Low complexity post-ordered iterative decoding for ... - IEEE Xplore
Low Complexity Post-Ordered Iterative Decoding For Generalized Layered SpaceTime Coding Systems Meixia Tao and Roger S . K. Cheng Center for Wireless Information Technology* Electrical & Electronic Engineering Department The Hong Kong University of Science & Technology Clear Water Bay, Kowloon, Hong Kong
Abstract-In this paper we refer to the combination of BLAST and space-time coding (STC) for multi-input multioutput systems as generalized layered space-time coding (GLST). Post-ordered decoding algorithm is introduced based on the generalization of the original BLAST ordering detection algorithm. The performance is analyzed through comparison to that of pre-ordered decoding with and without power allocation. Interleavered GLST with a new iterative process is also proposed. It can efficiently exploit full receive antenna diversity and thus significantly improve the system overall performance. Due to hard interference cancellation (IC) and ML decoder in the iterations, the new iterative decoding is much less complex than conventional turbo processing where soft IC and MAP decoder were applied.
I. INTRODUCTION The demand for high data rate and high quality in wireless communications is growing rapidly. Recent theoretical information studies in [ 1][2] have shown that the spectral efficiency can be increased dramatically by employing multiple transmit and multiple receive antennas. A new multi-input multi-output (MIMO) transmission scheme developed by Bell-Lab [3][4][5], known as BLAST, is a practical and efficient way to approach this high spectral efficiency. A simple serial decoding method which combines interference suppression (Zero-Forcing) and interference cancellation (IC) techniques, is applied to detect the transmit signals. However neither the transmit or the receive antenna diversity is fully exploited due to this simple detection algorithm. A new family of codes, space-time codes (STC) proposed by Tarokh, et a1 [7] is another promising approach to achieve high spectral efficiency and power efficiency in multiple-antenna communication systems by introducing both spatial and temporal correlation between signals transmitted on different transmit antennas through coding. The maximum likelihood (ML) decoding is achieved by using Viterbi decoder. Excellent performance was shown by computer simulation. However the decoding complexity is increased exponentially with the increase of the number of transmit antennas and the spectral efficiency.
*
The combination of BLAST and STC is straightforward and is referred to as generalized layered space-time codes (GLST) in this paper. The general framework is to partition all the available transmit antennas into several groups and applies STC on each group. Similar to BLAST, the signals transmitted by different antenna groups in GLST are not jointly coded. Within each antenna group, the signals are space-time coded, hence the transmit antenna diversity is increased and the required minimum number of receive antennas is correspondingly reduced. Similar to STC, the design of the codes within each group in GLST is aimed to achieve maximum diversity gain and coding gain, which, however, has much less complexity due to the smaller number of antennas. Similar ideas can be found in [8][12], where space-time trellis codes and space-time block codes are combined with BLAST respectively. Different antenna groups are assigned with different transmission power in [81, hence the decoding order for each group is fixed, namely, the group with more power is decoded earlier. We refer to this scheme as preordered decoding with power allocation. However the power allocation scheme in [SI is ad hoc. The optimum power allocation for GLST is then discussed in our companion paper [13], where we argue that the optimum power allocation should be most attractive under very low complexity requirement. In this paper we focus on different decoding algorithms with low decoding complexity. First, post-ordered decoding algorithm is introduced by generalizing the original zero-forcing V-BLAST ordering algorithm [4]. Its performance is analyzed by comparison to that of the pre-ordered decoding. Second, interleavered GLST with a new low complexity iterative decoding is also proposed. This scheme applies hard interference cancellation (IC) and ML decoding, hence the complexity is considerably lower than conventional turbo processing [lO][l1][12] where soft IC and MAP coder were deployed. It can efficiently utilize full receive antenna diversity and significantly improve the system overall performance. The remainder of this paper is organized as follows. The system structure of GLST is briefly reviewed in Section 11. The post-ordered decoding algorithm is discussed and
This work is supported in part by the Hong Kong RGC. Emails of the authors are {mxtao,eecheng} .ee.ust.hk
0-7803-7097-1/01/$10.00 02001 IEEE
1137
simulation results are presented in Section 111. In Section IV we describe the proposed interleavered GLST with iterative decoding method and analyze its performance through simulations. Finally conclusions are drawn in Section V. 11. SYSTEM MODEL FOR GENERALIZED LAYERED SPACE-TIME CODING
A MIMO system equipped with n transmit antennas and m receive antennas is considered and denoted by a (n,m) system. The channel is assumed to be quasi-static Rayleigh flat fading, i.e. the channel coefficients are kept constant within one frame and changed independently from one frame to the other frame. The channel state information (CSI) is assumed perfectly estimated at the receiver but not known at the transmitter. We illustrate the baseband transmission structure of GLST in Fig. 1 . A block of B input bits is sent to a serial-toparallel converter to produce q bit strings of length B,, B2, .. ., B, with BI+B2+...+B,=B. Each block B,, l<j
Abstract-In this paper we refer to the combination of BLAST and space-time coding (STC) for multi-input multioutput systems as generalized layered space-time coding (GLST). Post-ordered decoding algorithm is introduced based on the generalization of the original BLAST ordering detection algorithm. The performance is analyzed through comparison to that of pre-ordered decoding with and without power allocation. Interleavered GLST with a new iterative process is also proposed. It can efficiently exploit full receive antenna diversity and thus significantly improve the system overall performance. Due to hard interference cancellation (IC) and ML decoder in the iterations, the new iterative decoding is much less complex than conventional turbo processing where soft IC and MAP decoder were applied.
I. INTRODUCTION The demand for high data rate and high quality in wireless communications is growing rapidly. Recent theoretical information studies in [ 1][2] have shown that the spectral efficiency can be increased dramatically by employing multiple transmit and multiple receive antennas. A new multi-input multi-output (MIMO) transmission scheme developed by Bell-Lab [3][4][5], known as BLAST, is a practical and efficient way to approach this high spectral efficiency. A simple serial decoding method which combines interference suppression (Zero-Forcing) and interference cancellation (IC) techniques, is applied to detect the transmit signals. However neither the transmit or the receive antenna diversity is fully exploited due to this simple detection algorithm. A new family of codes, space-time codes (STC) proposed by Tarokh, et a1 [7] is another promising approach to achieve high spectral efficiency and power efficiency in multiple-antenna communication systems by introducing both spatial and temporal correlation between signals transmitted on different transmit antennas through coding. The maximum likelihood (ML) decoding is achieved by using Viterbi decoder. Excellent performance was shown by computer simulation. However the decoding complexity is increased exponentially with the increase of the number of transmit antennas and the spectral efficiency.
*
The combination of BLAST and STC is straightforward and is referred to as generalized layered space-time codes (GLST) in this paper. The general framework is to partition all the available transmit antennas into several groups and applies STC on each group. Similar to BLAST, the signals transmitted by different antenna groups in GLST are not jointly coded. Within each antenna group, the signals are space-time coded, hence the transmit antenna diversity is increased and the required minimum number of receive antennas is correspondingly reduced. Similar to STC, the design of the codes within each group in GLST is aimed to achieve maximum diversity gain and coding gain, which, however, has much less complexity due to the smaller number of antennas. Similar ideas can be found in [8][12], where space-time trellis codes and space-time block codes are combined with BLAST respectively. Different antenna groups are assigned with different transmission power in [81, hence the decoding order for each group is fixed, namely, the group with more power is decoded earlier. We refer to this scheme as preordered decoding with power allocation. However the power allocation scheme in [SI is ad hoc. The optimum power allocation for GLST is then discussed in our companion paper [13], where we argue that the optimum power allocation should be most attractive under very low complexity requirement. In this paper we focus on different decoding algorithms with low decoding complexity. First, post-ordered decoding algorithm is introduced by generalizing the original zero-forcing V-BLAST ordering algorithm [4]. Its performance is analyzed by comparison to that of the pre-ordered decoding. Second, interleavered GLST with a new low complexity iterative decoding is also proposed. This scheme applies hard interference cancellation (IC) and ML decoding, hence the complexity is considerably lower than conventional turbo processing [lO][l1][12] where soft IC and MAP coder were deployed. It can efficiently utilize full receive antenna diversity and significantly improve the system overall performance. The remainder of this paper is organized as follows. The system structure of GLST is briefly reviewed in Section 11. The post-ordered decoding algorithm is discussed and
This work is supported in part by the Hong Kong RGC. Emails of the authors are {mxtao,eecheng} .ee.ust.hk
0-7803-7097-1/01/$10.00 02001 IEEE
1137
simulation results are presented in Section 111. In Section IV we describe the proposed interleavered GLST with iterative decoding method and analyze its performance through simulations. Finally conclusions are drawn in Section V. 11. SYSTEM MODEL FOR GENERALIZED LAYERED SPACE-TIME CODING
A MIMO system equipped with n transmit antennas and m receive antennas is considered and denoted by a (n,m) system. The channel is assumed to be quasi-static Rayleigh flat fading, i.e. the channel coefficients are kept constant within one frame and changed independently from one frame to the other frame. The channel state information (CSI) is assumed perfectly estimated at the receiver but not known at the transmitter. We illustrate the baseband transmission structure of GLST in Fig. 1 . A block of B input bits is sent to a serial-toparallel converter to produce q bit strings of length B,, B2, .. ., B, with BI+B2+...+B,=B. Each block B,, l<j
