GPRS system by ... - UBC ECE
Compatible Improvement of the GSM/GPRS System by Means of Delay Diversity Jan Mietzner and Peter A. Hoeher
Magnus Sandell
Information and Coding Theory Lab (ICT) University of Kiel, Germany
Toshiba Telecommunication Research Laboratory Bristol, United Kingdom
{jm,ph}@tf.uni-kiel.de http://www.tf.uni-kiel.de/ict
[email protected]
ICC 2003, Anchorage, Alaska, USA May 11-15, 2003
1
Currently: In many current cellular systems two (or more) Tx antennas are used at the BS, where the Tx signal is simultaneously transmitted over each antenna.
Data
BS
Jan Mietzner ICT, University of Kiel
1
Currently:
Enhancement:
In many current cellular systems two (or more) Tx antennas are used at the BS, where the Tx signal is simultaneously transmitted over each antenna.
“Space-time” processing. Goal: Compatibility, i.e., preferably few changes w.r.t. current systems.
Data
Data
BS
ST− processing
BS
Jan Mietzner ICT, University of Kiel
2
Simple Example: Delay Diversity
I Wittneben, 1993 I Seshadri and Winters, 1994
Jan Mietzner ICT, University of Kiel
2
Simple Example: Delay Diversity
I Wittneben, 1993 I Seshadri and Winters, 1994
Idea: Shown here:
Apply a delay at the second Tx antenna.
Significant performance improvements may be obtained using the same receiver. (Example: GSM/GPRS System)
Jan Mietzner ICT, University of Kiel
2
Simple Example: Delay Diversity
I Wittneben, 1993 I Seshadri and Winters, 1994
Idea: Shown here:
Apply a delay at the second Tx antenna.
Significant performance improvements may be obtained using the same receiver. (Example: GSM/GPRS System)
=⇒ Delay diversity may be offered by network operators even in existing systems, since the standard is not affected at all.
Jan Mietzner ICT, University of Kiel
3
General Context (I)
I Wireless data services: – Require reliable transmission of high data rates. – Normally asymmetric:
Major part of overall traffic in downlink (DL) direction (e.g., download of large amount of data by mobile users).
Jan Mietzner ICT, University of Kiel
3
General Context (I)
I Wireless data services: – Require reliable transmission of high data rates. – Normally asymmetric:
Major part of overall traffic in downlink (DL) direction (e.g., download of large amount of data by mobile users).
I Space-Time Codes (STC): – Special class of space-time processing schemes requiring solely multiple Tx antennas, whereas multiple Rx antennas are optional.
−→
Well suited to enhance the crucial DL.
Jan Mietzner ICT, University of Kiel
3
General Context (I)
I Wireless data services: – Require reliable transmission of high data rates. – Normally asymmetric:
Major part of overall traffic in downlink (DL) direction (e.g., download of large amount of data by mobile users).
I Space-Time Codes (STC): – Special class of space-time processing schemes requiring solely multiple Tx antennas, whereas multiple Rx antennas are optional.
−→
– Examples:
Well suited to enhance the crucial DL.
Space-Time Trellis Codes (STTC), Space-Time Block Codes (STBC). Delay diversity may be interpreted as the simplest special case of a STTC.
Jan Mietzner ICT, University of Kiel
4
General Context (II)
I Efficiency of STC in fading environments due to a diversity gain: – Individual transmission paths are subject to independent fading, i.e., probability that all paths are simultaneously corrupted is smaller.
−→
Lower bit error rates accomplished.
Jan Mietzner ICT, University of Kiel
4
General Context (II)
I Efficiency of STC in fading environments due to a diversity gain: – Individual transmission paths are subject to independent fading, i.e., probability that all paths are simultaneously corrupted is smaller.
−→
Lower bit error rates accomplished.
I In 2.5G/3G systems, typically adaptive channel coding/ modulation is applied.
−→
Any means to improve power efficiency (e.g., utilization of diversity) leads to an improved bandwidth efficiency.
Jan Mietzner ICT, University of Kiel
4
General Context (II)
I Efficiency of STC in fading environments due to a diversity gain: – Individual transmission paths are subject to independent fading, i.e., probability that all paths are simultaneously corrupted is smaller.
−→
Lower bit error rates accomplished.
I In 2.5G/3G systems, typically adaptive channel coding/ modulation is applied.
−→
Any means to improve power efficiency (e.g., utilization of diversity) leads to an improved bandwidth efficiency.
=⇒ Enhancement of DL direction by means of STC for the purpose of higher data rates is very attractive.
Jan Mietzner ICT, University of Kiel
5
Outline
I Transmitter structure for the GSM/GPRS DL improved by means of delay diversity I Simulation results for a typical urban (TU) channel model I Analytical results and optimization of the delay at the second Tx antenna I Conclusions
Jan Mietzner ICT, University of Kiel
6
Compatible Transmitter Structure for the GSM/GPRS DL (I)
I GPRS (‘General Packet Radio Service’): – GPRS is used for the transfer of packet-switched data. – GSM/GPRS is often referred to as a ‘2.5G system’.
I Original GSM/GPRS transmitter structure: – Channel coding & interleaving according to adaptive channel coding schemes ‘CS 1-4’.
Jan Mietzner ICT, University of Kiel
6
Compatible Transmitter Structure for the GSM/GPRS DL (I)
I GPRS (‘General Packet Radio Service’): – GPRS is used for the transfer of packet-switched data. – GSM/GPRS is often referred to as a ‘2.5G system’.
I Original GSM/GPRS transmitter structure: – Channel coding & interleaving according to adaptive channel coding schemes ‘CS 1-4’.
I Compatible upgrade: – Transmitter:
The same signal is transmitted from both antennas, using a delay δT at the second antenna (T symbol duration).
– Receiver:
The same receiver may be used as in the conventional system.
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
– The conventional choice is δ = 0.
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
– The conventional choice is δ = 0. – For delay diversity, typically δ = 1 is chosen (optimal in case of a flat fading channel).
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
– The conventional choice is δ = 0. – For delay diversity, typically δ = 1 is chosen (optimal in case of a flat fading channel). – Question: Optimal choice of δ in case of frequency-selective fading channel?
Jan Mietzner ICT, University of Kiel
8
Simulation Results for the TU Channel Model
I Uncoded transmission I Delay parameter δ = 1, 2, 3 I 1 or 2 Rx antennas I Channel perfectly known at the receiver I Root-raised-cosine Rx filter I Max-Log-MAP equalizer/detector
Jan Mietzner ICT, University of Kiel
8
Simulation Results for the TU Channel Model
0
10
(1x1)−System (2x1)−Delay Diversity
I Uncoded transmission
(2x2)−Delay Diversity
I Delay parameter δ = 1, 2, 3
I Channel perfectly known at the receiver
δ=1
BER
I 1 or 2 Rx antennas
−1
10
−2
10
δ=2
δ=1
I Root-raised-cosine Rx filter
δ=3
I Max-Log-MAP equalizer/detector 0
4.7 dB
10 dB
−3
10
3 dB
3
6
9
12
15
18
21
E /N (dB) s
0
Jan Mietzner ICT, University of Kiel
8
Simulation Results for the TU Channel Model
0
10
(1x1)−System (2x1)−Delay Diversity
I Uncoded transmission
(2x2)−Delay Diversity
I Delay parameter δ = 1, 2, 3
I Channel perfectly known at the receiver
δ=1
BER
I 1 or 2 Rx antennas
−1
10
−2
10
δ=2
δ=1
I Root-raised-cosine Rx filter
δ=3
I Max-Log-MAP equalizer/detector 0
4.7 dB
10 dB
−3
10
3 dB
3
6
9
12
15
18
21
E /N (dB) s
=⇒
0
With delay diversity, significant gains w.r.t. conventional system. Maximum gain for δ = 3.
Jan Mietzner ICT, University of Kiel
9
Analytical Results and Optimization of the Delay Parameter (I)
RAKE receiver bound (RRB):
Lower bound on the bit error probability of a slowly time-varying ISI channel.
I Maximum likelihood (ML) detection assumed (particularly, perfect knowledge of the channel coefficients in the receiver). Individual channel coefficients are assumed to fade independently.
Jan Mietzner ICT, University of Kiel
9
Analytical Results and Optimization of the Delay Parameter (I)
RAKE receiver bound (RRB):
Lower bound on the bit error probability of a slowly time-varying ISI channel.
I Maximum likelihood (ML) detection assumed (particularly, perfect knowledge of the channel coefficients in the receiver). Individual channel coefficients are assumed to fade independently.
L
RRB Pb
1X = 2 l=0
L Y ν =0 ρν 6= ρl
ρl ρl − ρν
!
· 1 − q
1 1+
No 1 Es ρl
(1)
– L: Channel memory length Es: Mean energy per data symbol No: Single-sided noise power density ρl : Mean power of the lth channel coefficient (0 ≤ l ≤ L)
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
−→
Method to remove static ISI from the channel coefficients to tighten the bound.
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
−→
Method to remove static ISI from the channel coefficients to tighten the bound.
I Delay diversity:
Exploit the fact that same signal is transmitted over both Tx antennas.
−→ Derive equivalent single Tx antenna channel model.
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
−→
Method to remove static ISI from the channel coefficients to tighten the bound.
I Delay diversity:
Exploit the fact that same signal is transmitted over both Tx antennas.
−→ Derive equivalent single Tx antenna channel model. −→ Specifically, the mean power of the lth coefficient of the equivalent channel model results as Z ρl (δ) =
τmax
p(τ )
2
|g(lT −τ )| + |g(lT −δ −τ )|
2
dτ .
(2)
0
– g(t): p(τ ):
Overall impulse response of pulse shaping filter and receiver filter Pdf proportional to the delay power density profile (e.g., GSM 05.05 propagation profile)
Jan Mietzner ICT, University of Kiel
11
Analytical Results and Optimization of the Delay Parameter (III)
I Truncated equalizer/detector: Trellis-based equalizer/detector of length Leq , only takes the first Leq +1 channel coefficients into account (Leq < L).
−→ Sum and product in the RRB are from 0 to Leq . −→ Neglected channel coefficients cause residual ISI, resulting in a transformed SNR denoted as Es/No0.
Jan Mietzner ICT, University of Kiel
11
Analytical Results and Optimization of the Delay Parameter (III)
I Truncated equalizer/detector: Trellis-based equalizer/detector of length Leq , only takes the first Leq +1 channel coefficients into account (Leq < L).
−→ Sum and product in the RRB are from 0 to Leq . −→ Neglected channel coefficients cause residual ISI, resulting in a transformed SNR denoted as Es/No0.
Finally:
Modified RRB as a function of delay parameter δ applied at Tx antenna 2, given different equalizer/detector lengths Leq (1 Rx antenna assumed).
RRB Pb (δ)
1 = 2
Leq X l=0
Leq Y ν =0 ρν 6= ρl
ρl (δ) ρl (δ) − ρν (δ)
!
· 1 − r
1 1+
No0 1 Es ρl (δ)
(3)
Jan Mietzner ICT, University of Kiel
12
Analytical Results and Optimization of the Delay Parameter (IV)
I Example:
GSM propagation profile TU, Es/No = 10 dB
Jan Mietzner ICT, University of Kiel
12
Analytical Results and Optimization of the Delay Parameter (IV)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
b
rrb P (δ) RRB
10
I Case #1:
Leq = L
−2
10
Obviously, δ should be chosen as δ ≥ 3. Neither δ = 0 nor δ = 1 is optimal.
−3
10
−4
10
0
1
2
δ
3
4
5
Jan Mietzner ICT, University of Kiel
13
Analytical Results and Optimization of the Delay Parameter (V)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
10
b
rrb P (δ) RRB
L eq = 4
I Case #2:
Leq < L
−2
10
Example:
−3
10
Leq = 4
L eq = L
−4
10
0
1
2
δ
3
4
5
Jan Mietzner ICT, University of Kiel
14
Analytical Results and Optimization of the Delay Parameter (VI)
I Discussion:
ρl (δ)
Leq
L=2
Small δ : RRB follows the curve for Leq = L. l
Medium δ : Significant fractions of ρl (δ) are neglected by the equalizer.
ρl (δ)
Leq
L=3
−→ Increased bit error probability. l
ρl (δ)
Large δ : Further increase of δ does not lead to additional performance loss.
Leq
L=7
l
Jan Mietzner ICT, University of Kiel
15
Analytical Results and Optimization of the Delay Parameter (VII)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
10
b
rrb P (δ) RRB
L eq = 4
L eq = 3
L eq = 2
L eq = 5
I Case #2:
−2
10
−3
10
L eq = 6
0
Rule-of-thumb: Choose δ ≈ bLeq /2c.
L eq = 7
L eq = L
Optimum for δ (rule−of−thumb)
−4
10
Leq < L
1
2
δ
3
4
5
Jan Mietzner ICT, University of Kiel
15
Analytical Results and Optimization of the Delay Parameter (VII)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
10
b
rrb P (δ) RRB
L eq = 4
L eq = 3
L eq = 2
L eq = 5
I Case #2:
−2
10
−3
10
L eq = 6
0
Rule-of-thumb: Choose δ ≈ bLeq /2c.
L eq = 7
L eq = L
I GSM/GPRS:
1
2
δ
3
4
Typically Leq = 5
=⇒ Near optimum for δ = 2.
Optimum for δ (rule−of−thumb)
−4
10
Leq < L
5
Jan Mietzner ICT, University of Kiel
16
Conclusions
I General context: Usefulness of STC for 2.5G/3G wireless systems −→ Higher data rates by exploiting spatial diversity.
I GSM/GPRS system: – Transmitter structure improved by means of delay diversity. – Performance improvements accomplished for different delays.
I Analytical results: – Modified RAKE receiver bound as a function of the delay parameter δ applied at Tx antenna 2. – Optimization of δ , given different equalizer/detector lengths Leq ≤ L.
Jan Mietzner ICT, University of Kiel
Magnus Sandell
Information and Coding Theory Lab (ICT) University of Kiel, Germany
Toshiba Telecommunication Research Laboratory Bristol, United Kingdom
{jm,ph}@tf.uni-kiel.de http://www.tf.uni-kiel.de/ict
[email protected]
ICC 2003, Anchorage, Alaska, USA May 11-15, 2003
1
Currently: In many current cellular systems two (or more) Tx antennas are used at the BS, where the Tx signal is simultaneously transmitted over each antenna.
Data
BS
Jan Mietzner ICT, University of Kiel
1
Currently:
Enhancement:
In many current cellular systems two (or more) Tx antennas are used at the BS, where the Tx signal is simultaneously transmitted over each antenna.
“Space-time” processing. Goal: Compatibility, i.e., preferably few changes w.r.t. current systems.
Data
Data
BS
ST− processing
BS
Jan Mietzner ICT, University of Kiel
2
Simple Example: Delay Diversity
I Wittneben, 1993 I Seshadri and Winters, 1994
Jan Mietzner ICT, University of Kiel
2
Simple Example: Delay Diversity
I Wittneben, 1993 I Seshadri and Winters, 1994
Idea: Shown here:
Apply a delay at the second Tx antenna.
Significant performance improvements may be obtained using the same receiver. (Example: GSM/GPRS System)
Jan Mietzner ICT, University of Kiel
2
Simple Example: Delay Diversity
I Wittneben, 1993 I Seshadri and Winters, 1994
Idea: Shown here:
Apply a delay at the second Tx antenna.
Significant performance improvements may be obtained using the same receiver. (Example: GSM/GPRS System)
=⇒ Delay diversity may be offered by network operators even in existing systems, since the standard is not affected at all.
Jan Mietzner ICT, University of Kiel
3
General Context (I)
I Wireless data services: – Require reliable transmission of high data rates. – Normally asymmetric:
Major part of overall traffic in downlink (DL) direction (e.g., download of large amount of data by mobile users).
Jan Mietzner ICT, University of Kiel
3
General Context (I)
I Wireless data services: – Require reliable transmission of high data rates. – Normally asymmetric:
Major part of overall traffic in downlink (DL) direction (e.g., download of large amount of data by mobile users).
I Space-Time Codes (STC): – Special class of space-time processing schemes requiring solely multiple Tx antennas, whereas multiple Rx antennas are optional.
−→
Well suited to enhance the crucial DL.
Jan Mietzner ICT, University of Kiel
3
General Context (I)
I Wireless data services: – Require reliable transmission of high data rates. – Normally asymmetric:
Major part of overall traffic in downlink (DL) direction (e.g., download of large amount of data by mobile users).
I Space-Time Codes (STC): – Special class of space-time processing schemes requiring solely multiple Tx antennas, whereas multiple Rx antennas are optional.
−→
– Examples:
Well suited to enhance the crucial DL.
Space-Time Trellis Codes (STTC), Space-Time Block Codes (STBC). Delay diversity may be interpreted as the simplest special case of a STTC.
Jan Mietzner ICT, University of Kiel
4
General Context (II)
I Efficiency of STC in fading environments due to a diversity gain: – Individual transmission paths are subject to independent fading, i.e., probability that all paths are simultaneously corrupted is smaller.
−→
Lower bit error rates accomplished.
Jan Mietzner ICT, University of Kiel
4
General Context (II)
I Efficiency of STC in fading environments due to a diversity gain: – Individual transmission paths are subject to independent fading, i.e., probability that all paths are simultaneously corrupted is smaller.
−→
Lower bit error rates accomplished.
I In 2.5G/3G systems, typically adaptive channel coding/ modulation is applied.
−→
Any means to improve power efficiency (e.g., utilization of diversity) leads to an improved bandwidth efficiency.
Jan Mietzner ICT, University of Kiel
4
General Context (II)
I Efficiency of STC in fading environments due to a diversity gain: – Individual transmission paths are subject to independent fading, i.e., probability that all paths are simultaneously corrupted is smaller.
−→
Lower bit error rates accomplished.
I In 2.5G/3G systems, typically adaptive channel coding/ modulation is applied.
−→
Any means to improve power efficiency (e.g., utilization of diversity) leads to an improved bandwidth efficiency.
=⇒ Enhancement of DL direction by means of STC for the purpose of higher data rates is very attractive.
Jan Mietzner ICT, University of Kiel
5
Outline
I Transmitter structure for the GSM/GPRS DL improved by means of delay diversity I Simulation results for a typical urban (TU) channel model I Analytical results and optimization of the delay at the second Tx antenna I Conclusions
Jan Mietzner ICT, University of Kiel
6
Compatible Transmitter Structure for the GSM/GPRS DL (I)
I GPRS (‘General Packet Radio Service’): – GPRS is used for the transfer of packet-switched data. – GSM/GPRS is often referred to as a ‘2.5G system’.
I Original GSM/GPRS transmitter structure: – Channel coding & interleaving according to adaptive channel coding schemes ‘CS 1-4’.
Jan Mietzner ICT, University of Kiel
6
Compatible Transmitter Structure for the GSM/GPRS DL (I)
I GPRS (‘General Packet Radio Service’): – GPRS is used for the transfer of packet-switched data. – GSM/GPRS is often referred to as a ‘2.5G system’.
I Original GSM/GPRS transmitter structure: – Channel coding & interleaving according to adaptive channel coding schemes ‘CS 1-4’.
I Compatible upgrade: – Transmitter:
The same signal is transmitted from both antennas, using a delay δT at the second antenna (T symbol duration).
– Receiver:
The same receiver may be used as in the conventional system.
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
– The conventional choice is δ = 0.
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
– The conventional choice is δ = 0. – For delay diversity, typically δ = 1 is chosen (optimal in case of a flat fading channel).
Jan Mietzner ICT, University of Kiel
7
Compatible Transmitter Structure for the GSM/GPRS DL (II)
I Transmitter structure (baseband representation):
from MAC Layer
CS 1−4
Data Symbols x(k)
TS
Burst Align− ment
TS
1
Pulse Shaping 2
δT
– The conventional choice is δ = 0. – For delay diversity, typically δ = 1 is chosen (optimal in case of a flat fading channel). – Question: Optimal choice of δ in case of frequency-selective fading channel?
Jan Mietzner ICT, University of Kiel
8
Simulation Results for the TU Channel Model
I Uncoded transmission I Delay parameter δ = 1, 2, 3 I 1 or 2 Rx antennas I Channel perfectly known at the receiver I Root-raised-cosine Rx filter I Max-Log-MAP equalizer/detector
Jan Mietzner ICT, University of Kiel
8
Simulation Results for the TU Channel Model
0
10
(1x1)−System (2x1)−Delay Diversity
I Uncoded transmission
(2x2)−Delay Diversity
I Delay parameter δ = 1, 2, 3
I Channel perfectly known at the receiver
δ=1
BER
I 1 or 2 Rx antennas
−1
10
−2
10
δ=2
δ=1
I Root-raised-cosine Rx filter
δ=3
I Max-Log-MAP equalizer/detector 0
4.7 dB
10 dB
−3
10
3 dB
3
6
9
12
15
18
21
E /N (dB) s
0
Jan Mietzner ICT, University of Kiel
8
Simulation Results for the TU Channel Model
0
10
(1x1)−System (2x1)−Delay Diversity
I Uncoded transmission
(2x2)−Delay Diversity
I Delay parameter δ = 1, 2, 3
I Channel perfectly known at the receiver
δ=1
BER
I 1 or 2 Rx antennas
−1
10
−2
10
δ=2
δ=1
I Root-raised-cosine Rx filter
δ=3
I Max-Log-MAP equalizer/detector 0
4.7 dB
10 dB
−3
10
3 dB
3
6
9
12
15
18
21
E /N (dB) s
=⇒
0
With delay diversity, significant gains w.r.t. conventional system. Maximum gain for δ = 3.
Jan Mietzner ICT, University of Kiel
9
Analytical Results and Optimization of the Delay Parameter (I)
RAKE receiver bound (RRB):
Lower bound on the bit error probability of a slowly time-varying ISI channel.
I Maximum likelihood (ML) detection assumed (particularly, perfect knowledge of the channel coefficients in the receiver). Individual channel coefficients are assumed to fade independently.
Jan Mietzner ICT, University of Kiel
9
Analytical Results and Optimization of the Delay Parameter (I)
RAKE receiver bound (RRB):
Lower bound on the bit error probability of a slowly time-varying ISI channel.
I Maximum likelihood (ML) detection assumed (particularly, perfect knowledge of the channel coefficients in the receiver). Individual channel coefficients are assumed to fade independently.
L
RRB Pb
1X = 2 l=0
L Y ν =0 ρν 6= ρl
ρl ρl − ρν
!
· 1 − q
1 1+
No 1 Es ρl
(1)
– L: Channel memory length Es: Mean energy per data symbol No: Single-sided noise power density ρl : Mean power of the lth channel coefficient (0 ≤ l ≤ L)
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
−→
Method to remove static ISI from the channel coefficients to tighten the bound.
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
−→
Method to remove static ISI from the channel coefficients to tighten the bound.
I Delay diversity:
Exploit the fact that same signal is transmitted over both Tx antennas.
−→ Derive equivalent single Tx antenna channel model.
Jan Mietzner ICT, University of Kiel
10
Analytical Results and Optimization of the Delay Parameter (II) I Tightening the RRB: – Channel coefficients normally comprise both static ISI (due to pulse shaping and receiver filter) and dynamic ISI (due to physical channel). – Diversity is solely due to dynamic ISI. Hence, the RRB overestimates the degree of diversity actually utilized, i.e., the bound is too optimistic.
−→
Method to remove static ISI from the channel coefficients to tighten the bound.
I Delay diversity:
Exploit the fact that same signal is transmitted over both Tx antennas.
−→ Derive equivalent single Tx antenna channel model. −→ Specifically, the mean power of the lth coefficient of the equivalent channel model results as Z ρl (δ) =
τmax
p(τ )
2
|g(lT −τ )| + |g(lT −δ −τ )|
2
dτ .
(2)
0
– g(t): p(τ ):
Overall impulse response of pulse shaping filter and receiver filter Pdf proportional to the delay power density profile (e.g., GSM 05.05 propagation profile)
Jan Mietzner ICT, University of Kiel
11
Analytical Results and Optimization of the Delay Parameter (III)
I Truncated equalizer/detector: Trellis-based equalizer/detector of length Leq , only takes the first Leq +1 channel coefficients into account (Leq < L).
−→ Sum and product in the RRB are from 0 to Leq . −→ Neglected channel coefficients cause residual ISI, resulting in a transformed SNR denoted as Es/No0.
Jan Mietzner ICT, University of Kiel
11
Analytical Results and Optimization of the Delay Parameter (III)
I Truncated equalizer/detector: Trellis-based equalizer/detector of length Leq , only takes the first Leq +1 channel coefficients into account (Leq < L).
−→ Sum and product in the RRB are from 0 to Leq . −→ Neglected channel coefficients cause residual ISI, resulting in a transformed SNR denoted as Es/No0.
Finally:
Modified RRB as a function of delay parameter δ applied at Tx antenna 2, given different equalizer/detector lengths Leq (1 Rx antenna assumed).
RRB Pb (δ)
1 = 2
Leq X l=0
Leq Y ν =0 ρν 6= ρl
ρl (δ) ρl (δ) − ρν (δ)
!
· 1 − r
1 1+
No0 1 Es ρl (δ)
(3)
Jan Mietzner ICT, University of Kiel
12
Analytical Results and Optimization of the Delay Parameter (IV)
I Example:
GSM propagation profile TU, Es/No = 10 dB
Jan Mietzner ICT, University of Kiel
12
Analytical Results and Optimization of the Delay Parameter (IV)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
b
rrb P (δ) RRB
10
I Case #1:
Leq = L
−2
10
Obviously, δ should be chosen as δ ≥ 3. Neither δ = 0 nor δ = 1 is optimal.
−3
10
−4
10
0
1
2
δ
3
4
5
Jan Mietzner ICT, University of Kiel
13
Analytical Results and Optimization of the Delay Parameter (V)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
10
b
rrb P (δ) RRB
L eq = 4
I Case #2:
Leq < L
−2
10
Example:
−3
10
Leq = 4
L eq = L
−4
10
0
1
2
δ
3
4
5
Jan Mietzner ICT, University of Kiel
14
Analytical Results and Optimization of the Delay Parameter (VI)
I Discussion:
ρl (δ)
Leq
L=2
Small δ : RRB follows the curve for Leq = L. l
Medium δ : Significant fractions of ρl (δ) are neglected by the equalizer.
ρl (δ)
Leq
L=3
−→ Increased bit error probability. l
ρl (δ)
Large δ : Further increase of δ does not lead to additional performance loss.
Leq
L=7
l
Jan Mietzner ICT, University of Kiel
15
Analytical Results and Optimization of the Delay Parameter (VII)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
10
b
rrb P (δ) RRB
L eq = 4
L eq = 3
L eq = 2
L eq = 5
I Case #2:
−2
10
−3
10
L eq = 6
0
Rule-of-thumb: Choose δ ≈ bLeq /2c.
L eq = 7
L eq = L
Optimum for δ (rule−of−thumb)
−4
10
Leq < L
1
2
δ
3
4
5
Jan Mietzner ICT, University of Kiel
15
Analytical Results and Optimization of the Delay Parameter (VII)
GSM propagation profile TU, Es/No = 10 dB
I Example:
RRB as a function of δ 0
10
−1
10
b
rrb P (δ) RRB
L eq = 4
L eq = 3
L eq = 2
L eq = 5
I Case #2:
−2
10
−3
10
L eq = 6
0
Rule-of-thumb: Choose δ ≈ bLeq /2c.
L eq = 7
L eq = L
I GSM/GPRS:
1
2
δ
3
4
Typically Leq = 5
=⇒ Near optimum for δ = 2.
Optimum for δ (rule−of−thumb)
−4
10
Leq < L
5
Jan Mietzner ICT, University of Kiel
16
Conclusions
I General context: Usefulness of STC for 2.5G/3G wireless systems −→ Higher data rates by exploiting spatial diversity.
I GSM/GPRS system: – Transmitter structure improved by means of delay diversity. – Performance improvements accomplished for different delays.
I Analytical results: – Modified RAKE receiver bound as a function of the delay parameter δ applied at Tx antenna 2. – Optimization of δ , given different equalizer/detector lengths Leq ≤ L.
Jan Mietzner ICT, University of Kiel
