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86 CHAPTER 3 (a) Transmitter Frequency Carrier frequency Bandwidth (1+α) / T c (b) Power spectrum (c) Rake receiver c(t) Recovered data * Time-domain despreading Rake combining –τ L–1 –τ 0 * h L–1 SC-CDMA signal Received signal Time-domain spreading c(t) h 0 Data integrate & dump Data demodulation De-interleaving & channel decoding + Data modulation Chip shaping Channel coding & interleaving f c Figure 5. Transmitter/receiver structure for SC-CDMA with rake combining spread signal, resulting in the MC-CDMA signal. MC-CDMA with SF =1is OFDM. The GI insertion is necessary to avoid the orthogonality destruction among N c subcarriers due to the presence of multipaths with different time delays. The GI length needs to be larger than the maximum time delay difference among multipaths. At the receiver, after removing the GI, the received signal is decom- posed by N c -point FFT into N c subcarrier components. The distortion of the signal spectrum due to frequency-selective fading is compensated by using one-tap FDE. The equalized subcarrier components are parallel-to-serial (P/S) converted into the time-domain spread signal, followed by despreading as in SC-CDMA receiver. FDE can be jointly used with antenna diversity reception for further performance improvement in MC-CDMA. Among various FDE weights, it was shown that the use of minimum mean square error (MMSE) weight provides the best bit error rate (BER) performance. This is because the MMSE weight can provide the best compromise between the noise enhancement and suppression of frequency- selectivity. MC-CDMA with MMSE-FDE provides much better BER performance than SC-CDMA with coherent rake combining. Because of this, until recently, research attention was shifted from SC techniques to MC techniques such as MC- CDMA and OFDM SF =1. But, as will be shown in this chapter, FDE can FUNDAMENTALS OF SINGLE-CARRIER CDMA TECHNOLOGIES 87 (a) Transmitter (b) Power spectrum FrequencyCarrier frequency Bandwidth 1/T c Data Channel coding & interleaving Data modulation Insertion of GI #0 Time-domain spreading c(t) IFFTS/P Conversion to freq domain spread signal MC-CDMA signal (c) Receiver Frequency-domain equalization Removal of GI De-interleaving & channel decoding Data demodulation Recovered data P/S Time-domain despreading Received signal #N c –1 f c w(0) w(k) c(t) w(N c –1) Integrate & dump FFT Figure 6. Transmitter/receiver structure for MC-CDMA also be applied to SC-CDMA with much improved performance compared to rake combining. SC-CDMA is considered again as a promising access technique similar to MC-CDMA. 4. FREQUENCY-DOMAIN EQUALIZATION The application of MMSE-FDE to SC-CDMA can replace the coherent rake combining with much improved BER performance. First, FDE for SC-CDMA is shown. However, the residual inter-chip interference (ICI) is present after MMSE- FDE and this will limit the BER performance improvement. The ICI cancellation can be used to reduce the residual ICI and hence improve the BER performance. These are presented here. 4.1 MMSE Equalization Transmitter/receiver structure of multicode SC-CDMA with FDE is illustrated in Figure 7. We assume that C data streams are simultaneously transmitted. At the 88 CHAPTER 3 (b) Receiver Received data Data de-modulation Removal of GI Scramble code FFT AWGN w(0) w(k) w(N c –1) Frequency-domain equalization Integrate and dump Orthogonal spreading code Multicode despreading Insertion of GI Data Data modulation (a) Transmitter Scramble code Code-multiplexing Orthogonal spreading code Multicode spreading IFFT Figure 7. Multicode SC-CDMA transmitter/receiver structure transmitter, the uth binary data sequence is transformed into a data modulated symbol sequence {d u n; n = 0 ∼ N c /SF −1}, u = 0 ∼ C −1, and then spread by multiplying an orthogonal spreading sequence c u t with spreading factor SF. The resulting C chip sequences are added and further multiplied by a common scramble sequence c scr t to make the resulting multicode SC-CDMA chip sequence white-noise like. C is called code-multiplexing order. This is called multicode spreading. Then, the orthogonal multicode SC-CDMA chip sequence is divided into a sequence of blocks of N c chips each and then the last N g chips of each block are copied as a cyclic prefix and inserted into the GI placed at the beginning of each block as shown in Figure 8. The GI-inserted multicode SC-CDMA chip sequence GI SF chips SF chips • • • N c chipsN g chips Copy Figure 8. Block structure FUNDAMENTALS OF SINGLE-CARRIER CDMA TECHNOLOGIES 89 {ˆst t =−N g ∼N c −1} in a block can be expressed, using the equivalent lowpass representation, as (3) ˆst = 2E c T c st mod N c where E c and T c denote the chip energy and the chip duration, respectively, and st is given by (4) st = C−1 u=0 d u t/SF c u t mod SF c scr t for t =0 ∼N c −1, where c u t=c scr t=1 and x represents the largest integer smaller than or equal to x. The chip block {ˆst t =−N g ∼N c −1} is transmitted over a frequency-selective fading channel and received by a receiver. After the removal of the GI, the received chip sequence {rt;t =0 ∼N c −1} in a block is decomposed by N c -point FFT into N c subcarrier components {Rk; k =0 ∼ N c −1} (the terminology “subcarrier” is used for explanation purpose although subcarrier modulation is not used). The kth subcarrier component Rk can be written as (5) Rk = N c −1 t=0 rt exp −j2k t N c = 2E c T c HkSk +k where Sk, Hk and k are the kth subcarrier components of st, the channel gain and the noise component due to the additive white Gaussian noise (AWGN), respectively. Hk corresponds to Hf, t defined by Eq. (2), but with f =k/(N c T c ; time dependency of the channel gain is dropped since we are assuming very slow fading channel for simplicity. FDE is carried out similar to MC-CDMA. Rk is multiplied by the FDE weight wk as (6) ˆ Rk = wkRk = 2E c T c Sk ˆ Hk+ ˆ k where ˆ Hk = wkHk and ˆ k = wkk are the equivalent channel gain and the noise component after performing FDE, respectively. As the FDE weight, 90 CHAPTER 3 maximal ratio combining (MRC), zero forcing (ZF), equal gain combining (EGC) and minimum mean square error (MMSE) weights are considered. They are given by (7) wk = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ H ∗ k for MRC H ∗ k Hk 2 for ZF H ∗ k Hk for EGC H ∗ k Hk 2 + C SF E s N 0 −1 for MMSE where E s /N 0 (=E c SF/N 0 is the average received signal energy per data symbol-to- AWGN power spectrum density ratio and * denotes the complex conjugate operation. One-shot observation of the equivalent channel gain ˆ Hk and the noise ˆ k for MMSE, ZF and MRC weights are illustrated in Figure 9.AnL = 16-path fading channel is assumed. Also plotted in the figure is the original channel gain Hk. The MRC weight enhances the frequency-selectivity of the channel after equalization. Using the ZF weight, the frequency-nonselective channel can be perfectly restored after equalization (of course, only if the channel estimation is ideal), but the noise enhancement is produced at the subcarrier where the channel gain drops. However, the MMSE weight can avoid the noise enhancement by giving up the perfect restoration of the frequency-nonselective channel (the MMSE weight minimizes the mean square error between Sk and ˆ Rk. Among these FDE weights, the MMSE weight can provide the best compromise between the noise enhancement and suppression of frequency-selectivity and therefore, gives the best BER performance. After MMSE-FDE, N c -point IFFT is applied to obtain the time-domain multicode SC-CDMA chip sequence as (8) ˆrt = 1 N c N c −1 k=0 ˆ Rk exp j2t k N c = 2E c T c 1 N c N c −1 k=0 ˆ Hk st +ˆt +ˆt where st in the first term represents the transmitted chip sequence, ˆt is the residual inter-chip interference (ICI) component and ˆt is the noise component. ˆt can be expressed as (9) ˆt = 2E c T c 1 N c N c −1 k=0 ˆ Hk ⎡ ⎣ N c −1 =0 =t s exp j2k t − N c ⎤ ⎦ Note that if ˆ Hk = constant, ˆt =0 (i.e., this is the case of ZF-FDE and no ICI is produced). The residual ICI degrades the achievable BER performance (this is FUNDAMENTALS OF SINGLE-CARRIER CDMA TECHNOLOGIES 91 0.01 0.1 1 10 Subcarrier index k |H (k)| (a) Original channel gain 250 0 50 100 150 200 0.01 0.1 1 10 Subcarrier index k MMSE MRC ZF (b) Equivalent channel gain 2500 50 100 150 200 Equivalent channel gain |H (k)| 〈 –10 0 10 Subcarrier index k ZF MMSE MRC (c) Noise 250050 100 150 200 〈 Noise Re[ Π (k)] Figure 9. One-shot observation of equivalent channel gain and noice after FDE 92 CHAPTER 3 explained later). Multicode despreading is carried out on ˆrt to obtain the decision variable for the data modulated symbol sequence {d u n; n = 0 ∼ N c /SF −1}, u = 0 ∼C −1, as (10) ˆ d u n = 1 SF n+1SF−1 t=nSF ˆrtc ∗ u t mod SFc ∗ scr t based on which data demodulation is done. An arbitrary spreading factor SF can be used for the given value of FFT window size N c . This property allows variable rate transmission even when FDE is used in SC-CDMA systems. Figure 10 plots the BER performance of multicode SC-CDMA using MMSE- FDE for SF=16, obtained by computer simulation, as a function of the average received bit energy-to-AWGN noise power spectrum density ratio E b /N 0 . QPSK data modulation and an L = 16-path frequency-selective Rayleigh fading channel having a uniform power delay profile (E[h l 2 =1/L are assumed. For comparison, 1.E–05 1.E–04 1.E–03 1.E–02 Average BER 1.E–01 1.E+00 Average received E b /N 0 (dB) QPSK N c = 256, N g = 32 L = 16-path uniform power delay profile SF = 16 C = 1 4 8 16 × MMSE-FDE Rake combining Theoretical lower bound 250 5 10 15 20 Figure 10. BER performance of multicode SC-CDMA with MMSE-FDE FUNDAMENTALS OF SINGLE-CARRIER CDMA TECHNOLOGIES 93 the BER performance of coherent rake combining and theoretical lower-bound are also plotted. When C =1, MMSE-FDE and rake combining can achieve almost the same BER performance. However, when C ≥4, the BER performance using rake combining significantly degrades due to strong ICI and exhibits large BER floors. MMSE-FDE can always achieve better BER performance than rake combining and no BER floors are seen. However, although MMSE-FDE provides much better BER performance, the BER performance degrades as the code-multiplexing order C increases since the orthogonality distortion among codes is produced due to the residual ICI ˆt. As the frequency-selectivity becomes stronger (or L increases), the complexity of the rake receiver increases since more correlators are required for collecting enough signal power for data demodulation. However, unlike rake receiver, the complexity of MMSE-FDE receiver is independent of the channel frequency-selectivity. The use of FDE can alleviate the complexity problem of the rake receiver arising from too many paths in a severe frequency-selective channel. These suggest that SC-CDMA with MMSE-FDE is a promising broadband access as MC-CDMA for 4G wireless networks. 4.2 Inter-chip Interference (ICI) Cancellation Although MMSE-FDE can significantly improve the BER performance of orthogonal multicode SC-CDMA, there is still a big performance gap to the theoretical lower-bound as shown in Figure 10. This is due to the residual ICI after MMSE-FDE, given by Eq. (9). An ICI cancellation technique can be introduced into MMSE-FDE to improve the BER performance. The ICI in SC-CDMA with SF=1 is equivalent to the inter-symbol interference (ISI) in the non-spread (i.e., SF=1) SC transmissions; the ISI cancellation techniques can be found in the literature. Similar to ISI cancellation for MC-CDMA, ICI cancellation for SC-CDMA can be carried out either in the time-domain or in the frequency-domain after performing MMSE-FDE. For the frequency-domain ICI cancellation, the replicas of frequency components {Mk; k = 0 ∼ N c −1} of the residual ICI ˆt in Eq. (9) are subtracted from ˆ Rk k = 0 ∼N c −1 after MMSE-FDE. Mk is given by (11) Mk = N c −1 t=0 ˆtexp −j2k t N c = 2E c T c ˆ Hk− 1 N c N c −1 k =0 ˆ Hk Sk A joint MMSE-FDE and ICI cancellation is repeated in an iterative fashion so as to improve the accuracy of the ICI replica generation. Figure 11 shows the structure of joint MMSE-FDE and ICI cancellation. 94 CHAPTER 3 IFFT FFT Multicode despreading Data demodulation Symbol replica generation Multicode spreading MMSE weight & ICI replica generation Received chip sequence Received data ICI replica w(k) Iteration Delay FFT – • • •• • • • • •• • • Figure 11. Joint MMSE-FDE and ICI cancellation The ith iteration is described below. After performing MMSE-FDE with the MMSE weight w i k , ICI cancellation is performed in the frequency-domain as (12) ˜ R i k = ˆ H i k − ˜ M i k where ˆ H i k =w i kHk is the equivalent channel gain and ˜ M i k is the replica of Mk which is given, from Eq. (11), as (13) ˜ M i k = ⎧ ⎪ ⎨ ⎪ ⎩ 0 for i =0 2E c T c ˆ H i k −A i ˜ S i−1 k for i>0 where ˜ S i−1 k is the kth frequency component of the soft decision transmitted chip block replica ˜s i−1 t (which is generated by feeding back the (i −1)th ICI cancellation result) and A i is given by A i = 1 N c N c −1 k=0 ˆ H i k(14) N c -point IFFT is performed on ˜ R i k k = 0 ∼N c −1to obtain the time-domain chip sequence for multicode despreading. A series of joint MMSE-FDE and ICI cancellation, N c -point IFFT, multicode despreading, data symbol replica generation, and multicode spreading is repeated a sufficient number of times. Finally, data-demodulation is carried out to obtain the received data. The MMSE weight w i k minimizes the mean square error (MSE) Eek 2 for the given Hk, i.e., E ek 2 w i k =0, where ek is the equalization error between ˜ R i k after the ICI cancellation and Sk of the transmitted signal st and is defined as (15) ek = ˜ R i k −A i Sk FUNDAMENTALS OF SINGLE-CARRIER CDMA TECHNOLOGIES 95 The MMSE weight is given as (16) w i k = H ∗ k i−1 Hk 2 + E c N 0 −1 where i−1 is an interference factor determined by feeding back the (i −1)th iteration result and given by (17) i−1 ≈ N c −1 t=0 ¯s i−1 t 2 − ˜s i−1 t 2 where ¯s i−1 t is the hard decision replica of transmitted chip block. The BER performance for the case of SF = 16 is plotted in Figure 12 with the code-multiplexing order C as a parameter. When C =1, the BER performance approaches the theoretical lower-bound by about 0.5 dB. As C increases, the BER 1.E–05 1.E–04 1.E–03 Average BER 1.E–02 1.E–01 17 Average received E b / N 0 (dB) QPSK L = 16 SF = 16 Lower bound w/ ICI cancellation (i = 3) w/o ICI cancellation C = 1 = 4 = 8 = 16 × 2712 Figure 12. Simulated BER performance with joint MMSE-FDE and ICI cancellation [...]... = 4) Perfect FD-PIC 1.E – 01 2D-ZF FDE detection 1.E – 02 Average BER Iterative joint MMSE-FDE/ FD-PIC FD V-BLAST 1.E – 03 2D-MMSE FDE detection SC-CDMA (4, 4)SDM QPSK mod SF = C = 64, Nc = 256, L = 16, uniform power delay profile (β = 0) 1.E – 04 Perfect FD-PIC 1.E – 05 0 5 10 15 20 Average received Eb /N0 per antenna (dB) 25 30 Figure 16 BER performance of full code-multiplexed SC-CDMA using (4, 4)... SC-CDMA 10 4 QPSK L = 16, uniform profile (β = 0dB), fDT = 10 4 10–5 2 4 6 8 10 12 Average received Eb /N0 (dB) 14 16 Figure 21 BER performance comparison of 2D block spread and conventional SC-CDMA when SF = 16 t f when SF = 16 For block spread SC-CDMA, SFu SFu = U 16/U is assumed for all users When the system is lightly loaded (i.e., U = 8), conventional SC-CDMA using MUD exhibits better BER performance... conventional SC-CDMA using MMSE-MUD 8 c0=[1,1,1,1,1,1,1,1]T 4 c0=(1,1,1,1) 8 c1=[1,1,1,1,−1,−1,−1,−1]T 2 c0=[1,1]T c8=[1,1,-1,-1,1,1,-1,-1]T 2 4 c1=[1,1,−1,−1]T 8 U=1 c3=[1,1,−1,−1,−1,−1, 1,1]T c1=1 0 8 c4=[1,−1,1,−1,1,−1, 1,−1]T 4 c2=[1,−1,1,−1]T 4 N=1 2 c2=[1,−1]T 1 N=2 N =4 Figure 20 OVSF code tree 8 8 c5=[1,−1,1,−1,−1,1,−1,1]T 8 c6=[1,−1,−1,1,1,−1,−1,1]T 4 c3=[1,−1,−1,1]T 8 c7=[1,−1,−1,1,−1,1,1,−1]T N=8 110... ; m = 0 ∼ t 4 t 4 1} If U =4 cu is selected from {cm ; m = 0 ∼ 3}, e.g., cu = c2 = 1 −1 1 −1 T , and f 4 t 2 cu can also be selected from {cm ; m = 0 ∼ 3} If U = 2, then cu is selected from {cm ; t 2 f 8 m = 0 ∼ 1}, e.g., cu = c1 = 1 −1 T , and cu can be selected from {cm ; m = 0 ∼ 7} When U = 1, 2D block spreading reduces to the conventional 1D spreading 7 .4 BER Performance The BER performance of... ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ for Nt = 4 ⎟ ⎟ ⎠ where Rq nr k is the kth frequency component of the chip block received by the nr th receive antenna in the qth time interval, and wnr nt k is the MMSE weight given as 1.E–01 w/STTD w/o STTD C=1 1.E–02 × =4 Average BER =8 = 16 1.E–03 QPSK 1.E– 04 Nc = 256, Ng = 32 SF = 16 L = 16, Nt = 2, Nr = 1 1.E–05 0 5 10 Average received E b /N0 (dB) 15 Figure 14 BER performance of SC-CDMA... performance of full code-multiplexed SC-CDMA using (4, 4)SDM is plotted in Figure 16 as a function of the average received Eb /N0 per receive antenna Nt × Nr channels are independent Rayleigh fading channels having an L = 16path uniform power delay profile ( = 0dB) Iterative joint MMSE-FDE/FD-PIC is superior to 2D-ZF FDE detection, 2D-MMSE FDE detection, and FD V-BLAST For comparison, the BER performance... profile (β = 0dB), fDT = 10 4 10–5 2 4 10 6 8 12 Average received Eb /N0 (dB) 14 16 Figure 22 BER performance comparison of 2D block spread SC- and MC-CDMA when SF = 16 f (i.e., SFu = 1 , the frequency-diversity gain cannot be obtained in MC-CDMA, but larger frequency-diversity gain can still be obtained in SC-CDMA Therefore, 2D block spread SC-CDMA provides much better BER performance than MC-CDMA 8 HYBRID... 1) The LLR values are computed for c = 0 ∼ C − 1 and for all the bits in the symbol Turbo decoding is performed using these LLR values as soft input after rate matching Then, error detection is performed and retransmission is requested if errors are detected The throughput performance in bps/Hz of SC-CDMA with MMSE-FDE when turbo coded HARQ is used are shown in Figure 25 for fD Tblk = 0 001 (fD denotes... Gaussian variables with variance 2N0 /Tc /SF u If the channel is timeinvariant (i.e., Hu m = Hu 0 for m = 0 ∼SF u − 1), the MAI is removed since H = cu cu SFu u − u , where · is the delta function 7.2 Two-dimensional Block Spreading 1D block spread SC-CDMA is a single-rate transmission In the next generation mobile communications, a flexible support of low-to-high multi-rate services is required The suppression... close to that for the single antenna transmission case, 1D-MMSE FDE is used instead of 2D-MMSE FDE for i ≥ 1 Joint 1D-MMSE FDE is performed as (36) i i ˆ Rnit k = w nt k R nt k 1 04 CHAPTER 3 i i i where R nit k = R 0 nt k · · · R Nr −1 nt k T and w nit k = w 0 nt k · · · i w Nr −1 nt k is the 1D-MMSE FDE weight vector, given by (37) 6.3 w i nt k = H Hnt k H Hnt k Hnt C · Ec k + N0 −1 −1 BER Performance . a promising broadband access as MC-CDMA for 4G wireless networks. 4. 2 Inter-chip Interference (ICI) Cancellation Although MMSE-FDE can significantly improve the BER performance of orthogonal. blocks for despreading and data demodulation. (b) N t =3 and 4 When N t =3 and 4, four consecutive chip blocks s q t t =0 ∼N c −1, q =0 ∼3, are encoded. STTD encoding for N t =3 and 4 can. fading channel with uniform power delay profile ( = 0 dB), and ideal channel estimation. The BER performance using frequency-domain STTD is plotted in Figure 14 for SF=16. For comparison, the single
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