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A Low Complexity Frequency Domain Equalization for EDGE P. Dinakar
R. David Koilpillai
Department of Electrical Engineering Indian Institute of Technology Madras Chennai, India
Department of Electrical Engineering Indian Institute of Technology Madras Chennai, India
[email protected]
[email protected]
Abstract In this paper, a new low-complexity frequency-domain based technique is proposed for channel equalization and symbol detection of an Enhanced Data Rate for GSM (EDGE) cellular system, which uses 8-PSK modulation. The proposed method exploits the guard interval and tail symbols present in the EDGE slot structure and uses the tail symbols as partial Cyclic Prefix in the frequency domain equalizer. The effect of the missing cyclic prefix is diminished by iterative reconstruction of the complete cyclic prefix. In the developed framework, the advantages of over-sampling and diversity reception are explored to improve the system performance with a minimal additional complexity. The performance of the proposed system is demonstrated by computer simulations. Also, the performance gain by exploiting over-sampling and receiver diversity is presented.
1. Introduction EDGE (Enhanced Data rate for GSM Evolution) is one of the third generation (3G) wireless communication standards which enables a smooth evolution beyond GSM (2G). This transition from GSM to EDGE is achieved by retaining the spectral characteristics of GSM specifications [1]. EDGE has a time frame and burst structure almost identical to that of GSM, but can achieve significantly higher data rates because it provides 8-PSK modulation. The widely used MLSE equalizer is postulated as a suitable technique for GSM which uses a binary GMSK modulation scheme. However in EDGE, the introduction of 8-PSK will require the MLSE trellis to have 8L states, where L is the channel memory which can be as high as 6, which is computationally complex [2] [3]. To limit the computational complexity, some alternative methods are proposed in the literature, the Reduced-State Sequence Estimation (RSSE) [4] and the Delayed-Decision Feedback Sequence Estimation (DDFSE) [3] which provides a good tradeoff between performance and computational complexity. In this paper, a new, low-complexity frequencydomain based receiver for EDGE is proposed. The
proposed technique exploits the burst structure and the presence of tail symbols as specified in the standard [5]. Then, the performance of the proposed receiver is presented. The paper also presents two techniques namely fractionally-spaced equalizer and diversity reception which further enhance the receive performance. This paper is organized as follows. In Section II, the system model under consideration and the EDGE TDMA slot structure is introduced. The proposed algorithm along with the performance enhancement possibilities are discussed in Section III. Section IV presents the simulation results which demonstrate the system performance. Finally, Section V draws the conclusion and possible future extensions.
2. System Model The block diagram of the Transmitter-Channel-Receiver chain is shown in Fig 1. In the transmitter, the coded data bits are inserted into the EDGE burst (Time Slot - Fig. 2) along with the training sequence and tail bits[5][7]. This block of bits are 8-PSK modulated (3 bits/symbol), upsampled and filtered through the transmit filter. Here, the
Figure 1: System Model transmit filter has a partial response pulse shaping which spans for three symbols. The signal generated out of the
transmitter is passed to a channel which has multipath and Rayleigh fading. Then noise is added to the channel filtered signal. The noisy-channel distorted signal is fed to the receive chain which performs the symbol detection.
In cyclic prefix reconstruction procedure, the missing CP is treated as time-domain distortion and frequencydomain equalization is applied as if it has sufficient CP. Once the block is equalized followed by symbol detection, the detected symbols are treated as the recreated CP and its convolution effect is reflected on the received samples as given in equation (1). When L ≤ 3,
Figure 2: EDGE Burst (Time Slot) Structure
yCP [n] = yr [n] When L > 3,
3. Proposed Receiver Algorithm In the new receiver architecture proposed here, in recovery of the transmitted information, is done by utilizing the lower complexity of frequency domain equalizer (FDE). Generally, to employ the FDE, the presence of a cyclic prefix in the transmitted burst is needed[8][9]. The proposed receiver utilizes the tail symbols as a partial cyclic prefix. As described in the standard specifications [5], the tail symbols of the EDGE burst is given in Fig. 3 and it is evident that the tail symbols can be treated as cyclic prefix of length 3.
yCP [n] = yr [n]+
L X
c∗ (l)xd [n+N −1][1−u[n−l+3]]
l=4
(1) where c[l] is the channel impulse response and u[n] is unit step function defined as 0 for n < 0 and 1 for n >= 0. After inducing the convolution effect of the recreated CP, the FDE is again applied on received symbols. This is iteratively done and hence the missing CP can be reconstructed. 3.1. Fractionally-Spaced FDE On the developed platform, the benefit of over-sampling is explored. In the literature[12], it has been shown that, frequency domain equalization along with oversampling (Fractionally-Spaced Equalization) can achieve better performance when compared with a symbolspaced equalizer.
Figure 3: Tail Symbols as specified in standards Using the tail symbols as cyclic prefix, the received EDGE burst can be equalized by frequency domain equalization without any modification. Here, the preceeding tail symbols are discarded and only a block of 145 (Data(58)+Training Sequence(26)+Data(58)+Tail(3)) samples are passed on to the FDE. Here-after we refer the block length (145) as N. In the equalization process, if the channel memory is longer than 3, the cyclic prefix is insufficient and FDE will yield sub-optimal performance. In such scenario, the missing cyclic prefix can be constructed by ”Cyclic Prefix Reconstruction” technique [10]. Here, the presence of the guard interval introduces zero (or very low) inter-block interference which is exploited in the reconstruction.
Figure 4: FDE along with Cyclic Prefix Reconstruction
Figure 5: Fractionally-Spaced (2X) Frequency-Domain Equalizer In our development, over-sampling factor of 2 (i.e., 2 samples per symbol) is considered. Here, after the receive filter, the baseband signal are passed at 2x rate to the equalizer. For 2x case [12], the Λe,0 and Λe,1 represents the equalizer coefficients as shown in Fig. 5 and are defined as Λe,0
= [E[0] E[1] · · · E[N − 1]]T
Λe,1
= [E[N ] E[N + 1] · · · E[2N − 1]]T
Let vk = [E ∗ [k] E ∗ [k + N ]]T , where k = 0, · · · , N − 1. The equalizer co-efficient can be computed using equation (2) 2R−1 ck (2) vk = H k−1 c k Rk c k Where, Rk ck
= ε[qk qH k ] = [C[k] C[k + N ]]T
In this receiver structure, when the number of receiver antennas increases, the probability that the equalizer sees a null in given frequency bin decreases [11] and hence the zero-forcing based FDE will perform comparably to a MMSE-based FDE. So, the zero-forcing based FDE can be adopted for receive diversity to further reduce the computational complexity at a negligible performance degradation.
4. Simulation Results
in which C[k] represents the discrete Fourier transform of the estimated channel. Rk represents the correlation matrix of qk , where qk is the Fourier transform of the input noise. 3.2. Receive Diversity When the receiver has more than one receive antenna, the performance of the Equalizer can further be improved and it can efficiently combat the effects of the Rayleigh fading channel. Receiver antenna diversity can be easily incorporated into the proposed FDE based receiver with a lower complexity overhead as compared to timedomain equalizer based receivers [11]. Figure (6), shows the receiver structure with antenna diversity along with frequency domain equalization.
In this section we show the performance of the proposed algorithm presented in Section III. In the simulations, the transmit filter is a Gaussian as defined in GSM and introduces ISI of three symbols. In the channel model, each ray is assumed to undergo Rayleigh fading independent of other rays. On the channel filtered signal, additive white Gaussian noise (AWGN) is added. The amount of noise added is determined by the desired Eb/No ratio. In Fig. 7, the bit error rate performance of the FDE along with cyclic prefix reconstruction algorithm is demonstrated. Here, the BER performance with no CP, only tail symbols (Insufficient CP) and reconstructed CP with single iteration are compared with ideal CP case. In this simulation, a 6-tap symbols spaced exponentially decaying channel is used and the FDE coefficients are computed based on MMSE criterion. For shorter channels, the tail symbols alone will operate as the required CP, which enables us to ”turn off” the CP reconstruction process for such cases resulting in further complexity reduction. 0
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Figure 6: FDE with Receive Diversity Here the Fourier transformed receive signal after equalization Yeq [k] is given by H Yeq [k] = ED,ZF [k]Yr,in [k]
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Ideal Cyclic Prefix No Cyclic Prefix Partial CP (Tail Symbols) CP−Reconstructed
(3)
where
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Eb/No (dB)
Yr,in [k] = [Yr,1 [k] Yr,2 [k] · · · Yr,M [k]]T and the zero-forcing based equalizer coefficients are given by ED,ZF [k] =
[C1,D [k] C2,D [k] · · · CM,D [k]]T PM 2 i=1 |Ci,D [k]|
(4)
where Ci,D is the Fourier transform of the channel seen by the ith receive path and k = 0, · · · , N − 1. Here M donates the number of receive antennas.
Figure 7: BER performance with No, Partial and Reconstructed Cyclic Prefix when compared to ideal CP case In Fig. 8, the performance gain of 2x oversampling and having a fractionally-spaced FDE equalizer is demonstrated. Here, a zero-forcing based FDE is used and the bit error rate performance of symbolsspaced FDE is compared with fractionally-spaced FDE. The performance of adopting receive diversity is demon-
strated in Fig. 9. The plot compares the performance of 1Rx case (both Zero-forcing and MMSE based) with 2 Rx case (Zero-forcing based). The simulation to demon0
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6. References [1] A. Furuskar, S. Mazur, E Muller, and H. Olofsson, ”EDGE: Enhanced Data Rates for GSM and TDMA 136 Evolution,” IEEE Personal Communications, vo1.6, pp.56-66, June 1999.
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[2] Wolfgang H. Gerstacker, and Robert Schober, ”Equalization Concepts for EDGE”, IEEE Transactions on Wireless Communication, VOL. 1, NO. 1, January 2002
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[3] A. Duel-Hallen and C. Heegard, ”Delayed decisionfeedback sequence estimation,” IEEE Trans. Communication, Vol. 37, PP.428-436, May 1989.
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[4] V. M. Eyuboglu and S. U. Quereshi, ”Reduced-state sequence estimation with set partitioning and decision feedback,” IEEE Trans. Communication, Vol 36, pp. 1320, Jan 1988.
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Figure 8: Performance Comparison of Symbol-Spaced and Fractionally-Space FDE (Zero-Forcing based)
[5] ”GSM Recommendations : Modulation - TS 45.004 version 4.0.0,” Phase +2, Release 4, 3GPP [6] ”GSM Recommendations : Radio Transmission and Reception - TS 45.005 version 4.0.0,” Phase +2, Release 4, 3GPP
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[7] ”GSM Recommendations : Multiplexing and multiple access on the radio path - TS 05.02 version 4.11.0,” Phase +2, 3GPP
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[8] D. Falconer, S.L. Ariyavisitdul, A. BenyaminSeeyar and B. Eidson. ”Frequency domain equalization for single-carrier broadband wireless systems”, IEEE Communication Magazine, vol. 40. pp. 58-66. Apr. 2002.
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1 Rx Ant. − ZF based FDE 2 Rx Ant. − ZF based FDE 1 Rx Ant. − MMSE based FDE
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Figure 9: BER performance of FDE with receive diversity
[9] H. Sari, G. Karam, and I. Jeanclaude, ”FrequencyDomain Equalization of Mobile Radio and Terrestrial Broadcast Channels”, Proceedings of GLOBECOM ’94, San Francisco, CA, pp. 1-5, Nov.-Dec. 1994.
strate the performance of fractionally-space equalizer and receive diversity uses ideal cyclic prefix where, the transmitter uses a cyclic prefix longer than the channel memory in place of guard interval.
[10] Y. Li, S. McLaughlin and D.G.M. Cruickshank, ”Bandwidth efficient single carrier systems with frequency domain equalization”, Electronics Letters, Vol 41, No 15, July 2005
5. Conclusion and Future Work
[11] H. Witschnig, G. Strasser, R. Weigel, A. Springer ”Antenna Diversity Techniques for a Single Carrier System with Frequency Domain Equalization - An Overview”
In this paper, we presented a lower-complexity frequency-domain equalizer based receiver for the EDGE standard. The performance gain by using over-sampling and receive diversity are also demonstrated through simulation. It is forced that these performance enhancement techniques have to be integrated with CP-reconstruction. Also, the algorithm should be extended to support fast time-varying channels (cases with high Doppler frequency).
[12] P. P. Vaidyanathan, and B. Vrcelj, ”Theory of fractionally spaced cyclic-prefix equalizers”, Proceedings of ICASSP 2002, vol.2, pp.1277-1280, 2002.
