Chapter 3 Spectrally Efficient Multi-user Coded Cooperation
4.1 Protocols of CP-Coded Cooperation
Look at the performance bound in eq. (3.28), we can see that the diversity gain comes from the independent channels of user U in the broadcast phase and relay 1 phase. Further more, additional diversity is gained from U channel by using 2 Alamouti space-time code in relay phase. Thus the total diversity gain compared to direct transmission protocol is 2 1 3+ = . There is another factor in (3.28) that contributes to the overall performance: the Hamming weight of the sub-codewords
(d d ). As long as b, r d d are not zeros, diversity order of 3 is achieved. Since that, b, r it is natural to think that if more than two sub-codes are separated from the base code and transmitted by independent channels, higher diversity order can be achieved without the help of space-time code. The second type of coded cooperation is proposed based on these principles.
4.1.1 Code Structure and System Model
The main idea of CP-coded cooperation is to let every sub-codeword of a base codeword transmitted through independent channels. Thus the number of sub-codes depends on the number of independent channels we have.
For 2-user case, we partition the base code into three sub-codes, one is for the source and the other two are for the relays (See Fig. 4-1). The sub-codeword for the source is still called broadcast sub-codeword, but for the other two sub-codewords for the relays, we tag them with numbers (ex. 1st, 2nd relay sub-codeword, etc.), each relay sub-codewords are transmitted by different relays. The code structure is shown in Fig.
4-2.
Fig. 4-1. Channel use of CP-coded cooperation with two users (TDMA)
Fig. 4-2. Structure of codeword in CP-coded cooperation (2-user case)
Note that the code-structure is different from the one in Chapter 3 and [18]. We expect a diversity order of 3 is gained for each user data since the data is partitioned into three parts. The analysis will be given in Section 4.2.
Assume quasi-static fading channel similar to the channel used in ST-coded cooperation, the received signal at the destination in broadcast phase is
broadcast
( ) ( ) ( ) ( )
At relay phase, the received signal can be written as
( ) ( ) ( ) ( ) respectively. Assuming ML detection, the detected signal for user U is 1
( ) ( ) ( ) ( ) signals are combined at the destination to rebuild the base codeword. Then the destination decodes the base codeword using Viterbi decoder.
This protocol can be easily extended to cases with more users, for example, a 4-user protocol is shown below.
Fig. 4-3. Channel use of CP-coded cooperation with four users (TDMA)
Fig. 4-4. Structure of codeword in CP-coded cooperation (4-user case)
This time the base code is partitioned into five sub-codes, the first one is for broadcasting and the other four is for relaying (four relays). Note that the four relay sub-codewords are still transmitted by different users.
The main difference between ST-coded cooperation and CP-coded cooperation is 1 2 3 4
the number of sub-codes used. In ST-coded cooperation, the number is fixed to two sub-codes: one for broadcasting and one for relaying. It is the space-time code to change with different number of users. However, CP-coded cooperation uses different number of sub-codes to match the number of users participated in the cooperation.
4.1.2 Case of Information Exchange Failure
CP-coded cooperation is more flexible than ST-coded cooperation to the case of data exchange failure; the latter needs all users to exchange data successfully to apply space-time code, while the former doesn’t. For example, in a 4-user scheme, if error occurs in the exchange of data between user U and 1 U , they can’t cooperate with 2 each other so the diversity gain will be lower due to the loss of one independent channel. However, they can still cooperate with U and 3 U , so it has no effect to the 4 error rates of U and 3 U data. 4
There are two kinds of reactions for a user when decoding error occurs: notify other users (method 1) or do nothing (method 2). More specific description will be given in the following paragraph.
Method 1
The first method is the similar to the method used in ST-coded cooperation. Say, in a 4-user scheme, if user U fails to decode the information from 1 U , it will send 2 a notification signal to all other users. However, there is no need for all users to go back to no cooperation mode (like we do in 3.1.2), instead, only U takes this 2 notification signal. After receiving the notification, U and 1 U will go back to no 2 cooperation mode and transmit the corresponding sub-codewords by themselves. A figure plotted the channel use under above case is given in Fig. 4-5. From the figure
we can see that the sub-codewords (2nd sub-codeword of U and 11 st sub-codeword of U ) which should be sent by other users are now sent by its owners themselves 2
(U U , respectively). However, there’s no change for 1, 2 U and 3 U data. Thus full 4 diversity order can still be achieved for these two users, while diversity of order one will be lost for U and 1 U data. 2
Fig. 4-5. Channel use of 4-user CP-coded cooperation with bad user1 – user2 link, method 1
Method 2
The second method makes slightly modification to the first one. Since a long base codeword is partitioned into several sub-codewords, it may still be okay for the destination to decode if some of the sub-codewords are lost. That is, if a user fails to decode the information from other user in broadcast phase, it does nothing in the corresponding relay phase. The destination will hence lose that part of the base
time
codeword, but data can still be decoded from the remaining parts. This method will lead to some loss in not only diversity gain, but also coding gain; however, the major advantage is that users don’t need to notify others if decoding error occurs, hence the system complexity is less than the first method. Fig. 4-6 gives the example when data exchange failure occurs between U and 1 U . Note that compared with Fig. 4-5, 2 some sub-codewords are discarded instead of transmitted by their owner.
Fig. 4-6. Channel use of 4-user CP-coded cooperation with bad user1 – user2 link, method 2