Design and analysis of transmitter diversity using intentional frequency offset for wireless communications

TLDR: This work found that proper selections of the intentional frequency offset and interleaving depth can lead to good performance with traditional coded modulations (if enough antennas are used) using essentially the same simple demodulation structure as used in the traditional single-antenna PSAM.

Abstract: Coded modulation (usually with interleaving) is used in fading channel communications to achieve a good error performance. The major benefit from using coded modulation in fading channels is achieved if each code symbol of a codeword (or coded sequence) suffers statistically different fading (preferably independent fading). However, in many applications of mobile communications (e.g., in a metropolitan environment), a low vehicle speed (and hence, a small Doppler spread, f/sub D/) is very common. With a small Doppler spread, ideal or close-to-ideal interleaving is no longer feasible and all code symbols of a codeword would suffer highly correlated fading especially in stationary fading (f/sub D//spl ap/0). Coded modulations will thus suffer seriously degraded performance. Previous performance analyses based on ideal interleaving are not accurate when a small Doppler spread is encountered and the much used union bound error probability analysis is loose for small Doppler spreads. To rectify this situation, this paper presents an improved performance analysis of coded modulations with correlated fading and pilot-symbol-assisted modulation (PSAM). Transmitter diversity can generate the necessary time-varying fading to maintain the effectiveness of a coded signaling scheme which this paper examines in detail using an intentional frequency offset between antennas. This work found that proper selections of the intentional frequency offset and interleaving depth can lead to good performance with traditional coded modulations (if enough antennas are used) using essentially the same simple demodulation structure as used in the traditional single-antenna PSAM.

Figures

Fig. 1. The block diagram of the system with transmitter diversity and PSA.M.

Fig. 4. Autocorrelation of the MD process in stationary fading.

Fig. 10. Performance degradation caused by the assumption of ideal interleaving for the

Fig. 3. Bounding errors in stationary fading (f,g=O). A case of no diversity (f,=O) and interleaving depth = 10 is considered.

Full text

Purdue University
Purdue e-Pubs
ECE Technical Reports Electrical and Computer Engineering
11-1-1994
DESIGN AND ANALYSIS OF TNSMIER
DIVERSITY USING INTENTIONAL
FREQUENCY OFFSET FOR WIRELESS
COMMUNICATIONS
Wen-yi Kuo
Purdue University School of Electrical Engineering
Michael P. Fitz
Purdue University School of Electrical Engineering
Follow this and additional works at: hp://docs.lib.purdue.edu/ecetr
is document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for
additional information.
Kuo, Wen-yi and Fitz, Michael P., "DESIGN AND ANALYSIS OF TNSMIER DIVERSITY USING INTENTIONAL
FREQUENCY OFFSET FOR WIRELESS COMMUNICATIONS" (1994). ECE Technical Reports. Paper 204.
hp://docs.lib.purdue.edu/ecetr/204

D
ESIGN
AND
ANALYSIS
OF
T
RANSMITTER
D
IVERSITY
U
SING
I
NTENTIONAL
F
REQUENCY
O
F
F
S
E
T
F
OR
W
IRELESS
C
OMMUNICATIONS
TR
-
EE
94
-
35
N
O
V
E
M
B
E
R
1994

DESIGN AND ANALYSIS OF TRANSMITTER
DIVERSITY USING INTENTIONAL
FREQ-UENCY
OFFSET FOR WIRELESS COMMUNICATIONS
*
Wen
-
yi
Kuo
and Michael
P.
Fitz
School of Electrical Engineering
Purdue University
West Lafayette,
IN
47907
-
1285
email: wenyi@ecn.purdue.edu, mpfitz@ecn.purdue.eciu
FAX:
(3
17)
-
494
-
6440
*
This work supported
by
NSF
under Grant
NCR
91
15820.

TABLE OF CONTENTS
Page
...
...............................................................................
LIST CIF FiGURES
m
........................................................................................
ABSTRACT iv
.............................................................................
I
. INTIRODUCTION
1
I1 . ANALYTICAL MODELS ....................................................................
4
A
.
Signals Models ............................................................................
4
B
.
Transmitter Diversity with Intentional Frequency Offset .............................
6
C . Models for L-Diversity with Intentional Frequency Offset
..........................
7
.....................................................
A . Optimal Decoding
/
Demodulation
10
...............................................................
B
. Traditional Union Bound
11
..............................................................
C . Progressive Union Bound
13
................................
IV
. PE:RFORMANCE OF TRANSMI'ITER DIVERSITY
18
A
. Achieving ldeal Interleaving ............................................................ 18
................
A
-
1 Comparison between BCM and TCM for ideal interleaving
20
B
. Non-ideal Interleaving Performance
...................................................
20
..............................................................
. B.1 Example of BCM1 21
..............................................................
.
B.2 Example of TCMl 22
B
-
3 Degradation caused by Ideal Interleaving Assumption
.......................
22
..............................................................................
V . COIVCLUSION 28
........................................................................
LIST
OF
REFERENCES 29

LIST OF FIGURES
Figure Page
1
.
The
block diagram of the system with transmitter diversity and PSAM ..................
9
2
. Bounding errors in various fading rates
..................................................
16
3
.
Bounding errors in stationary fading
fi=O)
........................................
17
4
.
Auttxorrelation of the
NLD
process in stationary fading
...................................
24
5
. The effect of frequency offset and interleaving depth in stationary fading .............
24
6
.
Pefi. ormance gain of transmitter diversity for
BCMl
in stationary fading
.............
25
7
. The effect of frequency offset and interleaving depth in stationary fading fior
TCMl
..................................................................................................
25
8
.
Perfiormance gain of using transmitter diversity for the
TCMl
in stationary fading
.................................................................................................
-26
9
. Pefi~rmance degradation caused by the assumption of ideal interleaving for
BCMl
.................................................................................................
-26
10
. Performance degradation caused by the assumption of ideal interleaving for the
TCMl
.................................................................................................
27
...
lll

Frequently asked questions

Q1. What is the main benefit of using coded modulation in fading channels?

The major benefit of using coded modulation (usually clombined with interlea.ving) in fading channels is that time diversity can be achieved so that each code symbol of a codeword suffers a statistically different fading distortion (preferably independent fading). 

Q2. What is the baseband equivalent of the transmitted signal?

The baseband equivalent of the transmitted signal has the formwhere u(t) represents a square root unit energy Nyquist pulse shapel, T is the symbol duration and d, represents the modulation symbol which can either be a pilot modulationor a symbol from an interleaved codeword. 

Q3. What are the common techniques for estimating the MD process?

Common techniques for estimating the MD process are transmitted reference schemes such as PSAM [12-141 and tone calibration techniques [15-171. 

Q4. What is the cost of using intentional frequency offset in transmitting antennas?

using time offset in transmitting antennas requires an equalizer in the receiver and could significantly inflate the cost and complexity. 

Q5. What is the effect of frequency offset between antennas on fading?

The transmitter diversity using intentional frequency offset between antennas can generate the necessary time-varying fading and maintain the effectiveness of the colded signaling scheme. 

Q6. What is the way to provide diversity against fading without increasing the receive:r complexity?

One possible solution to provide diversity against fading without increasing the receive:r complexity is to employ transmitter diversity techniques. 

Q7. What is the way to achieve the optimal interleaving in fading situations?

By proper selection of the intentional frequency offset and the interleaving depth, ideal interleaving in any fading situations is now achievable. 

Q8. What is the s iga l to noise ratio?

of this paper, the s ig~~a l to noise ratio per information bit (SNR/bit) is defined asThe first step in the demodulation process is to pass the received signal. 

Q9. What is the SNRIbitdegradation of using simpler decoding?

The SNRIbitdegradation of using simpler decoding (41) as if ideal interleaving is achieved is around 1 dB (fo:r space diversity=2) or 0.4 dB (for space diversity=3) respectively.is the :2D-PUB of BCMl at Yb=14.65 dB.groupll . - - - - - . - . - Space Div.=2 A Optimal for Space Div.z.2 - - - - - Space Div.=3 Optimal for Space Div.z.3E Space Div.=4 N Optimal for Space Div.z.4- The authorI 1 1 The authorI 1 1 1 1 1 1 1 1 1 1 l The authorI The authorIfading. 

Q10. What is the way to achieve the optimal interleaving?

Ideal interleaving for coded modulation previously assumed in the literature is actually not feasible in slow fadingespecially in stationary fading if the transmitter diversity technique is not used. 

Q11. What is the criterion for achieving ideal interleaving?

(39) provides the criterion for achieving ideal interleaving with the flexibi1j.t~ of tradeoff between bandwidth expansion and buffer size with processing delay. 

Q12. What is the effect of frequency offset and interleaving depth on fading?

This work found that proper selections of the intentional frequency offset and interleaving depth can achieve less correlated fading or even independent fading (if enough antennas are used). 

Q13. What is the argument for achieving ideal interleaving?

Fig. 5 also demonstrates space diversity of 4 achieves the same lowest BEP as space diversity of 3 and this fact also matches their above argument about ideal interleaving that the block length of BCMl equals 3 so that more than 3 antennas will not improve the performance if ideal interleaving has already been achieved. 

Q14. What is the way to achieve ideal interleaving?

Especially for real world applications where higher order and longer length coded modulations are proposed and/or used (e.g., Reed-Solomon BCM, 128-state 128-QAM TCM etc.), ideal interleaving in slow fading is more difficult to attain. 

Q15. What is the tradeoff between amount of diversity and complexity?

using b-ansmitter diversity techniques in combination with receiver diversity techniques can attiiin the best tradeoff between amount of diversity and complexity.