Distributed Space-Time Coding in LTE Systems

This work was supported by the National Basic Research Program of China (“973” Program) under Grant No. 2007CB310602.

    Based on the recognition of the communication industry on “broadbandization of mobile communication” and the need to face the challenge of “mobilization of broadband access”, 3GPP has started the Long Term Evolution (LTE) process[1]. LTE technology is poised to bring about a system with high data rate, low delay and optimized packet service, and to provide powerful transmission means for future broadband wireless service. It will satisfy the need of subscribers at any time and anywhere for IP multi-media data service. The LTE-Advanced system is a smooth evolution from LTE and is compatible with LTE. The LTE-Advanced system supports a peak downlink rate of 1 Gbit/s and peak uplink rate of 500 Mbit/s, while, at the same time, attaching great importance to lowering costs and power consumption of terminal and network[2]. Given the current spectrum allocation policy, the target spectrum for such capacity is located in the high frequency band, in which both path loss and penetration loss are quite high. Thus, it is difficulty for good coverage. Being a key technology in the LTE-Advanced system, relay technology can well solve this problem and provide larger cell coverage and system capacity[3]. The complexity of a Relay Node (RN) is far below that of an Enhanced Node B (eNB). Also, with its compactness, light weight and convenience of site selection, expenditure and power consumption are saved for operators. This is why reasonable and efficient use of relay for data transmission has become a significant area of study[4].

1 Classification of Relays
Relays can be broken into three categories according to the way in which the received signal is processed. These three categories are Amplify and Forward (AF), Decode and Forward (DF)[5] and Demodulate and Forward (DMF)[6]. Suppose S is the signal sent by eNB, yr  is the signal received by RN, hs r  is the channel response from eNB to RN, n  is the noise at the RN side, Sr  is the signal of RN, and therefore:

    yr =hs r S +n    (1)

    Sr =f (yr )    (2)    
    AF simply amplifies yr  and sends it out without any other processing, that is: 
    Sr =ayr     (3)

    AF comes with simple algorithm and low delay, but it also amplifies noise and hence degrades reception performance.

    DF features rather high processing complexity. The transmitting end uses error correcting code to protect the data block to be sent. The RN receives and then decodes the whole data block. If the correct data information (through Cyclic Redundancy Check (CRC)) is obtained, the RN encodes and then sends the data out again, otherwise the RN is closed.

    DF keeps the influence of channel and noise out completely at the cost of quite complicated decoding and encoding and high forwarding delay. If the channel works in a bad condition, RN will discard a large number of packets, resulting in the link disconnection or data retransmission.

    DMF means that the RN adopts the maximum likelihood to demodulate received signals and then forwards them. That is:

  S =argmin‖yr -hs r S‖2    (5)

    Because of the different conditions of channels from eNB to different RNs and the different confidence levels of different RNs that demodulate and output signals, different weighting can be given to the demodulation and output of various RNs. The weight number is related to the channel conditions: The better (or worse) the channel conditions are, the higher (or lower) the confidence level of the demodulated and sent signals, and the greater (or smaller) the weight number will become. This forwarding mode that takes RN’s demodulation confidence level into considerations is referred to as Weighted Demodulate and Forward (WDMF).

    Compared with AF, WDMF reduces the less influence of noise. As compared with DF, WDMF features much less complexity and forwarding delay. WDMF has a good tradeoff between the relay complexity and performance. The performance curve of WDMF will be given in the later simulation part of this paper.

    According to the LTE standard, by the position of RN’s data processing in the protocol, there are Layer 1 RN, Layer 2 RN and Layer 3 RN[7]. AF and WDMF can function in these three types of RN, since only the physical layer functions are concerned. But as DF requires some MAC layer functions, including data segmentation and CRC, DF can only work on Layer 2 and Layer 3 RNs. We’ll only look at the technologies for the physical layer, which means no restrictions on the protocol stack of RN, that is, the following conclusions can be applied to all RNs.

2 Distributed Space-Time Coding (DSTC)
The DSTC system comes in two types according to the cooperation mode: user cooperation and relay cooperation.

    User cooperation means that User Equipment (UE) shares resources to help each other in data transmission. As shown in Figures 1 and 2, UE1 and 2 send their own data separately in the first two Time Slots (TS), receive data from each other due to the broadcast feature of the radio channel, and send the space-time code word at the same time in the next TS. The drawback of user cooperation is that the users’ processing workload and energy consumption are increased, including data demodulation and user synchronization. User fairness, data security and compatibility are issues in need of further research.

    Relay cooperation means that several RNs coordinate to provide users with data forwarding service. This mode prevents the data security problem that arises from user cooperation, and the synchronization between RNs works more easily under the control of eNB without the need for additional processing workload of users. Better still, functions leading to higher system capacity are workable in RN; for example, power allocation, relay selection and user management[8]. The simplest power allocation one in which the transmit power of the transmitting end equals the total transmit power of RN, while the transmit power between RNs is evenly allocated. This approach, though not optimal, is the easiest one to realize. Figures 3 and 4 show an example where the DSTC is adopted in RN cooperation: In uplink transmission, UE sends data in the first TS to RN1 and RN2, and the RN sends data with DSTC in the second and third TS to eNB.

    There can be several RNs in a cell. As shown in Figure 5, 6 RNs can be found in the cell. The dotted line in the figure stands for the scope within which the UE is controlled and managed by each RN, but the RN may still communicate with UE outside this scope. To decrease interference between RNs and within the whole cell, we will just look at a case where the relay link may exist between one UE and 2-4 RNs. Also because the complexity of space-time coding is related to the quantity of joining RNs, less RNs will translate into simpler design of space-time coding.

    Reasonable design of the DSTC will help achieve full diversity gain and quite big encoding gain, and very low encoding and decoding complexity as well[9]. The currently available design methods include orthogonal space-time coding and quasi-orthogonal space-time coding[10], random space-time coding and linear discrete coding[11]. If we define Sr  1,Sr  2,…,Sr N as the sending sign of the RNs, then the DSTC[12] is a process that have the vectors Sr  1,Sr  2,…,Sr N  mapped into a code word matrix , that is:

    The orthogonal design guarantees the orthogonal intersection between column vectors of the code word generator matrix. It features independent coding between signs through the use of linear processing alone and is able to obtain full diversity gain. If there are more than two RNs, however, the full rate multi-orthogonal generator matrix is impossible. When there are two, four or eight RNs, there is only the real orthogonal matrix, hence the design for a system is very limited .

    Quasi-orthogonal space-time coding is proposed for the design of full rate code, and the sub-spaces of its generator matrix are orthogonally intersected. This method is able to perform independent coding for sign pairs but does not guarantee full diversity gain. The orthogonal space-time design and quasi-orthogonal space-time design, if distributed, must have a central controlling node to order the number of lines of the code word matrix to be sent by the RNs.

    Both orthogonal space-time design and quasi-orthogonal space-time design feature simple coding structure but the code rate is below 1, and therefore they are the candidate approaches when the transmission rate is low. If the coding complexity does not matter, a code word with the code rate greater than 1 can be designed, for example, a distributed linear discrete code. The distributed linear discrete code is the linear combination of sent signs and their conjugate, with the code rate determined by the number of sent signs. Because higher code rate corresponds to higher coding complexity, the encoder practicability determines the maximum number of signs. The distributed linear dispersion code is capable of flexible code rate change to suit channel quality and improve average throughput, and it need not repetitively allocate coding matrix.

    It is noteworthy that the performance of DSTC will be seriously affected if RNs are not synchronized. To avoid the carrier synchronization between RNs, the code word matrix can be designed as diagonal matrix, that is, only one RN forwards signals at a TS when other RNs are shut down. In this way, only symbol synchronization and frame synchronization are needed. The simplest case occurs when the code word generator matrix is the unit matrix, namely, the sent signals are forwarded without being processed and this coding scheme leads to repetitive coding. The diagonal matrix coding scheme uses the Discrete Fourier Transform (DFT) matrix for encoding. This scheme does not require much synchronization but is not as good as other schemes in terms of coding gain. In the LTE system, because eNB can manage RN, RNs can be deemed, to some extent, as synchronized.

    We will look at the performance of DSTC in AF, DF, DMF and WDMF modes. The simulation conditions are: all channels conform to the unit complex Gaussian distribution; the modulation mode is Binary Phase Shift Keying (BPSK); two nodes; ten data block signs; Signal-to-Noise Radio (SNR) is defined as the ratio of total transmitting power to noise power.

    Figures 6-9 show the Bit Error Rate (BER) performance curves of distributed dispersion code (L-DSTC), unit matrix code (I-DSTC), orthogonal code (O-DSTC) and DFT diagonal matrix code (D-DSTC) respectively in four forwarding modes: AF, DF, DMF and WDMF. It can be concluded through comparing these curves that, in the case of low SNR, (because the channel from eNB to RN is not very good), BER in the DF mode is close to 1. This means RN is unable to decode correctly and all data blocks will be discarded. In the case of high SNR, the DF mode is able to correctly restore eNB-sent data at RN and at the same time avoid the influence of eNB-to-RN channel fading and noises, thus providing the best BER performance for the user. The DMF and WDMF modes can prevent influence from noise in the case of low SNR and the performance is better than that of AF. Anyway, in the case of high SNR, because there is little
noise influence, and relay demodulation error of the DMF mode is the main reason for the performance degradation, there is approximately 5 dB performance loss of DMF, when compared with AF. The WDMF mode suppresses the influence of relay demodulation error over the user and therefore, its performance is better than that of AF. In the case of high SNR, the WDMF mode gains approximately 2 dB gains when compared with AF, and has a performance loss of 1 dB if compared with the optimal DF performance. To conclude, the WDMF mode is completely suitable for the low complexity and high performance requirements of LTE relay technology.

    Figure 10 depicts the BER performance curves of L-DSTC, I-DSTC, O-DSTC and D-DSTC in the WDMF mode. The rank of the four DSTC generator matrixes equals 2, full diversity gain is nearly obtained in the case of high SNR. O-DSTC features even larger coding gain and therefore it boasts better performance than other three space-time codes. The cells of LTE is different from that of the full distributed network as the eNB of LTE can work as the central control node for all RNs to fulfill RN-RN synchronization and space-time code word assignment.

Besides, the low-complexity receiver of orthogonal space-time code requires less power consumption of the user terminal. In other words, O-DSTC is an optimal option for the LTE system when two (for any modulation satellite) or four (applies only to real modulation satellite) RNs are needed. Nevertheless, L-DSTC can translate into greater flexibility if adaptive modulation and coding (AMC) technology and RN selection technology are considered, as L-DSTC applies to any modulation mode and configuration of any number of RNs.

3 Selective Space-Time Relay
Reference [13] proves that in the DMF mode, the maximum space diversity gains obtainable by multi-relay transmission are half the quantity of RNs involved. That is to say, though better than that of DMF to some extent, the performance of WDMF in the case of high SNR is greatly affected by error forwarding. To improve the error forwarding situation of WDMF, some enhanced type of WDMF modes are proposed. There are two main categories: adaptive relay mode and selective relay mode. Reference [14] proposes to increase or decrease the RN’s transmitting power according to the reception SNR status to enhance the power of reliable relay signals and lower the power of unreliable relay signals. Reference [15] proposes to take the minimized eNB BER as the target selective DMF, and if an RN’s reception SNR is greater than a predefined setting, the RN can perform signal relay; otherwise it cannot. The selective relay mode is more realizable than the adaptive one and can still function even if the direct channel does not exist. Therefore, the selective DMF relay mode is more suitable for the LTE system. However, due to the forwarding error and reception noise, a precise BER expression is very hard to formulate for the distributed space-time relay system. To calculate the BER, Reference [15] introduces a high SNR likelihood and the result applies only to the binary modulation relay system. More importantly, the abovementioned research considers only the cases with repetitive coding. Error forwarding is a much more serious problem in the distributed space-time relay system due to the fact that demodulation errors will be further encoded by RN.
To address the issue of error forwarding in the DSTC system, Reference [16] proposes two predefined threshold-based selective DMF modes: centralized selective relay and distributed selective relay. Both modes apply to any modulation constellation and any number of RNs, and have inherited the threshold selection mechanism put forward by Reference [15]. The centralized selective relay mode takes demodulation error and treats it as an equivalent interference noise. This way, the new SNR can be defined and the objective of threshold selection is to maximize such equivalent SNR. Because it is necessary to obtain the information of all average channels of all the relay system, the centralized selective relay needs to the centralized control module equipped to the eNB, or a certain RN to calculate the reception SNR threshold of all RNs and broadcast the result to the RNs. The distributed selective relay mode treats every relay channel and RN as equivalent channels, and every RN need only judge whether the signal it transmits to the receiver will increase the error probability of the equivalent channel. With the distributed selective relay mode, every RN need only know the average channel information of its own reception and transmission channels, and therefore channel information interaction between RNs is not necessary. It is noteworthy that if O-DSTC or D-DSTC is taken as the coding scheme, it is necessary to redesign the coding matrix and re-allocate code word when the number of working RNs changes. To prevent excessive information interaction between RN and eNB, L-DSTC can prove a good solution. The LTE-A system has not yet determined the RN-RN interaction process and therefore the two proposed selective relay modes are expected to work as useful references for the LTE-A system. Figure 11 depicts the system simulation with four RNs and where the size of the data block is 4. The simulation shows that the selective relay mode is able to improve power gains by about 2 dB and the centralized selective relay mode is slightly better than the distributed selective relay mode.

4 Conclusions
The following conclusions are obtained through analysisof various distributed space-time relay modes:

    (1) RN-based relay cooperation technology can be applied to the current LTE standard;

    (2) In terms of tradeoff between complexity and performance, WDMF is the optimal mode for the distributed space-time relay system of LTE;

    (3) For the 2-RN relay system, the orthogonal design-based DSTC is optimal. But for the purpose of less RN-RN information interaction and to adapt to any number of RNs and any modulation constellation, the distributed dispersion code is recommended;

    (4) The relay selection with certain criteria noticeably improves the performance of DSTC in the DMF mode.

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[Abstract] Relay is considered as one of the candidate key technologies of LTE-advanced for it brings broader cell coverage and higher system capacity. Distributed Space-Time Coding (DSTC) not only exploits the spatial diversity from the relay structure, but also brings some coding gains. According to the performances of existing DSTC schemes, the Demodulate-and-Forward (DMF) scheme is the best candidate for DSTC in LTE-Advanced system. Moreover, a threshold-based selective relaying scheme for DSTC is proposed to solve the error propagation of DMF. This scheme can achieve excellent performance gains at the cost of little system complexity.