Chapter 3 Spectrally Efficient Multi-user Coded Cooperation
4.2 Performance Bounds of CP-Coded Cooperation
Using the same technique in Section 3.2, we find the diversity gain through the evaluation of the pairwise error probability of 2-user CP-coded cooperation. Let
time
1 2
, ,
b r r
N N N denote the length of the broadcast, 1st relay and 2nd relay sub-codewords in Fig. 4-2. From (4.3) we can rewrite the detected signal for user U in symbol-wise 1 form:
where the index i denotes the ith element of the corresponding vector in (4.3). Thus the base codeword after combining is
( ) and 2nd relay sub-codewords, respectively.
The received SNR in the three phases are
( )
Hence the error probability of each symbol in (4.5) can be expressed as
( )
Again we assume BPSK modulation, thus iNe =1 and dmin2 = . Define user 4 U ’s 1
codeword as x=
[
x1 x2 " xN]
. The symbol error probability thatz
i is decided as an erroneous symbol li i
In the end, we can write the pairwise error probability of the received codeword conditioned on known channel in the form similar to (3.15)
(
)
( ) ( ) ( ) technique used in Section 3.2.1 to evaluate the pairwise error probability. Thus we have(
)
02 2( )1 1 121( ) 1 22( )2 1 destination at broadcast phase and between user U U and destination at relay 1, 2 phase, respectively. It can be seen that when all of the distance parameters d d b, r1 and d are not zeros, diversity order of 3 can be achieved. r2Diversity of more user case can be easily proved by the same method in this Section. For example, a 4-user scheme with base code partitioned into five parts has diversity order of 5 since it utilized the independent channels h1( )b ,h1( )r ,h2( )r ,h3( )r and
( )
4
hr (for U ). 1
Union bounds for BER and FER of these protocols can be calculated by the same method in Section 3.2.2, so we skip this part and look directly to the case of data exchange failure.
4.2.1 Impact of Data Exchange Failure
We analyze the impact of imperfect inter-user channel to the overall performance of user U data. Both method 1 and method 2 in Section 4.1.2 will be considered. 1
Method 1
Denote Pf u, as the rate of data exchange failure between users. In 2-user case, the probability of successful cooperation is
(
1−Pf u,)
and the probability of going back to no cooperation mode is Pf u, . Thus the overall performance can be written as( )
,2 1 , , ,
f f user f u f nocoop f u
P =P −P +P P (4.12)
where Pf,2user is the FER of 2-user CP-coded cooperation, which can be calculated from (4.11); Pf nocoop, is the FER when no cooperation is performed, it can be
calculated by replacing h2( )r in (4.10) with h1( )r , since the sub-codeword is now sent by U itself. Evaluating the pairwise error probability under above situation, we 1 have
Note that the diversity is lost comparing with (4.11). Also note that (4.12) is in similar form to (3.39), thus loss of diversity to the overall FER is expected at high SNR.
In 4-user case, full diversity can be achieved for user U data if and only if the 1 links between it and other three users are available. Thus the probability of 4-user cooperation is
(
1−Pf u,)
3. If one of the users doesn’t decode successfully, the situation becomes 3-user cooperation scheme and the probability of this condition is( )
2the same way as Pf nocoop, in 2-user case described above. The overall FER at the destination is
The only difference between method 1 and method 2 is the value of
,3 , ,2 f user f user
P P and Pf nocoop, ; since some of the codewords are discarded in method 2, it will lose some coding gain. The overall FER is calculated using the same equations as method 1, that is, (4.12) for 2-user case and (4.14) for 4-user case.
Consider 2-user case for instance, Pf nocoop, is calculated simply by setting the
term
Note the difference between (4.13) and (4.15). The distance value in the second term is changed from
(
dr1+dr2)
to d , this is because the sub-codeword for r1 U is 2 discarded instead of transmitted by U . 1The difference between (4.13) and (4.15) implies loss of coding gain when method 2 is used, but the diversity gain is preserved.
4.3 Computer Simulations
We now simulate the proposed CP-coded cooperation protocols and compare them with the performance bounds. Two base codes will be used: [15 17 13 15]
(rate-1/4) and [15 17 13 15 13 17] (rate-1/6). The constraint length is 4 and the frame size is 260 bits. 2-user and 4-user cases will be considered; all users are equipped with single antenna and are communicating with the same destination. To isolate the diversity gain from the cooperation, the destination is equipped with only one antenna.
However, more antennas can be used to further enhance the system reliability.
Fig. 4-7 shows the FER of CP-coded cooperation using 1/6 code. The puncturing pattern is [1 1 0 0 0 0] for the broadcast sub-code. For 2-user case, the puncturing patterns for the 1st and 2nd relay sub-codes are [0 0 1 1 0 0], [0 0 0 0 1 1], respectively;
Conventional coded cooperation (union bound) Conventional coded cooperation
Proposed CP-coded (2-user) (union bound) Proposed CP-coded (2-user)
Proposed CP-coded (4-user) (union bound) Proposed CP-coded (4-user)
Fig. 4-7. Simulations and bounds of frame error rate (FER) in CP-coded cooperation. Equal uplink SNR, base code [15 17 13 15 13 17]
Comparing with the performance bounds evaluated in Section 4.2 (dotted line with diamonds), we can see that 2-user CP-coded cooperation is consistent with the bound and achieves diversity of order 3. It also holds for 4-user case (line and dotted line with down-triangles). At FER of 10−3, 2-user case (line with diamonds) has nearly 4dB margin comparing to conventional coded cooperation (line with squares)
proposed by [18], and 3dB more is gained by using 4-user code partition. Note that all protocols in Fig. 4-7 have equal data rate, equal spectral efficiency and equal power consumption to single user case (line with circles).
Fig. 4-8 uses the same cooperative protocols as Fig. 4-7, but with a shorter base code: [15 17 13 15]. The puncturing pattern of the broadcast sub-code is [1 1 0 0]. For 2-user case, they are [0 0 1 0] and [0 0 0 1] for 1st relay and 2nd relay sub-code; for
Conventional coded cooperation (union bound) Conventional coded cooperation
Proposed CP-coded (2-user) (union bound) Proposed CP-coded (2-user)
Proposed CP-coded (4-user)
Fig. 4-8. Simulations and bounds of frame error rate (FER) in CP-coded cooperation. Equal uplink SNR, base code [15 17 13 15]
Note that the base code is equal to the base code used in Chapter 3, so this figure gives a comparison of performance between CP- and ST-coded cooperation (Fig. 3-3).
From the figure we can see that in 2-user case (line with diamonds), both protocols have similar performances. But in 4-user case (line with down triangles), the performance gain using CP-coded cooperation is not that significant compared to ST-coded cooperation. It is due to the fact that applying code partitioning on a short base code will generate sub-codes with very short code length, which leads to small distances between codewords (Note that the period of the puncturing pattern in 4-user case is made twice longer to separate the four relay sub-codes). Look closer to the pairwise error probability in (4.11), small distance parameters d db, r1,d will widen r2 the low-SNR-effect region of the resulting FER expressions, that means although full diversity can still be gained, it is only at higher SNR region.
Fig. 4-9 shows the performance degradation in case of data exchange failure.
Rate-1/6 base code is used. The rate of data exchange failure is set to 0.1 and we use method 1 for the relay reaction. From the figure it is clear that simulation result of both 2-user (diamonds) and 4-user (down triangles) cases matches its union bounds (dash line and dash line with dots), which is calculated using the formulas in Section 4.2.1. Comparing the simulation result with perfect cooperation case (line with diamonds for 2-user; line with down triangles for 4-user), we can see the performance degradation due to the diversity loss, but even with high failure rate, CP-coded cooperation still has approximately 4dB and 7dB margin for 2-user and 4-user case, respectively, comparing to the conventional coded cooperation. (at overall FER of 10−3)
0 2 4 6 8 10 12 14 16 18 20
Conventional coded cooperation (inter-user FER=0.1) CP-coded (2-user) (inter-user FER = 0.1, method 1) (union bound)
CP-coded (2-user) (inter-user FER=0.1, method 1) CP-coded (2-user) (perfect inter-user)
CP-coded (4-user) (inter-user FER = 0.1, method 1) (union bound)
CP-coded (4-user) (inter-user FER=0.1, method 1) CP-coded (4-user) (perfect inter-user)
Fig. 4-9. Frame error rate (FER) with imperfect inter-user channels. Equal uplink SNR, generator [15 17 13 15 13 17], inter-user FER=0.1, method 1
Fig. 4-10 simulates in the same condition as Fig. 4-9, except that we use method 2 for the relay reaction. The dash line and the dash line with dots demonstrate the union bounds for 2-user and 4-user cooperation under method 2, respectively. The simulation results (diamonds and down triangles) are in consistent with the analyzed bounds. Comparing Fig. 4-10 with Fig. 4-9, it can be found that there is about 0.7dB loss in 2-user cooperation when method 2 is used; it is 0.8dB in 4-user case. The loss is due to the fact that some sub-codewords are discarded when error occurs in data exchange. As mentioned in the end of Section 4.1.2, this is the tradeoff for lower system complexity.
0 2 4 6 8 10 12 14 16 18 20
Conventional coded cooperation (inter-user FER=0.1) CP-coded (2-user) (inter-user FER = 0.1, method 2) (union bound)
CP-coded (2-user) (inter-user FER=0.1, method 2) CP-coded (2-user) (perfect inter-user)
CP-coded (4-user) (inter-user FER = 0.1, method 2) (union bound)
CP-coded (4-user) (inter-user FER=0.1, method 2) CP-coded (4-user) (perfect inter-user)
Fig. 4-10. Frame error rate (FER) with imperfect inter-user channels. Equal uplink SNR, generator [15 17 13 15 13 17], inter-user FER=0.1, method 2
4.4 Summary
In this Chapter we demonstrate the protocols and performances of Code Partition (CP) coded cooperation. It achieves diversity gain by partitioning a long base code into several short sub-codes and sending them by different users (independent channels). It has similar performance compared to the ST-coded cooperation in Chapter 3 (equal spectral efficiency, equal diversity gain for a given number of users), but has lower system complexity since no space-time code is used. Besides, it has lower requirements for the inter-user channels; full cooperation can still be achieved
for other user when some of the users failed to exchange information. An alternative way for the relays to react to data exchange failure is presented to further simplify the system with reasonable loss of coding gain.
Chapter 5
Conclusions and Future Works
In this thesis, we develop two modified protocols of coded cooperation that enable the users, each equipped with a single antenna, to fully exploit the spatial diversity in the channel without losing spectral efficiency. Channel coding is assumed available for protecting the transmitted data. These protocols separate the codeword into two parts. Each user broadcast the first part (broadcast sub-codeword) to all other users, including the destination. After acquiring the data of other users by decoding the received broadcast sub-codeword, they use it to generate the second part (relay sub-codeword). The second codeword is transmitted with the help of all users using a space-time code or by partitioning it into several parts for each user. These sub-codewords are thus received at the destination through independent channels. For 2-user cooperation, we analyze the performance of the proposed protocols by evaluating the pairwise error probabilities and the BERs as well as FERs.
In Chapter 2, we review the concept of conventional cooperation and coded cooperation. There is spectral efficiency loss for conventional cooperative protocols due to the half-duplex hardware limitation, and we demonstrate how coded cooperation solves these problems by separating the transmit codeword for different purposes. In addition, the potential benefits inherent in coded cooperation is pointed
out: all users know each other’s data after the broadcast phase, which implies a virtual MISO system with the number of transmit antennas equal to the number of users.
In Chapter 3, we propose the first protocol that utilizes the potential benefits of coded cooperation, which is called space-time (ST) coded cooperation. It uses space-time code at the relay phase to enhance the reliability of relay sub-codewords, thereby enhancing the reliability of the transmitted data. Various space-time codes are chosen according to the number of users. For example, Alamouti code can be used in a 2-user scheme and 4 4× orthogonal space-time block code can be used in a 4-user scheme. It is shown in Section 3.2 that the diversity gain in relay sub-codeword reflects on the overall performance. Since the lengths of sub-codes remain unchanged regardless of the number of users in cooperation, the spectral efficiency is preserved while higher diversity order can be achieved with more users. However, the ST-coded cooperation has harsh requirements for inter-user channels because it requires all users to exchange data successfully to apply space-time code. Analyses and simulations reveal the performance degradation due to this factor. The degradation is rather large in the 4-user case, thus we propose an adaptive algorithm to compensate for it.
The second protocol, which is called code partitioning (CP) coded cooperation, is proposed in Chapter 4. It partitions the relay sub-codeword into several parts based on the number of users and makes each of them transmitted by a different user. Thus every part of the base codeword will be transmitted through an independent channel.
We prove it by analysis that CP-coded cooperation achieves same the diversity order as the ST-coded one. In case of data exchange failure, it is also more robust. We have shown in Section 4.1.2 that its diversity order is maintained even when some of the links between users are broken. A modified method for data exchange failure is proposed to further simplify the system complexity with a reasonable tradeoff in
coding gain. By this method, users do not need to know if other users receive their messages well, so feedback information is not needed.
The main contributions of this thesis are that two protocols based on coded cooperation are proposed to effectively exploit the benefits of cooperative transmissions. We introduce the concept of applying space-time code and code partitioning to the relay sub-codeword. The two protocols achieve higher system reliability but use equal channel resources as the direct transmission scheme. Both of them are highly flexible for different numbers of users. The larger the number of users that join cooperation, the higher the diversity gain that can be achieved. The code structure is also flexible to choose; it may be implemented using block or convolutional codes, or various methods of partitioning the codewords (puncturing, product codes, parallel and serial concatenation, etc.). Considering the case of data exchange failure in real wireless communications, we have proposed an adaptive algorithm to enhance the robustness of ST-coded cooperation. For CP-coded cooperation, we demonstrate its robustness against data exchange failure. Moreover, we exploit the advantages of CP-coded cooperation by using “blind cooperation” to make the scheme extremely simple.
Some issues that are not considered in this thesis may have considerable effect to the coded cooperative system and are worth future research. The first one is the spectral efficiency loss caused by feedback messages between users. In some of the proposed protocols, a user needs to notify others in case of data exchange failure, thus additional channel resource must be allocated. Although the resource needed is small compared to conventional cooperation, it still causes some loss in spectral efficiency.
The second one is the synchronization problem, which is critical in systems using space-time codes. The third one is the choice of cooperative partners. Although there
further investigation according to the specific protocols used. The final one is power allocation, which is not possible in ST-coded cooperation but may be helpful in CP-coded cooperation.
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