The single carrier-frequency division multiple access (SC-FDMA) system is a new system that was adopted in the standardization of the upcoming 3GPP long-term evolution (LTE). Designing diversity-achieving schemes for the SC-FDMA system is a challenging task. The codes adopted should not affect the peak-to-average power ratio (PAPR) among other constraints. In this paper, we consider the design of cooperative diversity schemes for SC-FDMA systems in the uplink direction. Specifically, two relay-assisted distributed space-time/frequency codes are proposed. The proposed distributed space-frequency code (SFC) achieves full spatial diversity in the uplink fast-fading channels, where a diversity of order three can be achieved. The proposed code keeps a low PAPR, which is a good feature of the system. A minimum mean square error (MMSE) decoder is used at the receiver of the destination node. Moreover, we propose a bandwidth-efficient distributed space-time code (STC) for slow-fading relay channels. A decode-and-forward (DF) protocol is used at the relay node, and the possibility of erroneous decoding is taken into account. Simulation results demonstrate the performance improvement of the proposed schemes.
Future broadband wireless networks should meet stringent requirements such as high data rate services over dispersive channels with high transmission reliability. Since the wireless resources such as the bandwidth and power are very scarce, they cannot cope with the increasing demand for higher data rates. Furthermore, wireless channels suffer from several impairments such as fading, shadowing, and multiuser interference that can degrade the system performance. In order to achieve such high bit rates and at the same time to meet the Quality of Service (QoS) requirements, orthogonal frequency division multiple access (OFDMA) is considered a mature technique to mitigate the problem of frequency selectivity and intersymbol interference (ISI) with other well-known advantages [
It is well known that the multiple-input multiple-output (MIMO) systems can significantly improve the capacity and reliability of the communication over fading channels using spatial multiplexing and/or space-time coding. Applying MIMO techniques for the SC-FDMA system was considered in [
In this paper, we propose relay-assisted distributed space-time/frequency codes for SC-FDMA systems in the uplink direction. The proposed distributed SFC is achieved in two phases, and the code does not affect significantly the PAPR of the transmitted signal. This code is suitable for fast-fading channels, where the channel gain changes from block to block. The coding is applied within each transmitted block. As the two coded symbols may experience different channel gains within one transmitted block, direct application of Alamouti decoding using maximum likelihood detection (MLD) over one symbol may degrade the performance especially with a large number of allocated subcarriers per user. Therefore, an MMSE decoder is used at the receiver to overcome this problem with a slight increase in the decoding complexity. Furthermore, we propose a distributed STC for the slow-fading channel environment. The proposed code is more spectrally efficient than the classical DSTC schemes. The proposed code achieves a transmission rate of 2/3. For the two proposed codes, the DF protocol is considered and erroneous decoding at the relay node is taken into account. If the relay cannot decode correctly in the first phase, it remains idle in the second phase.
The rest of the paper is organized as follows. Section
In this section, we present the system model for the conventional SC-FDMA system. In the following sections, the operations
The SC-FDMA system model of user
SC-FDMA system model of user
Illustration for the localized subcarriers allocation in the frequency domain for
In this section, we present the proposed cooperative diversity scheme for the SC-FDMA system based on DSFC. The proposed protocols utilize the SFC in the uplink SC-FDMA systems. We will consider Alamouti-like coding in which two users cooperate to send their information to the destination node. We will consider the DF protocol at the relay node.
Consider the uplink transmission in the SC-FDMA system. The users in the system help each other to transmit, cooperatively, to the destination node in the second phase. Consider an example of two users sharing
The transmitted signals for the proposed distributed SFC using the DF protocol in the frequency domain.
Time slot ( | User 1 | User 2 | ||
1 | — | — | ||
2 | − |
Two cooperative users in the uplink SC-FDMA network. (a) Phase I, (b) Phase II.
Listening phase
Cooperation phase
In the second phase, user 1 sends his own data on the band
As mentioned above, the signals transmitted in the second phase from both users constitute an Alamouti-like SFC, which achieves a diversity of order two. Furthermore, the signal transmitted in the first phase can also be exploited and combined with the signal received in the second phase at the receiver of the destination node. In the following analysis, we distinguish between two protocols regarding the received signal at the destination node in the first phase.
In the first phase, each user transmits his information to his partner. The destination node ignores the signals in this phase. In the second phase, in the case of correct decoding, both users communicate with the destination node to form the SFC on the bands
This protocol differs from Protocol I in that the signals transmitted in the first time slot are received by the destination node and combined with the coded signals in the second time slot. In the case of a fast fading channel, the channel state changes from block to block. Therefore, a diversity of order three can be obtained as will be explained later. Further investigation of this type of nonorthogonal transmission to increase the spatial diversity was presented in [
In this subsection, the proposed distributed SFC with the DF protocol is considered, where each terminal is equipped with a single antenna. Table
In the first time slot (
In the second time slot (
Note that the decoding of the received sub-vectors in (
Illustration of the proposed distributed SFC structure for user 1 for one-way cooperation on the band
Scheme I: Classical Scheme
Scheme II: Proposed in [
Proposed coding scheme
It should be noted that (
In this section, we present the proposed bandwidth-efficient distributed STC that achieves better spectral efficiency than the classical scheme. The proposed scheme is illustrated in Table
The transmitted signals in the frequency domain for the proposed distributed STC with the DF protocol.
Time slot ( | User 1 | User 2 | ||
1 | — | — | ||
2 | — | — | ||
3 |
In the first time slot, user 1 uses both his own subcarriers and his partner’s subcarriers to transmit his information to the destination node. We argue that there is no practical limitation for the user to use both the subcarriers allocated to him and to his partner. At the same time (
Due to the symmetry in cooperation in the two bands
Both users decode correctly, that is,
In this case, the received signals at the destination node can be expressed as
User 2 decodes correctly and user 1 does not, that is,
User 2 fails to decode whereas user 1 decodes correctly, that is,
Both user 1 and user 2 fail to decode correctly, that is,
It should be noted that for the receiver of the destination node to combine the received signals, the state of each node, whether it has decoded correctly or not, should be forwarded to the destination node. This can be accomplished by sending one bit from each user to the destination to indicate whether the user could decode the received signal from his partner, correctly, or not.
In this section, we verify the performance of the proposed cooperative diversity schemes via computer simulations. The uplink direction of the SC-FDMA system is considered. A total of
Figure
Performance comparison between MMSE decoding and Alamouti MLD decoding for the proposed distributed SFC with different number of subcarriers allocated to each user using Protocol I.
Figure
SER versus SNR for the proposed distributed SFC for user 1 considering both Protocol I and Protocol II.
The complementary cumulative distribution functions (CCDFs) of the PAPR of the transmitted signals at the relay node for the proposed scheme, the classical scheme, and scheme II proposed in [
Performance comparison of the CCDF of the PAPR between the proposed distributed SFC, classical schemes, and uncoded SC-FDMA at the relay node.
Performance comparison between the proposed scheme and the scheme proposed in [
The SER performance comparison between the proposed distributed STC and the classical coding scheme is shown in Figure
SER performance comparison between the proposed distributed STC and the classical scheme with different inter-user channel variances.
It can also be seen that the proposed scheme has a better performance than the classical distributed STC, when all channel variances are equal to one. As the inter-user channel variance increases and other channels variances are equal to one, the performance loss of the proposed scheme increases compared to the classical scheme, because case 1 will be the dominant case, and the additional noise component in (
In this paper, we have proposed cooperative diversity schemes that are suitable for SC-FDMA systems in the uplink direction. The proposed distributed SFC achieves a full spatial diversity and keeps the low PAPR of the SC-FDMA systems. The SER performance loss of the proposed code is approximately negligible compared to the classical scheme. As the classical simple Alamouti decoding degrades the performance, we have used the MMSE decoding with a small increase in the complexity. Furthermore, we have proposed a distributed STC that is suitable for slow fading channels. The proposed code achieves a transmission rate of 2/3. Simulation results indicate that a better performance is achieved with small inter-user channel variances compared to the classical scheme. With a strong source-relay channel, the proposed code achieves a full diversity with a small performance loss.