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Bit-Interleaved Time-Frequency Coded Modulation for OFDM Systems Over Time-Varying Channels Defeng (David) Huang, Member, IEEE, Khaled Ben Letaief, Fellow, IEEE, and Jianhua Lu
Abstract—Orthogonal frequency-division multiplexing (OFDM) is a promising technology in broadband wireless communications, with its ability to transform a frequency-selective fading channel into multiple flat-fading channels. However, the time-varying characteristics of wireless channels induce the loss of orthogonality among OFDM subcarriers, which was generally considered harmful to system performance. In this paper, we propose a bit-interleaved time-frequency coded modulation (BITFCM) scheme for OFDM to achieve both the time and frequency diversity inherent in broadband time-varying channels. We will show that the time-varying characteristics of the channel are beneficial to system performance. Using the BITFCM scheme, and for relatively low maximum normalized Doppler frequency, a reduced-complexity maximum-likelihood decoding approach is proposed to achieve good performance with low complexity. For high maximum normalized Doppler frequency, the intercarrier interference (ICI) can be large, and an error floor will be induced. To solve this problem, we propose two ICI-mitigation schemes by taking advantage of the second-order channel statistics and the complete channel information, respectively. It will be shown that both schemes can reduce the ICI significantly. Index Terms—Bit-interleaved coded modulation (BICM), intercarrier interference (ICI), orthogonal frequency-division multiplexing (OFDM), time diversity.
I. INTRODUCTION
O
RTHOGONAL frequency-division multiplexing (OFDM) [1], [2] is a promising technology in broadband communications, due to its spectrum efficiency and low complexity. When OFDM is used in wireless communications, the frequency diversity induced by the frequency-selective characteristics of the channel can be exploited by interleaving and coding. Recently, bit-interleaved coded modulation (BICM) [3]–[6] was investigated in fading channels, and it was shown that superior performance due to the high diversity order can be achieved. As a result, [7] proposed using BICM in OFDM systems to exploit the frequency-varying characteristics of
Paper approved by Y. Li, the Editor for Wireless Communication Theory of the IEEE Communications Society. Manuscript received December 3, 2003; revised June 3, 2004. This work was supported in part by the Hong Kong Telecom Institute of Information Technology and in part by the Hong Kong Research Grant Council. D. Huang was with the Center for Wireless Information Technology, Electrical and Electronic Engineering Department, Hong Kong University of Science and Technology, Kowloon 190, Hong Kong. He is now with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected]). K. B. Letaief is with the Center for Wireless Information Technology, Electrical and Electronic Engineering Department, Hong Kong University of Science and Technology, Kowloon 190, Hong Kong (e-mail:
[email protected]). J. Lu is with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected]). Digital Object Identifier 10.1109/TCOMM.2005.851561
broadband channels. However, by employing the frequency-domain characteristics alone, it cannot be justified that the diversity order is high enough for some channel profiles, even when an ideal interleaver is employed. For example, in [8], it was shown that the maximum diversity order that an OFDM system can achieve by exploiting the frequency-domain characteristics alone is the number of distinct paths in the channel. To improve the diversity order, multiple transmit and/or multiple receive (MIMO) antennas have been proposed for use in OFDM systems to achieve space diversity [8], [9]. Besides the frequency and space diversity, time diversity induced by the time-varying characteristics of wireless channels can also be exploited using coding and interleaving [10]. It was shown in [11] that time diversity can be achieved by code-division multiple-access (CDMA) systems using an enhanced Rake receiver. The time-varying characteristics of wireless channels induce the loss of orthogonality among subcarriers in OFDM systems. This results in intercarrier interference (ICI), and is considered harmful [2] to system performance. On the other hand, the time diversity inherent in the channel is beneficial to system performance. As a result, if we can propose a way to make use of the time diversity and reduce the impact of ICI as well, system performance will be improved significantly. For uncoded OFDM systems, it was shown in [12] that the time diversity could be achieved through the use of equalization in the time domain. However, to the best of our knowledge, no previous work considered the time diversity achieved by coded OFDM systems. In this paper, we propose a bit-interleaved time-frequency coded modulation (BITFCM) scheme for OFDM systems. The proposed scheme can exploit both the time-varying and frequency-varying nature of the channels, thus resulting in high diversity order and good performance. Compared with the BICM scheme in [7], where only frequency diversity is exploited, the proposed BITFCM scheme can achieve much better performance, especially over a channel with only a small number of distinct paths. The decoding delay of the proposed scheme is a little higher than that in [7]. However, this is not a critical issue, especially for wireless data communications or broadcasting systems. The proposed scheme can also be easily combined with MIMO antennas to achieve even better performance. In this paper, we assume that the time-varying channels are completely known, and a coherent modulation scheme such as quadrature amplitude modulation (QAM) or multiple phase-shift keying (MPSK) is used. In this case, the optimal decoding approach to the BITFCM scheme based on the maximum-likelihood (ML) decoding criterion should jointly
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consider the modulation constellation, channel state information (CSI), and the coding trellis. This results in a huge state space, which makes the system implementation infeasible. To deal with the complexity issue, for a specific subcarrier, we take the signals from other subcarriers as interference. We will show that the ICI can be neglected when the maximum normalized Doppler frequency is low. As a result, a reduced-complexity ML decoding scheme can be used. Using the reduced-complexity ML scheme, the channels can be regarded as quasi-static, thus, reducing the complexity of channel estimations. When the maximum normalized Doppler frequency is high, the ICI can be so prominent that an error floor at the bit-error rate (BER) values of practical interest is induced. As a result, the performance is much worse than that with relatively lower maximum normalized Doppler frequency. To solve this problem, equalization schemes [12]–[14] are typically employed. In such equalization schemes, the inverse of a large matrix is required, and this results in huge complexity. Furthermore, the performance is not necessarily good, due to the noise enhancement. In this paper, given the channel second-order statistics, a linear ICI mitigation scheme based on the minimum mean-square error (MMSE) criterion is investigated. It is then shown that such a scheme can improve the signal-to-interference power ratio (SIR) to about 5 dB at an extremely high maximum normalized Doppler frequency. When the channel information is completely known, we propose an interference cancellation (IC) scheme to reduce the ICI. The proposed IC scheme works in an iterative fashion, where the decoded data in previous iterations is used to generate the interference so that it can be cancelled out. Simulation results show that the performance of the proposed IC scheme approaches that of the system where the interference is completely removed. After removing the interference using the proposed IC scheme, it is observed that the performance of the OFDM with BITFCM and a higher maximum normalized Doppler frequency is always better than that with a lower one. This paper is organized as follows. The system model is given in Section II. In Section III, the proposed BITFCM scheme is presented, along with the reduced-complexity ML decoding. The ICI analysis and the ICI-mitigation scheme based upon the linear MMSE combining are discussed in Section IV. The IC scheme using perfect channel information is presented in Section V. Finally, simulation results and concluding remarks are presented in Sections VI and VII, respectively.
assuming perfect time synchronization, the sampled received signal is as follows: (2) where , denotes the sampled time-varying CIR at the th sample of the duration of the th OFDM symbol, and is the additive white Gaussian noise (AWGN) term. After the discrete Fourier transform (DFT) processing, the signal in the frequency domain is given by
(3) where (4) (5) and
(6) Based upon (3), we can take the equivalent frequency-domain channel as a multiple-input multiple-output (MIMO) , and output , system with input . Then, we define the equivalent frequency-dowith . From main channel matrix by (5) and (6), we have (7) where ation
in the superscript denotes conjugate transpose oper(8)
and we have (9), shown at the bottom of the next page. For convenience, we define the following vectors:
II. OFDM SYSTEM MODEL We consider an OFDM system with subcarriers. The information symbol at the th subcarrier of the th OFDM symbol . After inverse discrete Fourier transform is denoted by (IDFT) processing and guard-interval insertion, the signal is given by (1) is the length of the guard interval. We assume that the where length of the channel impulse response (CIR), denoted by , is . After guard-interval removal at the receiver and less than
where in the superscript denotes transpose. We can then write (3) into a vector form as follows: (10) III. BIT-INTERLEAVED TIME-FREQUENCY CODED MODULATION FOR OFDM A. BITFCM The proposed BITFCM scheme for OFDM systems is as shown in Fig. 1. The coding scheme can be any binary code.
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Fig. 1.
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BITFCM for OFDM systems.
Suppose that a codeword is transmitted, where is a coding scheme defined over the binary label alphabet {0,1}. Without loss of generality, the codeword is assumed to be transmitted over consecutive OFDM symbols. The constellation set used is assumed to be the same for all the subcarriers, which is denoted by with size . Then, each information symbol carries coded bits, and the length of the codeword is in bits. After ideal random interleaving, the bits in the codeword can be denoted by (11) where is the coded bit at the th label of the th subcarrier , at the th OFDM symbol. After mapping, the coded bits are converted into the information symbol at the th subcarrier of the th OFDM symbol. The codeword is then OFDM symbols, which are denoted by the converted into . At the receiver, the received vector codeword after DFT processing is given by
(12) where ..
from to is one-to-one, we can use the following metric for the optimal ML receiver: (16) is the norm of . where Using the above optimal ML decoder, both time- and frequency-domain diversity can be achieved. For the ML decoding, we should form a trellis considering both the coding scheme and the channel. However, the number of states in the trellis is huge. relates to , for a coding Since scheme with code rate , the size of the state space induced by . For example, given the channel alone is on the order of (quaternary phase-shift keying (QPSK) modulation), that and , the size of the state space induced by the , which is infeasible to be channel is then on the order of implemented. To deal with this issue, Part B of this section will present a reduced-complexity ML scheme, which is effective for low maximum normalized Doppler frequency values (i.e., , where is the maximum Doppler frequency, and is the duration of one OFDM symbol). For high maximum normalized Doppler frequency values, schemes to mitigate ICI are presented in Sections IV and V.
(13)
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B. Reduced-Complexity ML Decoding (14) The optimal ML decision about the transmitted codeword is made according to the following rule: (15) where tioned on
and
When the maximum normalized Doppler frequency is small, as will be shown from the ICI analysis in Section IV, the nondiagonal elements of the equivalent frequency-domain channel matrix are small. As a result, from (16), the following metric can be used for decoding:
is the probability density function of condi. Since the mapping and interleaving process
(17)
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
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For the BITFCM scheme, the metric can be calculated bit by denote the subset of all the information symbols bit. Let . According to [4], whose th bit label has the value we can then use the following reduced-complexity metric: (18) where
When the maximum Doppler frequency is large, the SIR is low, and this can induce an error floor to system performance. To solve this problem, we can reduce the length of the OFDM symbol, which results in a low maximum normalized Doppler frequency value and ICI reduction. However, the ratio of the guard interval to the OFDM symbol duration is increased, and this results in low spectrum efficiency. Another option is to use the ICI-mitigation schemes presented in Sections IV and V. IV. ICI ANALYSIS AND ICI MITIGATION USING LINEAR MMSE COMBINING
(19) is the metric for the th bit at the th subcarrier of the th OFDM symbol. Compared with (15) or (16), the metric given by (18) and (19) is obviously suboptimal. However, by using (18) and (19), the complexity of the decoder is significantly reduced. The trellis used at the receiver is exactly the same as that in the coding scheme, and a conventional Viterbi decoder can be used following the bit metric calculation. Using (18) and (19) for metric calculation, the second term in (3) is actually considered as ICI. When the ICI is perfectly removed, for convenience, we denote the minimum required by for a specific quality of service (QoS) requirement (measured by BER). In an environment with ICI, the minimum to achieve the required QoS is then given by required
In this section, we analyze the ICI (induced by the timevarying channel) power of the OFDM system and propose an ICI-mitigation scheme using linear MMSE combining. In practical OFDM systems, the number of subcarriers is normally large. As a result, the ICI can be considered as Gaussian distributed and its power is determined by the variance [1], [12], [15]. To elaborate on the ICI analysis, we rewrite (12) into the following form: (22) where denotes a diagonal matrix with the main diagis matrix with the main onal elements given by , and diagonal elements set to zeros. The second term of the above equation is then the ICI, and its power is given by
(20) SIR where is the data transmission rate, is the bandwidth used ( is the spectrum efficiency of the system), and SIR is the signal-to-interference power ratio due to ICI. From (20), it can be seen that ICI can be neglected as long as SIR
(21)
To satisfy the above requirement, we can adjust , the spectrum efficiency, and/or the SIR. In wireless communications, the QoS requirement is relatively fixed. For example, the BER value at the output of the inner decoder is normally required to be about for data transmission. When the spectrum efficiency and QoS requirements are fixed, we can adopt a coding scheme to to satisfy (21). One way to achieve this is through reduce the use of a coding scheme that exploits the frequency, time, and/or space diversity. In [7], the frequency-domain diversity is achieved through the use of BICM in the frequency domain. As can be a result, over a channel rich in frequency diversity, easily reduced to as low as 20 dB for most practical OFDM systems. However, it was shown in [8] that the maximum diversity order achieved in the frequency domain alone is . Hence, we can expect that the BICM scheme in [7] can achieve good performance only when the number of distinct paths in the channel is large. When the channel lacks frequency diversity, we can use our proposed BITFCM scheme to achieve time diversity and reduce the required , and this results in superior performance. We note here that the proposed BITFCM scheme can also be used with MIMO antennas to achieve high diversity order and reduce the required .
(23) where is the average with respect to the random variables is the average with respect to the random variin and , is the average energy of the information symbols, ables in , and is the trace of the matrix in . In the above equaand tion, we assume that the random variables in the matrix , those in vector are independent, and where is the identity matrix. From (23) and after some manipulations, we can conclude that the power of the ICI is given by (24) where is the autocorrelation function of the th multipath component. For the classic Doppler frequency spectrum [1], the numerical results of the SIR are shown in Fig. 2. It can be seen that the SIR only depends on the maximum normalized Doppler frequency , and does not depend on the number of subcarriers in an values (less than 0.06), the SIR OFDM symbol. For small is more than 20 dB. As a result, (21) can be satisfied for most applications, and the impact of ICI on system performance can is large, the SIR can be very low (for be negligible. When
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is as be significantly improved. For example, even when large as 0.5, the SIR is still more than 5 dB. In Fig. 2, we also give the simulation results of an OFDM system with 64 subcarriers under the equal-gain two-ray Rayleigh fading channel. It can be seen that the numerical results coincide with the simulation results. V. INTERFERENCE CANCELLATION SCHEME When the channel information is perfectly known at the receiver, an IC scheme as shown in Fig. 3 can be employed. The proposed scheme works in an iterative way, and the reducedcomplexity ML decoding is employed in each iteration. After deinterleaving, the data are tentatively decoded by the Viterbi decoder. The interference is then produced and cancelled out using the following equation: (30) Fig. 2. SIR performance over time-varying channels with classic Doppler frequency spectrum. Solid lines denote the SIR performance with linear MMSE combining for ICI mitigation. Dotted lines denote the SIR performance without 64, 256, and 1024. ICI mitigation.
N=
example, it is less than 0 dB when is greater than 0.7) and the ICI cannot be neglected. In the following, we assume that the second-order channel-statistics information is available. We then propose an ICI-mitigation scheme using linear MMSE combining to improve the SIR. The received signals after DFT processing are linearly combined as follows:
is an estimation of using the tentatively decoded where , data in the previous iteration. Then in (19) are replaced by , and the bit metric1 is calculated accordingly. This process can proceed in an iterative fashion until a good performance is achieved. In the is known for the calculation of and the ideal scenario, interference is perfectly cancelled out. Using (22) and (30), the residual interference power is given by
(25) where the coefficients , based on the following MMSE criterion:
are obtained (26) (31)
where is the average of . After some manipulations, the weighting coefficients are obtained as follows: (27)
Assume that the symbol-error rate (SER) is in the previous iteration and the symbol errors are independent and identically distributed. Then, we have (32)
where
is the variance of the AWGN, and
where is a constant and satisfies for MPSK modulation. As a result, (31) is reduced to the following: (28) (33)
The MMSE (i.e., the ICI power after the linear MMSE combining) is then given by
MMSE
(29)
For the classic Doppler frequency spectrum, the numerical results of the SIR performance using the linear MMSE combining scheme is shown in Fig. 2. It can be seen that when the maximum normalized Doppler frequency is large, the SIR can
for MPSK modulation. For example, when the SER is in the previous iteration, the interference power is then less than 4% of that in the first iteration, which represents a huge reduction. Even though the above analysis is not rigorous, it still shows that the proposed IC scheme can significantly improve system performance. This is further justified by the simulation results in the next section. 1In the first iteration, we use the received signals bit metric (i.e., the exact form of (19) is used).
Y in (12) to calculate the
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Fig. 3. IC for OFDM systems with BITFCM.
Fig. 4. BER performance of the proposed scheme with 16 QAM over two-ray equal-gain Rayleigh fading channels (10 OFDM symbols in a frame).
VI. SIMULATION RESULTS In this section, we investigate the BER performance of an OFDM system with BITFCM. For the BITFCM scheme, we use the convolutional code as the binary code with code rate-1/2 and generators (133, 171) in octal. In the simulations, the OFDM symbols are grouped into frames with coding and random bit interleaving across the whole frame. In each OFDM symbol, there are 64 subcarriers. Furthermore, QAM modulation is used with Gray mapping. Throughout this section, the channel used is an equal-gain Rayleigh fading channel. The bandwidth of the channel is 500 kHz, and the carrier frequency is 1 GHz, as is the case in [14]. A. BER Performance Versus Maximum Normalized Doppler Frequency In this part, we simulate the proposed OFDM system with BITFCM for different maximum normalized Doppler frequencies. In the OFDM system, each frame consists of 10 OFDM symbols. In addition, a two-ray equal-gain Rayleigh fading channel model is used and assumed to be known. The BER performance of the proposed OFDM system with 16 QAM and 64 QAM is as shown in Figs. 4 and 5, respectively. For 16 QAM and using the reduced-complexity ML decoding scheme, it can be observed that the BER performance becomes better along with the increase of the maximum normalized Doppler , the performance frequency. For example, at a BER of
Fig. 5. BER performance of the proposed scheme with 64 QAM over two-ray equal-gain Rayleigh fading channels (10 OFDM symbols in a frame).
is improved by about 5 dB when the maximum normalized to .A Doppler frequency is increased from similar trend can be observed for 64 QAM when the maximum normalized Doppler frequency is below . When the maximum normalized Doppler frequency is , for 64 QAM, an error floor appears and the performance is very poor. When the ideal IC scheme (i.e., the ICI is completely known and cancelled out in the first iteration) is used and the maximum normalized Doppler frequency is , Fig. 4 shows that the performance can be improved by about 2 dB at for 16 QAM. For 64 QAM, a close observation a BER of from Fig. 5 shows that the IC scheme can be used to remove the error floor and significantly improve system performance. B. BER Performance Versus the Number of Distinct Paths in the Channel In this part, we model the frequency-domain diversity order of the channel by the number of distinct paths in the CIR. In our simulations, 10 OFDM symbols are grouped into a frame. The reduced-complexity ML decoding scheme is employed. Fig. 6 shows the BER performance of the OFDM systems with BITFCM and 16 QAM for 2, 4, and 8. As expected, along with the increase of the number of distinct paths in the channel, the BER performance is improved significantly. On the other hand, when the maximum normalized Doppler frequency is increased from to , the BER
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of OFDM symbols in a frame is presented.2 The modulation scheme is 16 QAM, and the maximum normalized Doppler fre. The decoding scheme used is the requency is duced-complexity ML decoding. Furthermore, a two-ray equalgain Rayleigh fading channel is employed. It can be seen that when there is only one OFDM symbol in a frame, an error floor . A close observation of the appears at the BER of about slopes of the BER curves shows that the diversity order is improved along with the increase of the number of OFDM symbols in a frame. By increasing the number of OFDM symbols per frame from 16 to 24, the performance improvement is within 1 dB at a BER of . On the other hand, the performance improvement is 4 dB when the number of OFDM symbols per frame is increased from 1 to 16. D. BER Performance With Channel Estimation Using Linear Interpolation Fig. 6. BER performance of the proposed scheme with 16 QAM over equal-gain Rayleigh fading channels (10 OFDM symbols in a frame).
Fig. 7. BER performance of the proposed scheme versus the number of OFDM symbols in a frame over two-ray equal-gain Rayleigh fading channels (16 QAM and a maximum normalized Doppler frequency of 2:6 10 ).
2
performance becomes better for all channels. However, when the frequency-domain diversity order is high, the performance improvement contributed by time diversity is not significant. For example, it is within 1 dB at a BER of for an eight-ray equal-gain Rayleigh fading channel. In contrast, when the frequency-domain diversity is low , the improvement is about 4 dB. C. BER Performance Versus Number of OFDM Symbols in a Frame To make the channels at adjacent subcarriers independent, the interleaving depth should be as large as possible. In Fig. 7, the BER performance of the proposed scheme versus the number
When the maximum normalized Doppler frequency is small, the reduced-complexity ML decoding scheme can be used. In this case, only the diagonal elements of the equivalent frequency-domain channel matrix are required. As a result, we can obtain all the CSI first and only use the diagonal elements of the equivalent frequency-domain channel matrix. On the other hand, the channels can also be regarded as quasi-static. That is, the channel is deemed to be constant within the period of one OFDM symbol, but may vary from symbol to symbol. Therefore, the equivalent frequency-domain channel matrix is diagonal. Obviously, this is an approximation to the real case. However, by doing so, the task of channel estimation can be significantly reduced. By exploiting the correlation in the time domain, extensive research (e.g., see [16], [17], and references therein) has been devoted to the quasi-static channel estimation for OFDM systems. When the maximum normalized Doppler frequency is large, the ICI cannot be neglected. To mitigate the effects of ICI, the linear MMSE combining scheme proposed in Section IV can be employed. However, this scheme can only work well for a system with low spectrum efficiency, due to the low SIR. For a system with high spectrum efficiency, the IC scheme in Section V should be used. In this case, the channels cannot be considered quasi-static.3 To obtain the time-varying channel information, several approaches (e.g., [12]–[14], [18], [19]) have been proposed. For example, in [19], it is shown that the channel can be predicted several milliseconds ahead using training symbols. In [18], a basis expansion channel model is used to achieve the time-varying channel-estimation task. Time correlations can also be employed to directly estimate the time-varying channel coefficients. In [12], the received time-domain training signals are used to estimate the channels 2In an ideal scenario, the interleaving is across a frame with an infinite number of OFDM symbols. The adjacent subcarriers can then be assumed independent. In this case, given that the ICI is completely removed, the performance is the same as that in a flat-fading channel. The analysis of the BICM scheme in a flat-fading channel can be found in [4]. 3We note here that when the channel is rich in frequency diversity (i.e., the number of distinct paths is large), the required is usually low, and the channel can be considered quasi-static. Only when the number of distinct paths is small, the IC scheme proposed in Section V should be used and the complete timevarying channels are required to be known. In this case, the freedom in the frequency domain is relatively low, and this eases the issue of channel estimation.
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Fig. 9. BER performance of the linear MMSE combining scheme over two-ray equal-gain Rayleigh fading channels (QPSK modulation is used).
same performance as that with ideal channel information. When the maximum normalized Doppler frequency is 0.051, the BER values. For very high performance degrades only at high is equal to 0.1), maximum normalized Doppler frequency ( an error floor appears. From Fig. 8(b), it can also be seen that for the IC scheme, one iteration is good enough. When the CSI is obtained by linear interpolations, the error floor is reduced by an order of magnitude using the IC scheme. Compared with that using ideal channel information, Fig. 8(b) shows that the performance degradation is still significant. As a result, more advanced channel-estimation schemes should be employed to further improve system performance. E. BER Performance With Linear MMSE Combining Fig. 8. BER performance of the proposed scheme over two-ray equal-gain Rayleigh fading channels. (Solid lines denote the performance with ideal channel information, and dotted lines denote the performance with the channel information obtained by linear interpolation). (a) Reduced-complexity ML decoding. (b) IC scheme.
based upon the MMSE criterion. In [14], CSI at the positions of the pilot symbols is first obtained. Then, the CSI at the positions of the data sequences is obtained by linear interpolation. In the following, we demonstrate the BER performance of the proposed scheme with CSI obtained by linear interpolation. Training sequences are assumed to be multiplexed before and after each OFDM symbol. For simplicity, we assume that CSI obtained at the training position is perfect.4 Between the training sequences, the CSI is obtained by linear interpolation, as proposed in [14]. The modulation constellation is 64 QAM and the two-ray equal-gain Rayleigh fading channel is used. From Fig. 8(a), it can be seen that for a low maximum normalized Doppler frequency value ( is less than or equal to 0.026), the performance of the reduced-complexity ML decoding scheme with CSI obtained by linear interpolation has the 4A simple way to achieve reasonably good channel estimation is to boost the power of the training sequences.
In this part, we use Fig. 9 to demonstrate the BER performance of an OFDM system with the aid of linear MMSE combining. In the OFDM system, 10 OFDM symbols consist of one frame, and QPSK modulation is used. Furthermore, a two-ray equal-gain Rayleigh fading channel model is used with the classic Doppler frequency spectrum. We use (18) and replaced by the output of the (19) for decoding with . For simplicity, we assume that linear MMSE combiner in (19) is known. It can be seen that BER performance can be improved by the linear MMSE combiner for all of the values shown in Fig. 9. VII. CONCLUSION In this paper, we have investigated a bit-interleaved timefrequency coded OFDM system, where the time diversity inherent in the time-varying channel can be achieved. Using the proposed scheme, system performance can be significantly improved along with the increase of the maximum normalized Doppler frequency. For a low maximum normalized Doppler frequency value, it was shown that the reduced-complexity ML decoding scheme can be employed. In contrast, for a high maximum normalized Doppler frequency value, the ICI can
HUANG et al.: BIT-INTERLEAVED TIME-FREQUENCY CODED MODULATION FOR OFDM SYSTEMS
be significantly large, and an error floor appears for the BER performance of practical interest. To solve this problem, we proposed two ICI-mitigation schemes. When the second-order statistics of the channel are known, a linear MMSE combining scheme was shown to be effective for extremely high maximum normalized Doppler frequency. When the channel information is completely known, an IC scheme was proposed to significantly improve system performance.
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Defeng (David) Huang (M’01–S’02–M’05) received the B. E. E. E. and M. E. E. E. degrees in electronic engineering from Tsinghua University, Beijing, China, in 1996 and 1999, respectively, and the Ph.D. degree in electrical and electronic engineering from the Hong Kong University of Science and Technology (HKUST), Kowloon, Hong Kong, in 2004. From 1998 to 2001, he was an Assistant Teacher and later a Lecturer with Tsinghua University. Currently, he is with the Department of Electronic Engineering, Tsinghua University. His research interests include wireless communications, OFDM, multiple-access protocol, space–time processing, channel estimation, and digital implementation of communication systems. Dr. Huang received the Hong Kong Telecom Institute of Information Technology Postgraduate Excellence Scholarship in 2004. Khaled Ben Letaief (S’85–M’86–SM’97–F’03) received the B.S. degree with distinction in 1984, and the M.S. and Ph.D. degrees in 1986 and 1990, respectively, all in electrical engineering, from Purdue University, West Lafayette, IN. From January 1985 and as a Graduate Instructor in the School of Electrical Engineering at Purdue University, he taught courses in communications and electronics. From 1990 to 1993, he was a Faculty Member with the University of Melbourne, Melbourne, Australia. Since 1993, he has been with the Hong Kong University of Science and Technology, Kowloon, where he is currently Professor and Head of the Electrical and Electronic Engineering Department. He is also the Director of the Hong Kong Telecom Institute of Information Technology, as well as the Director of the Center for Wireless Information Technology. His current research interests include wireless and mobile networks, broadband wireless access, OFDM, CDMA, and Beyond 3G systems. In these areas, he has published over 270 journal and conference papers and given invited talks as well as courses all over the world. He has served as consultant for different organizations, as well. Dr. Letaief is the founding Editor-in-Chief of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. He has served on the editorial board of other prestigious journals, including the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS—WIRELESS SERIES (as Editor-in-Chief) and the IEEE TRANSACTIONS ON COMMUNICATIONS. He has been involved in organizing a number of major international conferences and events. These include serving as the Technical Program Chair of the 1998 IEEE Globecom Mini-Conference on Communications Theory, as well as the Co-Chair of the 2001 IEEE ICC Communications Theory Symposium. In 2004, he served as the Co-Chair of the IEEE Wireless Communications, Networks and Systems Symposium, as well as the Co-Technical Program Chair of the 2004 IEEE International Conference on Communications, Circuits and Systems. He served as the Chair of the IEEE Communications Society Technical Committee on Personal Communications, and is a member of the IEEE ComSoc Technical Activity Council. He received the Mangoon Teaching Award from Purdue University in 1990; the Teaching Excellence Appreciation Award from the School of Engineering at HKUST (four times); and the Michael G. Gale Medal for Distinguished Teaching (highest university-wide teaching award and only one recipient/year is honored for his/her contributions). He is an IEEE Distinguished Lecturer of the IEEE Communications Society. Jianhua Lu received the B.S.E.E. and M.S.E.E. degrees from Tsinghua University, Beijing, China, in 1986 and 1989, respectively, and the Ph.D. degree in electrical and electronic engineering from the Hong Kong University of Science and Technology, Kowloon. Since 1989, he has been with the Department of Electronic Engineering, Tsinghua University, where he now serves as a Professor. His current research interests include broadband wireless communication, multimedia signal processing, satellite communication, and wireless networking. He has published more than 100 technical papers in international journals and conference proceedings. Dr. Lu has been an active member of professional societies, and he served as the Panel/Invited Session Chair of the 2003 IEEE International Symposium on Personal, Indoor, and Mobile Communications. He also delivered a keynote speech on Wireless Multimedia Communications at the CCF Young Computer Scientists and Engineers Forum (YOCSEF) of China. He is a Member of the IEEE Communication and Signal Processing Societies.
