IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 2, FEBRUARY 2008 677 Design of Cyclic Delay Diversity for Single Carrier Cyclic Prefix (SCCP) Transmissions with Block-Iterative GDFE (BI-GDFE) Receiver Ying-Chang Liang, Senior Member, IEEE, Wing Seng Leon, Member, IEEE, Yonghong Zeng, Senior Member, IEEE, and Changlong Xu, Senior Member, IEEE Abstract— Single carrier cyclic prefix (SCCP) modulation has been adopted as one of the physical layer air-interfaces for IEEE802.16 standards due to its less stringent requirement on peak-to-average power ratio (PAPR) than multicarrier modula- tion. As a single carrier transmission, however, the received SCCP blocks suffer from inter-symbol interference (ISI). The block iterative generalized decision feedback equalizer (BI-GDFE) is an effective interference cancellation scheme which generally shows performance improvement over linear equalizers. However, in order to achieve a significant gain, the channel must contain rich multipath components, and this may not necessarily be true in many systems. In this paper, we propose to apply cyclic delay diversity (CDD) to a SCCP system so that the possible performance improvement by using a BI-GDFE detector can be enhanced. The asymptotic performance of the proposed system is analyzed using random matrix results. We propose a scheme to determine the optimal delay parameter for CDD. Computer simulations have shown that by incorporating CDD into the transmitter and using a BI-GDFE receiver, the BER performance of the system can approach the MFB within several iterations for high SNR region. Index Terms— Cyclic delay diversity, single carrier cyclic prefix systems, iterative receiver, matched filter bound. I. I NTRODUCTION B ROADBAND wireless transmissions suffer from severe inter-symbol interference (ISI) due to time dispersion of the propagation channel. Multicarrier cyclic prefix (MCCP) modulation, such as orthogonal frequency division multiplex- ing (OFDM), is an effective technique to mitigate the ISI, by transforming a frequency selective channel into a set of fre- quency flat channels. However, MCCP modulation is inherent with high peak-to-average power ratio (PAPR), which requires stringent power amplifiers. Single carrier-cyclic prefix (SCCP) modulation is an alternative scheme to MCCP modulation, and it has been adopted by the IEEE 802.16 standards as one of the uplink physical layer air-interfaces [1]. From information theoretic point of view, OFDM is optimal in terms of capacity- achieving when water-filling based power control is applied. When equal power allocation scheme is used, OFDM and SCCP systems in fact yield the same amount of channel Manuscript received August 24, 2006; accepted October 23, 2006. The associate editor coordinating the review of this paper and approving it for publication was H. Jafarkhani. The authors are with the Institute for Infocomm Research, 21 Heng Mui Keng Terrace, Singapore 119613 (e-mail: {ycliang, wsleon, yhzeng, clxu}@i2r.a-star.edu.sg). Digital Object Identifier 10.1109/TWC.2008.060625. capacity. From receiver complexity point of view, OFDM is simple as the subchannels have been decoupled automatically, while SCCP in general needs more complicated receivers. On the other hand, SCCP systems offer several attractive qualities, such as having a more reasonable PAPR; furthermore, it has been shown that without using channel coding, a SCCP system may outperform an equivalent MCCP system [2]. This is due to the fact that there is inherent pre-coding across the transmission bandwidth. In fact, we may view SCCP as pre-coded OFDM where the pre-coding is performed by the discrete Fourier transform (DFT). More detailed comparisons for SCCP and OFDM can be found in [3], [5] and references therein. The ISI within SCCP blocks needs to be mitigated us- ing equalization. Although linear equalizers (zero-forcing equalizer and minimum mean-square-error equalizer) can be deployed, their performance is usually far away from the matched filter bound (MFB), which serves as the lowest bound for any type of receivers. To achieve a performance close to the MFB, maximum likelihood (ML) receiver is needed. ML detector however is generally impractical for implementation due to its exponential complexity with respect to the signal dimension and constellation size. Recently, the block-iterative generalized decision feedback equalizer (BI-GDFE) [6], [15] has been proposed which serves as one of the low-complexity, near-ML receivers specifically designed for systems with large signal dimensions. This equalizer is effective for combating multiple access interference (MAI) and inter-symbol inter- ference (ISI) for a variety of systems [15], [9]. The BI- GDFE iteratively performs interference cancellation on the received signal blocks, where the interferers are reconstructed using hard decisions from the previous iteration. Relying on a statistical reliability factor for each iteration, interference is reduced ultimately using successive iterations, and this improves the bit error rate (BER) performance of the system. It has been shown in [15] that the performance of the BI- GDFE can approach the matched filter bound (MFB) of a given system with several iterations if the channel contains rich multipath components. If the multipath components are not rich, however, it is difficult to exploit the potential of the BI-GDFE receivers in achieving the MFB. In this paper, transmit diversity techniques are used to enhance the frequency diversity of SCCP systems. While there exist different transmit diversity schemes, such as space-time 1536-1276/08$25.00 c  2008 IEEE