-ary dpsk m differential detection schemes for - ubc eceelhamt/index_files/563 project...
TRANSCRIPT
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Differential Detection Schemes for M-ary DPSK
Elham TorabiWireless Communications Course Project
April 2006
Department of Electrical & Computer EngineeringThe University of British Columbia
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Outline 2
1. Overview
2. Multiple-Symbol Differential Detection (MS-DD)
3. Multiple Differential Feedback Detection (MD-FD)
4. Reduced-state Viterbi Differential Detection (RSV-DD)
5. Conclusions
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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1. Overview 3
M -ary phase shift keying (M -ary PSK) is a bandwidth efficient, and thereforean attractive candidate for wireless communications, where available band-width is limited.
Coherent detection of PSK signals achieves good bit error rate (BER) perfor-mance in additive white Gaussian noise (AWGN) channel, but
Coherent detection requires carrier acquisition and tracking, which makesthe receiver implementation complex.
Carrier recovery is difficult, if not impossible, in fading environments.
Therefore, in applications where simplicity and robustness is important, dif-ferentially PSK (DPSK) modulation becomes a preferable alternative.
Since, conventional differential detection (DD) of M -ary DPSK signals resultsin inferior bit error rate (BER) performance compared to ideal coherent de-tection, different detection schemes for enhancing the performance of M -aryDPSK signals have been introduced in the literature.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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2. Multiple-Symbol Differential Detection for M -ary DPSK Signals 4
The key to this approach is extending the observation interval of two symbols,as in conventional differential detection (DD), to several symbol intervals, andperforming joint decision on several symbols simultaneously.
Considering M -ary PSK signal transmission over an AWGN channel:sn =
2Pejn, (1)
where P = Es/T denotes the constant signal power, Es is the signal energy,T denotes the symbol duration, and n = {2m/M ; m = 0, 1, . . . ,M 1}is the modulation phase. The received signal will be
rn = snejn + nn, (2)
where nn is a sample of AWGN with power 2 = 2N0/T , and n is a uniformly
distributed phase introduced by the channel in the interval (, ). When the received sequence of length N is observed
r = sej + n, (3)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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2. Multiple-Symbol Differential Detection for M -ary DPSK Signals 5
For differentially encoded PSK signals, where n = n1 + n, the decisionrule statistic is given as
choose if
rnN+1 +N2i=0 rniejNi2m=0 nim2 is maximum.
(4)
For N = 3 decision rule is simplified to
choose n and n1 if
{rnr
n1e
jn + rn1rn2ejn1 + rnrn2e
j(n+n1)}
is maximum.
(5)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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2. Multiple-Symbol Differential Detection for M -ary DPSK Signals 6
Figure 1: Implementation of multiple bit differential detector; N = 3.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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2. Multiple-Symbol Differential Detection for M -ary DPSK Signals 7
A simple upper bound on the average bit error probability Pb has been obtainedfor MS-DD, using the union bound:
Pb 1(N 1) log2 M
=
w (u, u) Pr { > |} , (6)
where u is the sequence of (N 1) log2 M information bits that produces at the transmitter, u denotes bits corresponding to detected .
w (u, u) is the Hamming distance between u and u, and Pr { > |}denotes the pairwise probability.
The upper bound for 4-DPSK, when N is obtained as
Pb 12erfc
(EbN0
). (7)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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2. Multiple-Symbol Differential Detection for M -ary DPSK Signals 8
6 6.5 7 7.5 8 8.5 9 9.5 1010
6
105
104
103
102
101
Eb/N0 (dB)
BE
R
4DPSK
N = 2Theoretical upper bound; N = 2N = 3Theoretical upper bound; N = 3N = 5Theoretical upper bound; N = 5N = Infinity
Figure 2: Bit error probability versus Eb/N0 for MS-DD of 4-DPSK. Simulation results along with theoretical upper bounds areshown.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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3. Multiple Differential Feedback Detection for M -ary DPSK Signals 9
The goal is to improve the BER performance by using symbol detectors withdelays larger than a symbol period and feeding back the detected symbols tothe detection unit.
This approach is based on minimizing the quadratic errors of the outputs ofL symbol detectors of orders j = 1, 2, . . . , L.
Figure 3: Conventional and decision-feedback detector for M-ary DPSK signals; L=3.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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3. Multiple Differential Feedback Detection for M -ary DPSK Signals 10
Considering M -ary DPSK signal transmission over AWGN channel:
The output of symbol detector of order j is given as
z(j)n = rnrnj = 2Panan1 anj+1 + n(j)n , (8)
where an = ejn.
The metric, which represents the quadratic error sum of the detector out-puts is given by
=z(1)n 2San2 + z(2)n 2Sanan12 +
+z(L)n 2Sanan1 anL+12 , L > 1. (9)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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3. Multiple Differential Feedback Detection for M -ary DPSK Signals 11
Simplifying the metric gives the decision rule as
an = maxan
Lj=1
{anMj} , (10)
with
Mj =
{z
(1)n
j=1an1an2 anj+1z(j)n j=2, 3, . . . , L.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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3. Multiple Differential Feedback Detection for M -ary DPSK Signals 12
Exact formulas for BER for M -ary DPSK, when correct symbols are fed backto decision unit have been obtained.
For 4-DPSK, as L the BER is given as
Pb 12
erfc
(EbN0
). (11)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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3. Multiple Differential Feedback Detection for M -ary DPSK Signals 13
3 4 5 6 7 8 9 1010
6
105
104
103
102
101
Eb/N0 (dB)
BE
R
4DPSK
L = 1Theoretical; L = 1L = 2Theoretical; L = 2L = 3Theoretical; L=3Theoretical; Coherent
Figure 4: Bit error probability versus Eb/N0 of MD-FD for 4-DPSK. Simulation results along with theoretical exact BERs whencorrect symbols have been fed back, are shown.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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4. Reduced-state Viterbi Differential Detection for M -ary DPSK Signals 14
This approach is a reduced-state Viterbi algorithm that incorporates feedbackinto the structure of path metric computations.
As a result, the number of states in the trellis is reduced to M , and for eachstate, the phase reference is estimated recursively in the trellis, along thesurviving path ending in each state.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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4. Reduced-state Viterbi Differential Detection for M -ary DPSK Signals 15
Considering M -ary DPSK signals through AWGN channel, and assumingtransmission of N -symbol sequence = {N, N1, . . . , 2, 1},the path metric in Viterbi algorithm is found to be
=N
n=1
n, (12)
where the branch metric n is
n = rn
(n
l=1
rnl exp jl1k=1
nk
)expjn
. (13)
The optimal decision rule is then obtained as = max
over. (14)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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4. Reduced-state Viterbi Differential Detection for M -ary DPSK Signals 16
Figure 5: Block diagram of RSV-DD.
The phase reference can be recursively estimated by
n1 (n1) = rn1 +n
l=2
l1(
rn1 exp jl1k=1
nk
)
= rn1 + n2(n2) exp jn1, (15)
where n1(n1) is an estimate of rn1, which is computed by feeding backthe sequence of symbols along the surviving path ending in state n1.
And, the branch metric for transition from state n1 to state n is cal-culated as
(n1 n) = [rn
n1(n1) expjn
]. (16)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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4. Reduced-state Viterbi Differential Detection for M -ary DPSK Signals 17
RSV-DD allows M paths to survive and traces back the most likely path Dsymbols back to output the decoded symbol. Therefore, there is a D-symboldecision delay, i.e., at each time n, nD is detected.
Figure 6: Trellis diagram for 4-DPSK.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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4. Reduced-state Viterbi Differential Detection for M -ary DPSK Signals 18
If only one single path is allowed to survive and symbol-by-symbol decision isperformed, RSV-DD reduces to its simplest version, known as decision feed-back DD (DF-DD).
DF-DD is equivalent to MD-FD using L = 1+1.
Approximate BER expressions of MF-DD for M -ary DPSK have been providedin the literature. The result for 4-DPSK, when = 1 is as follows
Pb = erfc
(EbN0
)1 12erfc
(EbN0
) . (17)
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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4. Reduced-state Viterbi Differential Detection for M -ary DPSK Signals 19
3 4 5 6 7 8 9 1010
6
105
104
103
102
101
100
Eb/N0 (dB)
BE
R
4DPSK
u = 0u = 0.5u = 0.6u = 0.9u = 1Theoretical; u = 0Theoretical; u = 0.5Theoretical; u = 0.6Theoretical; u = 0.9Theoretical; u = 1
Figure 7: Bit error probability versus Eb/N0 of RSV-DD for 4-DPSK. Simulation results along with theoretical approximatedBERs of DF-DD with same are shown.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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5. Conclusions 20
The BER performance of MS-DD improves by increasing the observation in-terval N , and can practically achieve the coherent detection performance byextending the observation interval to only a few symbols. However, decisionshould be performed over MN hypothesis symbols, which is rather compli-cated.
MD-FD is less complex than MS-DD, but it achieves slightly inferior BERperformance compared to MS-DD with the same total signal delay.
RSV-DD reduces the number of states in trellis of Viterbi algorithm to Mstates, which significantly reduces the computational complexity. Comparingto Viterbi DD that requires ML1-state Viterbi decoder, and ML branch met-ric computations.
RSV-DD requires only M 2 branch metric computations, and therefore it isML2 times less complex than Viterbi DD.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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5. Conclusions 21
The performance of RSV-DD is slightly inferior to Viterbi DD.
The performance of RSV-DD can be simply improved by increasing , andwithout increasing the complexity.
DF-DD achieves similar BER performance as MD-FD with compatible andL.
RSV-DD is superior to MD-DF, and DF-DD (compared at the same ). For 0.8 the performance difference between RSV-DD and DF-DD becomesvery small.
Elham Torabi : Differential Detection Schemes for M-ary DPSK
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Elham Torabi : Differential Detection Schemes for M-ary DPSK