Multi carrier and spread spectrum systems phần 7 ppsx

162 Implementation Issues coding, the systematic structure of the RS code allows one to shorten the code, i.e., remove the filled 239 − K zero bytes before transmission. Then, each coded packet of length K + 16 bytes will be serial bit converted. — At the end of the each packet, tailbits (e.g., 6 bits for memory 6) can be inserted for inner code trellis termination purposes. — A block consisting of [(K + 16) × 8 +6] bits is encoded by the inner convolutional mother binary code of rate 1/2. After convolutional coding, the puncturing operation is applied following the used inner code rate R for the given packet. This results in a total of [(K +16) × 8 + 6]/R bits. Finally, the punctured bits are serial-to-parallel converted and submitted to the symbol mapper. If the BER before RS decoding is guaranteed to be about 2 ·10 −4 , then with sufficient interleaving (e.g., 8 RS code words) for the same SNR values given in Table 4-3, a quasi error-free (i.e., BER < 10 −12 ) transmission after RS decoding is guaranteed. However, if no interleaving is employed, depending on the inner coding rate, a loss of about 1.5–2.5 dB has to be considered to achieve a quasi error-free transmission [20]. 4.4.3 Turbo Coding Recently, interest has focused on iterative decoding of parallel or serial concatenated codes using soft-in/soft-out (SISO) decoders with simple code components in an inter- leaved scheme [4][28][29][30][66]. These codes, after several iterations, provide near- Shannon performance [29][30]. We will consider here two classes of codes with iterative decoding: convolutional and block Turbo codes. These codes are already adopted in several standards. 4.4.3.1 Convolutional Turbo Coding By applying systematic recursive convolutional codes in an iterative scheme and by intro- ducing an interleaver between the two parallel encoders, impressive results can be obtained with so-called convolutional Turbo codes [4]. Convolutional Turbo codes are currently of great interest because of their good performance at low SNRs. Figure 4-38 shows the block diagram of a convolutional Turbo encoder. The code struc- ture consists of two parallel recursive systematic punctured convolutional codes. A block of encoded bits consists of three parts. The two parity bit parts and the systematic part which is the same in both code bit streams and, hence, has to be transmitted only once. The code bit sequence at the output of the Turbo encoder is given by the vector b (k) . a (k) b (k) convolutional encoder convolutional encoder puncturing puncturing interleaver Figure 4-38 Convolutional Turbo encoder Channel Coding and Decoding 163 deinterleaver deinterleaver interleaver convolutional decoder convolutional decoder interleaver sign(.)‘0’ insertion ‘0’ insertion l (k) a ^(k) Figure 4-39 Convolutional Turbo decoder In the receiver, the decoding is performed iteratively. Figure 4-39 shows the block diagram of the convolutional Turbo decoder. The component decoders are soft output decoders providing log-likelihood ratios (LLRs) of the decoded bits (see Section 2.1.7). The basic idea of iterative decoding is to feed forward/backward the soft decoder output in the form of LLRs, improving the next decoding step. In the initial stage, the non- interleaved part of the coded bits b (k) is decoded. Only the LLRs given by the vector l (k) at the input of the Turbo decoder are used. In the second stage, the interleaved part is decoded. In addition to the LLRs given by l (k) , the decoder uses the output of the first decoding step as apriori information about the coded bits. This is possible due to the separation of the two codes by the interleaver. In the next iteration cycle, this procedure is repeated, but now the non-interleaved part can be decoded using an apriori information delivered from the last decoding step. Hence, this decoding run has a better performance than the first one and the decoding improves. Since in each individual decoding step the decoder combines soft information from different sources, the representation of the soft information is crucial. It is shown in [29] and [30] that the soft value at the decoder input should be a LLR to guarantee that after combining the soft information at the input of the decoder LLRs are again available. The size of the Turbo code interleaver and the number of iterations essentially determine the performance of the Turbo coding scheme. The performance of Turbo codes as channel codes in different multi-carrier multi- ple access schemes is analyzed for the following Turbo coding scheme. The component codes of the Turbo code are recursive systematic punctured convolutional codes, each of rate 2/3, resulting in an overall Turbo code rate of R = 1/2. Since performance with Turbo codes in fading channels cannot be improved with a memory greater than 2 for a BER of 10 −3 [30], we consider a convolutional Turbo code with memory 2 in order to minimize the computational complexity. The component decoders exploit the soft output Viterbi algorithm (SOVA) [28]. The Turbo code interleaver is implemented as a random interleaver. Iterative Turbo decoding in the channel decoder uses 10 iterations. The SNR gain with Turbo codes relative to convolutional codes with R = 1/2and memory 6 versus the Turbo code interleaver size I TC is given in Figure 4-40 for the BER of 10 −3 . 164 Implementation Issues OFDM (OFDMA, MC-TDMA) MC-CDMA, MLSE/MLSSE MC-CDMA, MMSE equalizer 100 0.0 0.5 1.0 1.5 2.0 1000 10000 Turbo code interleaver size SNR gain in dB Figure 4-40 SNR gain with Turbo codes relative to convolutional codes versus interleaver size I TC The results show that OFDMA and MC-TDMA systems benefit more from the applica- tion of Turbo codes than MC-CDMA systems. It can be observed that the improvements with Turbo codes at interleaver sizes smaller than 1000 are small. Due to the large interleaver sizes required for convolutional Turbo codes, they are of special interest for non-real time applications. 4.4.3.2 Block Turbo Coding The idea of product block or block Turbo coding is to use the well-known product codes with block codes as components for two-dimensional coding (or three dimensions) [66]. The two-dimensional code is depicted in Figure 4-41. The k r information bits in the rows are encoded into n r bits, by using a binary block code C r (n r ,k r ). The redundancy of the code is r r = n r − k r and d r the minimum distance. After encoding the rows, the columns are encoded using another block code C c (n c ,k c ), where the check bits of the first code are also encoded. The two-dimensional code has the following characteristics — overall block size n = n r · n c , — number of information bits k r · k c , — code rate R = R r · R c ,whereR i = k i /n i , i = c, r,and — minimum distance d min = d r · d c . The binary block codes employed for rows and columns could be systematic BCH (Bose–Chaudhuri–Hocquenghem) or Hamming codes [48]. Furthermore, the constituent Channel Coding and Decoding 165 Data bits Parity bits Parity bits k r n r n c k c Figure 4-41 Two-dimensional product code matrix Tabl e 4-4 Generator polynomials of Hamming codes as block Turbo code components n i k i Generator 7 4 x 3 + x +1 15 11 x 4 + x +1 31 26 x 5 + x 2 + 1 63 57 x 6 + x +1 127 120 x 7 + x 3 + 1 codes of rows or columns can be extended with an extra parity bit to obtain extended BCH or Hamming codes. Table 4-4 gives the generator polynomials of the Hamming codesusedinblockTurbocodes. The main advantage of block Turbo codes is in their application for packet transmis- sion, where the interleaver as it is used in convolutional Turbo coding is not necessary. Furthermore, as block codes, block Turbo codes are efficient for high code rates. To match packet sizes, a product code can be shortened by removing symbols. In the two-dimensional case, either rows or columns can be removed until the appropriate size is reached. Unlike one-dimensional codes (such as Reed–Solomon codes), parity bits are removed as part of the shortening process, helping to keep the code rate high. As with convolutional Turbo codes, the decoding of block Turbo codes is done in an iterative way [66]. First, all the horizontal blocks are decoded then all the vertical received blocks are decoded (or vice versa). The decoding procedure is iterated several times to maximize the decoder performance. The core of the decoding process is the soft-in/soft- out (SISO) constituent code decoder. High-performance iterative decoding requires the constituent code decoders to not only determine a transmitted sequence, but also to yield a soft decision metric (i.e., LLR) which is a measure of the likelihood or confidence of each bit in that sequence. Since most algebraic block decoders do not operate with soft 166 Implementation Issues Tabl e 4-5 Performance of block Turbo codes in AWGN channel after three iterations BTC constituent codes Coded packet size Code rate E b /N 0 at BER = 10 −9 (23,17)(31,25) 53 bytes 0.596 4.5 dB (16,15)(64,57) 106 bytes 0.834 6.2 dB (56,49)(32,26) 159 bytes 0.711 3.8 dB (49,42)(32,31) 159 bytes 0.827 6.5 dB (43,42)(32,31) 159 bytes 0.945 8.5 dB inputs or generate soft outputs, such block decoders have primarily been used using the soft output Viterbi algorithm (SOVA) [28] or a soft output variant of the modified Chase algorithm(s) [6]. However, other SISO block decoding algorithms can also be used for deriving the LLR. The decoding structure of block Turbo codes is similar to that of Figure 4-39, where instead of convolutional decoders, the row and column decoders are applied. Note that here the interleaving is simply a read/write mechanism of rows and columns of the code matrix. The performance of block Turbo codes with three iterations for different packet sizes in an AWGN channel is given in Table 4-5. 4.4.4 OFDM with Code Division Multiplexing: OFDM-CDM OFDM-CDM is a multiplexing scheme which can better exploit diversity than conven- tional OFDM systems. Each data symbol is spread over several sub-carriers and/or several OFDM symbols, exploiting additional frequency- and/or time-diversity [36][37]. By using orthogonal spreading codes, self-interference between data symbols can be minimized. Nevertheless, self-interference occurs in fading channels due to a loss of orthogonality between the spreading codes. To reduce this degradation, an efficient data detection and decoding technique is required. The principle of OFDM-CDM is shown in Figure 4-42. data source channel decoder channel deinter- leaver deinter- leaver IOFDM symbol demapper channel encoder inter- leaver inter- leaver OFDM symbol mapper spreader (HT) detector (IHT) CSICSI CDM data sink Figure 4-42 OFDM-CDM transmitter and receiver Signal Constellation, Mapping, Demapping, and Equalization 167 123 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 4 BER 5 E b /N 0 in dB 678 OFDM-CDM, CC OFDM, CC OFDM, TC, I = 256 OFDM, TC, I = 1024 Figure 4-43 Performance of OFDM-CDM with classical convolutional codes versus OFDM with Turbo codes and interleaver size 256 and 1024, respectively MC-CDMA and SS-MC-MA can be considered special cases of OFDM-CDM. In MC- CDMA, CDM is applied for user separation and in SS-MC-MA different CDM blocks of spread symbols are assigned to different users. The OFDM-CDM receiver applies single-symbol detection or more complex multi- symbol detection techniques which correspond to single-user or multiuser detection tech- niques, respectively, in the case of MC-CDMA. The reader is referred to Section 2.1.5 for a description of the different detection techniques. In Figure 4-43, the performance of OFDM-CDM using classical convolutional codes is compared with the performance of OFDM using Turbo codes. The BER versus the SNR for code rate 1/2 and QPSK symbol mapping is shown. Results are given for OFDM- CDM with soft IC after the 1st iteration and for OFDM using Turbo codes with interleaver sizes I = 256 and I = 1024 and iterative decoding with 10 iterations. As reference, the performance of OFDM with classical convolutional codes is given. It can be observed that OFDM-CDM with soft IC and classical convolutional codes can outperform OFDM with Turbo codes. 4.5 Signal Constellation, Mapping, Demapping, and Equalization 4.5.1 Signal Constellation and Mapping The modulation employed in multi-carrier systems is usually based on quadrature ampli- tude modulation (QAM) with 2 m constellation points, where m is the number of bits transmitted per modulated symbol, and M = 2 m is the number of constellation points. The general principle of modulation schemes is illustrated in Figure 4-44, which is valid for both uplink and downlink. 168 Implementation Issues From encoder (serial bits) S/P 2 m QAM- Mapping • • b 0 b m −1 I Q K Mod K Mod Figure 4-44 Signal mapping block diagram Tabl e 4-6 Bit mapping with 4-QAM b 0 b 1 I Q 0 0 1 1 0 1 1 −1 1 0 −1 1 1 1 −1 −1 For the downlink, high-order modulation can be used such as 4-QAM (m = 2) up to 64- QAM (m = 6). For the uplink, more robust 4-QAM is preferred. Typically, constellation mappings are based on Gray mapping, where adjacent constellation points differ by only one bit. Table 4-6 defines the constellation for 4-QAM modulation. In this table, b l ,l = 0, ,m− 1, denotes the modulation bit order after serial to parallel conversion. The complex modulated symbol takes the value I + jQ from the 2 m point constellation (see Figure 4-45). In the case of transmission of mixed constellations in the downlink frame, i.e., adaptive modulation (from 4-QAM up to 64-QAM), a constant RMS should be guaranteed. Unlike the uplink transmission, this would provide the advantage that the downlink interference from all base stations has a quasi-constant behavior. Therefore, the output complex values are formed by multiplying the resulting I +jQ value by a normalization factor K MOD as shown in Figure 4-44. The normalization K MOD depends on the modulation as prescribed in Table 4-7. Symbol mapping can also be performed differentially as with D-QPSK applied in the DAB standard [14]. Differential modulation avoids the necessity of estimating the carrier phase. Instead, the received signal is compared to the phase of the preceding symbol [65]. However, since one wrong decision results in 2 decision errors, differential modulation performs worse than non-differential modulation with accurate knowledge of the channel in the receiver. Differential demodulation can be improved by applying a two-dimensional demodulation, where the correlation of the channel in time and frequency direction is taken into account in the demodulation [27]. Signal Constellation, Mapping, Demapping, and Equalization 169 00 Q I 10 01 b 0 b 1 b 0 b 1 b 2 b 3 b 4 b 5 1−1 −1 1 11 001011 000011 010011 011011 001010 000010 010010 011010 001000 000000 010000 011000 001001 000001 010001 011001 I 111011 110011 100011 101011 −7 −5 −3 −1 1 3 5 7 Q 111010 110010 100010 101010 111000 110000 100000 101000 111001 110001 100001 101001 111101 110101 100101 101101 111100 110100 100100 101100 111110 110110 100110 101110 111111 0001 Q 0101 0000 0100 1101 1001 1100 1000 13 I −3 −1 −1 −3 1 3 0010 0110 0011 b 0 b 1 b 2 b 3 0111 1110 1010 1111 1011 110111 100111 101111 001101 000101 010101 011101 −7 −5 −3 −11357 001100 000100 010100 011100 001110 000110 010110 011110 001111 000111 010111 011111 Figure 4-45 M-QAM signal constellation Tabl e 4-7 Modulation dependent normalization factor K MOD Modulation K MOD 4-QAM 1 16-QAM 1/ √ 5 64-QAM 1/ √ 21 4.5.2 Equalization and Demapping The channel estimation unit in the receiver provides for each sub-carrier n an esti- mate of the channel transfer function H n = a n e jϕ n . In mobile communications, each sub-carrier is attenuated (or amplified) by a Rayleigh or Ricean distributed variable a n =|H n | and phase distorted by ϕ n . Therefore, after FFT operation a correction of the amplitude and the phase of each sub-carrier is required. This can be done by a simple channel inversion, i.e., multiplying each sub-carrier by 1/H n . Since each sub- carrier suffers also from noise, this channel correction for small values of a n leads to a noise amplification. To counteract this effect, the SNR value γ n = 4|H n | 2 /σ 2 n of each sub-carrier (where σ 2 n is the noise variance at sub-carrier n) should be consid- ered for soft metric estimation. Moreover, in order to provide soft information for the channel decoder, i.e., Viterbi decoder, the received channel corrected data (after FFT 170 Implementation Issues • • • • • • FFT 1/H 0 1/H 1 g 1 g 0 Reliability estimation Reliability estimation Quantization Quantization P/S 1/H Nc−1 g Nc−1 Reliability estimation Quantization To decoder Equalization De-mapping and soft metric derivation Figure 4-46 Channel equalization and soft metric derivation and equalization with CSI coefficients) should be optimally converted to soft metric information. Thus, the channel-corrected data have to be combined with the reliability information exploitary channel state information for each sub-carrier, so that each encoded bit has an associated soft metric value and a hard decision that are provided to the Viterbi decoder. As shown in Figure 4-46, after channel correction, i.e., equalization, for each mapped bit of the constellation a reliability information is provided. This reliability information corresponds to the minimum distance from the nearest decision boundary that affects the decision of the current bit. This metric corresponds to LLR values (see Section 2.1.7) [65] after it is multiplied with the corresponding value of the SNR of each sub-carrier γ n = 4|H n | 2 /σ 2 n . Finally after quantization (typically 3–4 bits for amplitude and 1 bit for the sign), these soft values are submitted to the channel decoder. 4.6 Adaptive Techniques in Multi-Carrier Transmission As shown in Chapter 1, the radio channel suffers especially from time and frequency selectivity. Co-channel and adjacent channel interference (CCI and ACI) are further impairments that are present in cellular environments due to the high frequency reuse. Each terminal station may have different channel conditions. For instance, the terminal stations located near the base station receive the highest power which results in a high carrier-to-noise and -interference power ratio C/(N + I). However, the terminal station at the cell border has a lower C/(N + I). In order to exploit the channel characteristics and to use the spectrum in an effi- cient way, several adaptive techniques can be applied, namely adaptive FEC, adap- tive modulation, and adaptive power leveling. Note that the criteria for these adaptive Adaptive Techniques in Multi-Carrier Transmission 171 techniques can be based on the measured C/(N + I) or the received average power per symbol or per sub-carrier. These measured data have to be communicated to the transmitter via a return channel, which may be seen as a disadvantage for any adap- tive techniques. In TDD systems this disadvantage can be reduced, since the channel coefficients are typically highly correlated between successive uplink and downlink slots and, thus, are also available at the transmitter. Only if significant interference occurs at the receiver, this has to be communicated to the transmitter via a return channel. 4.6.1 Nulling of Weak Sub-Carriers The most straightforward solution for reducing the effect of noise amplification during equalization is the technique of nulling weak sub-carriers which can be applied in an adaptive way. Sub-carriers with the weakest received power are discarded at the trans- mission side. However, by using strong channel coding or long spreading codes, the gain obtained by nulling weak sub-carriers is reduced. 4.6.2 Adaptive Channel Coding and Modulation Adaptive coding and modulation in conjunction with multi-carrier transmission can be applied in several ways. The most commonly used method is to adapt channel coding and modulation during each transmit OFDM frame/burst, assigned to a given terminal sta- tion [16][17][18]. The most efficient coding and modulation will be used for the terminal station having the highest C/(N +I), where the most robust one will be applied for the terminal station having the worst C/(N + I) (see Figure 4-47). The spectral efficiency in a cellular environment is doubled using this adaptive technique [20]. An alternative technique that can be used in multi-carrier transmission is to apply the most efficient modulation for sub-carriers with the highest received power, where the most robust modulation is applied for sub-carriers suffering from multipath fading (see Figure 4-48). Furthermore, this technique can be applied in combination with power control to reduce out of band emission, where for sub-carriers located at the channel bandwidth border low-order modulation with low transmit power and for sub-carriers in the middle of the bandwidth higher order modulation with higher power can be used. BS TS 1 TS 2 TS 3 OFDM symbols up to 16-QAM mod. OFDM symbols up to 64-QAM mod. to TS 2 to TS 1 OFDM symbols with 4-QAM mod. to TS 3 d 1 d 3 d 2 d 3 > d 2 > d 1 Figure 4-47 Adaptive channel coding and modulation per OFDM symbol [...]... Proc IEEE International Symposium on Spread Spectrum Techniques and Applications (ISSSTA’96), Mainz, Germany, pp 1366–1 370 , Sept 1996 [ 37] Kaiser S., “OFDM code division multiplexing in fading channels,” IEEE Transactions on Communications, vol 50, pp 1266–1 273 , Aug 2002 [38] Kaiser S and Fazel K., “A flexible spread- spectrum multi- carrier multiple-access system for multimedia applications,” in Proc IEEE... MC-CDMA systems can be found in [77 ] and [81] 4 .7. 2 Non-Linearities Multi- carrier modulated systems using OFDM are more sensitive to high power amplifier (HPA) non-linearities than single -carrier modulated systems [75 ] The OFDM signal 178 Implementation Issues 100 phase noise without correction phase noise with correction 10−1 without phase noise BER 10−2 10−3 10−4 10−5 20 21 22 23 24 Eb /N0 in dB 25 26 27. .. on Personal, Indoor and Mobile Radio Communications (PIMRC’ 97) , Helsinki, Finland, pp 100–104, Sept 19 97 [39] Kaiser S and H¨ her P., “Performance of multi- carrier CDMA systems with channel estimation in two o dimensions,” in Proc IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’ 97) , Helsinki, Finland, pp 115–119, Sept 19 97 [40] Kamal S.S and Lyons R.G., “Unique-word... Systems, ENSTParis, 1989, PhD thesis [43] Ketchum J.W and Proakis J.G., “Adaptive algorithms for estimating and suppressing narrow band interference in PN spread- spectrum systems, ” IEEE, Transactions on Communications, vol 30, pp 913–924, May 1982 [44] Li Y., “Simplified channel estimation for OFDM systems with multiple transmit antennas,” IEEE Transactions on Wireless Communications, vol 1, pp 67 75 ,... (GLOBECOM’ 97) , Communication Theory Mini Conference, Phoenix, USA, pp 90–96, Nov 19 97 [35] Hsieh M.H and Wei C.H., “A low complexity frame synchronization and frequency offset compensation scheme for OFDM systems over fading channels,” IEEE Transactions on Communications, vol 48, pp 1596–1609, Sept 1999 [36] Kaiser S., “Trade-off between channel coding and spreading in multi- carrier CDMA systems, ” in... Furthermore, at high carrier frequencies (e.g., HIPERLAN/2 at 5 GHz) low cost RF transmit and receive oscillators can be applied at the expense of higher phase noise The main objective of this section is to analyze the performance of multi- carrier and multi- carrier CDMA transmission with a high number of sub-carriers in the presence of low cost oscillators with phase noise and HPAs with both AM/AM and AM/PM nonlinear... (single -carrier or multi- carrier) will have a high PAPR [21] Therefore, for the downlink both systems may have quite similar behavior To justify this, we additionally consider a single -carrier DS-CDMA system, where the transmitter consists of a spreader, transmit filter and the HPA The receiver is made out of the receive filter and the despreader, i.e., detector It should be noticed that the transmit and. .. division multiplexing (OFDM),” IEEE Transactions on Broadcasting, vol 47, pp 153–159, June 2001 [3] Berens F., Jung P., Plechinger J and Baier P.W., Multi- carrier joint detection CDMA mobile communications,” in Proc IEEE Vehicular Technology Conference (VTC’ 97) , Phoenix, USA, pp 18 97 1901, May 19 97 [4] Berrou C., Glavieux A and Thitimajshima P., “Near Shannon limit error-correcting coding and decoding:... MC-CDMA with pre-distortion Uplink multi- carrier transmission In this section we highlight the effects of the spreading code selection and detail the appropriate choice for the uplink and the downlink [61][64] In Section 2.1.4.2, upper bounds for the PAPR of different spreading codes have been presented for MC-CDMA systems Both uplink and downlink have been analyzed and it is shown that different codes... Switzerland, pp 1064–1 070 , May 1993 [5] B¨ lcskei H., Heath R.W and Paulraj A.J., “Blind channel identification and equalization in OFDM-based o multi- antenna systems, ” IEEE Transactions on Signal Processing, vol 50, pp 96–109, Jan 2002 [6] Chase D., “A class of algorithms for decoding block codes with channel measurement information,” IEEE Transactions on Information Theory, vol 18, pp 170 –182, Jan 1 972 [7] . on MC-CDMA systems can be found in [77 ] and [81]. 4 .7. 2 Non-Linearities Multi- carrier modulated systems using OFDM are more sensitive to high power ampli- fier (HPA) non-linearities than single -carrier. performance of multi- carrier and multi- carrier CDMA transmission with a high number of sub-carriers in the presence of low cost oscillators with phase noise and HPAs with both AM/AM and AM/PM non- linear. Division Multiplexing: OFDM-CDM OFDM-CDM is a multiplexing scheme which can better exploit diversity than conven- tional OFDM systems. Each data symbol is spread over several sub-carriers and/ or