [ ] n L D e n D Timing τ TED PLL − [ ] e n D Phase θ PED PLL { } − = φ ˆ τ − − θ ˆ − [ ] & j n D ˆ ˆ [ ] Re ( , , [ ]) e n D y c n D e Error signal from the TED { } τ − − − − n D n D n L D ˆ − = φ ˆ τ − − θ − [ ] j n D ˆ ˆ [ ] Im ( , , [ ]) e n D z c n D e Error signal from the PED θ − − − − n D n D n L D Note: - Matched filters estimate data symbols through VA implementation. - Derivative matched filters generate TED Error hence timing estimate. A discrete-time differentiator approximates the derivative. 10 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
Effect of large frequency offsets on TED and PED − π ν ˆ 2 [ ] m avg e { } x α [ m ] [ m ] ˆ r r ∈ κ { } S k , n k MF bank 2 n Interpolator − VA { ( )} g t ∈ κ k k MF bank ˆ S − c − { ( )} g t 1 n D ∈ κ τ n − k k ˆ [ D ] ϕ FED ˆ − − − n L D [ ] e n D DMF bank τ − Timing PLL TED { & ( )} g t [ n ] ∈ κ e k k ˆ − θ − [ ] j n D e Phase PLL PED − [ ] e n D Loop Filter VCO θ ν ˆ [ ] n FDD • Frequency offset on the order of the symbol rate 1/Ts - A non-data-aided (NDA) frequency recovery is done before attempting symbol sequence, timing and phase recovery. A Frequency Difference Detector (FDD) is employed for this purpose. - Timing recovery without the explicit recovery of phase (noncoherent) is more suitable as phase recovery is still difficult due to the average residual frequency jitter . ˆ v avg 11 Recovery for PAM based CPM Receivers > < Reduced-Complexity Joint Frequency, Timing and Phase
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