4 Implementation Issues A general block diagram of a multi-carrier transceiver employed in a cellular environment with a central base station (BS) and several terminal stations (TSs) in a point to multi-point topology is depicted in Figure 4-1. For the downlink, transmission occurs in the base station and reception in the terminal station and for the uplink, transmission occurs in the terminal station and reception in the base station. Although very similar in concept, note that in general the base station equipment handles more than one terminal station, hence, its architecture is more complex. The transmission operation starts with a stream of data symbols (bits, bytes or packets) sent from a higher protocol layer, i.e., the medium access control (MAC) layer. These data symbols are channel encoded, mapped into constellation symbols according to the designated symbol alphabet, spread (only in MC-SS) and optionally interleaved. The modulated symbols and the corresponding reference/pilot symbols are multiplexed to form a frame or a burst. The resulting symbols after framing or burst formatting are multiplexed and multi-carrier modulated by using OFDM and finally forwarded to the radio transmitter through a physical interface with digital-to-analog (D/A) conversion. The reception operation starts with receiving an analog signal from the radio receiver. The analog-to-digital converter (A/D) converts the analog signal to the digital domain. After multi-carrier demodulation (IOFDM) and deframing, the extracted pilot symbols and reference symbols are used for channel estimation and synchronization. After option- ally deinterleaving, despreading (only in the case of MC-SS) and demapping, the channel decoder corrects the channel errors to guarantee data integrity. Finally, the received data symbols (bits, bytes or a packet) are forwarded to the higher protocol layer for fur- ther processing. Although the heart of an orthogonal multi-carrier transmission is the FFT/IFFT opera- tion, synchronization and channel estimation process together with channel decoding play a major role. To ensure a low-cost receiver (low-cost local oscillator and RF components) and to guarantee a high spectral efficiency, robust digital synchronization and channel esti- mation mechanisms are needed. The throughput of an OFDM system not only depends on the used modulation constellation and FEC scheme but also on the amount of reference and pilot symbols spent to guarantee reliable synchronization and channel estimation. Multi-Carrier and Spread Spectrum Systems K. Fazel and S. Kaiser  2003 John Wiley & Sons, Ltd ISBN: 0-470-84899-5 116 Implementation Issues Spreader (only for MC-SS) Interleaver & Mapper OFDM D/A Analog front end Channel decoder Despreader (only for MC-SS) Demapper & Deinterl. IOFDM A/D Analog front end Deframing Framing Channel estimation Digital VCO Channel Transmitter, Tx Receiver, Rx AGC Channel state information (CSI) Window Sampling rate Tx data Rx data Channel encoder Frequency and time synchronization Figure 4-1 General block diagram of a multi-carrier transceiver In Chapter 2 the different despreading and detection strategies for MC-SS systems were analysed. It was shown that with an appropriate detection strategy, especially in full load conditions (where all users are active) a high system capacity can be achieved. In the performance analysis in Chapter 2 we assumed that the modem is perfectly synchronized and the channel is perfectly known at the receiver. The principal goal of this chapter is to describe in detail the remaining components of a multi-carrier transmission scheme with or without spreading. The focus is given to multi-carrier modulation/demodulation, digital I/Q generation, sampling, channel cod- ing/decoding, framing/deframing, synchronization, and channel estimation mechanisms. Especially for synchronization and channel estimation units the effects of the transceiver imperfections (i.e., frequency drift, imperfect sampling time, phase noise) are highlighted. Finally, the effects of the amplifier non-linearity in multi-carrier transmission are analyzed. 4.1 Multi-Carrier Modulation and Demodulation After symbol mapping (e.g., M-QAM) and spreading (in MC-SS), each block of N c complex-valued symbols is serial-to-parallel (S/P) converted and submitted to the multi- carrier modulator, where the symbols are transmitted simultaneously on N c parallel sub- carriers, each occupying a small fraction (1/N c ) of the total available bandwidth B. Figure 4-2 shows the block diagram of a multi-carrier transmitter. The transmitted baseband signal is given by s(t) = 1 N c +∞  i=−∞ N c −1  n=0 d n,i g(t − iT s ) e j 2πf n t ,(4.1) Multi-Carrier Modulation and Demodulation 117 Mapping S / P Pulse shaping g(t) Pulse shaping g(t) Pulse shaping g(t) + exp(j2pf 0 t) exp(j2pf 1 t) exp(j2pf Nc −1 t) s(t) . . . exp(j2pf c t) s RF (t) Figure 4-2 Block diagram of a multi-carrier transmitter where N c is the number of sub-carriers, 1/T s is the symbol rate associated with each sub-carrier, g(t) is the impulse response of the transmitter filters, d n,i is the complex constellation symbol, and f n is the frequency of sub-carrier n. We assume that the sub- carriers are equally spaced, i.e., f n = n T s ,n= 0, .,N c − 1.(4.2) The up-converted transmitted RF signal s RF (t) can be expressed by s RF (t) = 1 N c Re  +∞  i=−∞ N c −1  n=0 d n,i g(t − iT s ) e j 2π(f n +f c )t  = Re{s(t) e j 2πf c t } (4.3) where f c is the carrier frequency. As shown in Figure 4-3, at the receiver side after down-conversion of the RF sig- nal r RF (t), a bank of N c matched filters is required to demodulate all sub-carriers. The received basedband signal after demodulation and filtering and before sampling at sub- carrier frequency f m is given by r m (t) = [r(t)e −j 2πf m t ] ⊗ h(t) =  +∞  i=−∞ N c −1  n=0 d n,i g(t − iT s ) e j 2π(f n −f m )t  ⊗ h(t), (4.4) where h(t) is the impulse response of the receiver filter, which is matched to the trans- mitter filter (i.e., h(t) = g ∗ (−t)). The symbol ⊗ indicates the convolution operation. For simplicity, the received signal is given in the absence of fading and noise. After sampling at optimum sampling time t = lT s , the samples result in r m (lT s ) = d m,l , if the transmitter and the receiver of the multi-carrier transmission system fulfill both the ISI and ICI-free Nyquist conditions [65]. 118 Implementation Issues h(t) P / S h(t) h(t) exp(−j2pf 0 t) exp(−j2pf 1 t) exp(−j2pf Nc −1 t) Demapper r(t) t = lT s t = lT s t = lT s . . . r RF (t) exp(−j2pf c t) Figure 4-3 Block diagram of a multi-carrier receiver To fulfill these conditions, different pulse shaping filtering can be used: Rectangular band-limited system: Each sub-carrier has a rectangular band-limited transmission filter with impulse response g(t) = sin  π t T s  π t T s = sinc  π t T s  .(4.5) The spectral efficiency of the system is equal to the optimum value, i.e., normalized value of 1 bit/s/Hz. Rectangular time-limited system: Each sub-carrier has a rectangular time-limited trans- mission filter with impulse response g(t) = rect(t) =  10  t<T s 0otherwise (4.6) The spectral efficiency of the system is equal to normalized value 1/(1 + BT s /N c ).For large N c , it approaches the optimum normalized value of 1 bit/s/Hz. Raised cosine filtering: Each sub-carrier is filtered by a time-limited (t ∈{−kT  s ,kT  s }) square root of a raised cosine filter with roll-off factor α and impulse response [65] g(t) = sin  πt T  s (1 − α)  + kαt T  s cos  πt T  s (1 + α)  πt T  s  1 −  kαt T  s  2  ,(4.7) Multi-Carrier Modulation and Demodulation 119 where T  s = (1 + α)T s and k is the maximum number of samples that the pulse shall not exceed. The spectral efficiency of the system is equal to 1/(1+ (1 + α)/N c ).Forlarge N c , it approaches the optimum normalized value of 1 bit/s/Hz. 4.1.1 Pulse Shaping in OFDM OFDM employs a time-limited rectangular pulse shaping which leads to a simple digital implementation. OFDM without guard time is an optimum system, where for large num- bers of sub-carriers its efficiency approaches the optimum normalized value of 1 bit/s/Hz. The impulse response of the receiver filter is h(t) =  1if− T s <t  0 0otherwise (4.8) It can easily be shown that the condition of absence of ISI and ICI is fulfilled. In case of inserting a guard time T g , the spectral efficiency of OFDM will be reduced to 1 − T g /(T s + T g ) for large N c . 4.1.2 Digital Implementation of OFDM By omitting the time index i in (4.1), the transmitted OFDM baseband signal, i.e., one OFDM symbol with guard time, is given by s(t) = 1 N c N c −1  n=0 d n e j2π nt T s , −T g  t<T s ,(4.9) where d n is a complex-valued data symbol, T s is the symbol duration and T g is the guard time between two consecutive OFDM symbols in order to prevent ISI and ICI in a multipath channel. The sub-carriers are separated by 1/T s . Note that for burst transmission, i.e., burst formatting, a pre-/postfix of duration T a can be added to the original OFDM symbol of duration T  s = T s + T g so that the total OFDM symbol duration becomes T  = T s + T g + T a .(4.10) The pre-/postfix can be designed such that it has good correlation properties in order to perform channel estimation or synchronization. One possibility for the pre-/postfix is to extend the OFDM symbol by a specific PN sequence with good correlation properties. At the receiver, as guard time, the pre-/postfix is skipped and the OFDM symbol is rebuilt as described in Section 4.5. From the above expression we note that the transmitted OFDM symbol can be per- formed by using an inverse complex FFT operation (IFFT), where the demultiplexing is done by an FFT operation. In the complex digital domain this operation leads to an IDFT operation with N c points at the transmitter side and a DFT with N c points at the receiver side (see Figure 4-4). Note that for guard time and pre-/postfix L g samples are inserted after the IDFT operation at the transmitter side and removed before the DFT at the receiver side. Highly repetitive structures based on elementary operations such as butterflies for the FFT operation can be applied if N c is of the power of 2 [1]. Depending on the transmission media and the carrier frequency f c , the actual OFDM transmission systems employ from 120 Implementation Issues N c -Point IFFT D/A 0 1 N c − 1 N c + L g − 1 0 1 A/D 0 1 0 1 Transmitter Receiver N c − 1 N c − 1 P/S Guard time/ post/prefix insertion Guard time/ post/prefix removal N c + L g − 1 S/P N c -Point FFT L g −1 Figure 4-4 Digital implementation of OFDM 64 up to 2048 (2k) sub-carriers. In the DVB-T standard [16], up to 8192 (8k) sub-carriers are required to combat long echoes in a single frequency network operation. The complexity of the FFT operation (multiplications and additions) depends on the number of FFT points N c . It can be approximated by (N c /2) log N c operations [1]. Fur- thermore, large numbers of FFT points, resulting in long OFDM symbol durations T  s , make the system more sensitive to the time variance of the channel (Doppler effect) and more vulnerable to the oscillator phase noise (technological limitation). However, on the other hand, a large symbol duration increases the spectral efficiency due to a decrease of the guard interval loss. Therefore, for any OFDM realization a trade-off between the number of FFT points, the sensitivity to the Doppler and phase noise effects, and the loss due to the guard interval has to be found. 4.1.3 Virtual Sub-Carriers and DC Sub-Carrier By employing large numbers of sub-carriers in OFDM transmission, a high frequency resolution in the channel bandwidth can be achieved. This enables a much easier imple- mentation and design of the filters. If the number of FFT points is slightly higher than that required for data transmission, a simple filtering can be achieved by putting in both sides of the spectrum null sub-carriers (guard bands), called virtual sub-carriers (see Figure 4-5). Furthermore, in order to avoid the DC problem, a null sub-carrier can be put in the middle of the spectrum, i.e., the DC sub-carrier is not used. 4.1.4 D/A and A/D Conversion, I/Q Generation The digital implementation of multi-carrier transmission at the transmitter and the receiver side requires digital-to-analog (D/A) and analog-to-digital (A/D) conversion and methods for modulating and demodulating a carrier with a complex OFDM time signal. Multi-Carrier Modulation and Demodulation 121 Total channel bandwidth Guard band DC sub-carrier (not used) Unused sub-carriers i.e.Virtual sub-carriers Guard band Unused sub-carriers i.e.Virtual sub-carriers Useful bandwidth Figure 4-5 Virtual sub-carriers used for filtering 4.1.4.1 D/A and A/D Conversion and Sampling Rate The main advantage of an OFDM transmission and reception is its digital implementation using digital FFT processing. Therefore, at the transmission side the digital signal after digital IFFT processing is converted to the analog domain with a D/A converter, ready for IF/RF up-conversion and vice versa at the receiver side. The number of bits reserved for the D/A and A/D conversion depends on many param- eters: i) accuracy needed for a given constellation, ii) required Tx/Rx dynamic ranges (e.g., difference between the maximum received power and the receiver sensitivity), and iii) used sampling rate, i.e., complexity. It should be noticed that at the receiver side, due to a higher disturbance, a more accurate converter is required. In practice, in order to achieve a good trade-off between complexity, performance, and implementation loss typically for a 64-QAM transmission, D/A converters with 8 bits or higher should be used, and 10 bits or higher are recommended for the receiver A/D converters. However, for low-order modulation, these constraints can be relaxed. The sampling rate is a crucial parameter. To avoid any problem with aliasing, the sampling rate f samp should be at least twice the maximum frequency of the signal. This requirement is theoretically satisfied by choosing the sampling rate [1] f samp = 1/T samp = N c /T s = B. (4.11) However, in order to provide a better channel selectivity in the receiver regarding adjacent channel interference, a higher sampling rate than the channel bandwidth might be used, i.e., f samp >N c /T s . 4.1.4.2 I/Q Generation At least two methods exist for modulating and demodulating a carrier (I and Q generation) with a complex OFDM time signal. These are described below. Analog Quadrature Method This is a conventional solution in which the in-phase carrier component I is fed by the real part of the modulating signal and the quadrature component Q is fed by the imaginary part of the modulating signal [65]. The receiver applies the inverse operations using the I/Q demodulator (see Figure 4-6). This method has two drawbacks for an OFDM transmission, especially for large numbers 122 Implementation Issues Local oscillator f c Low pass filter A/D converter A/D converter cos(.) sin(.) I Q Sampling rate 1/T samp N c -point FFT (complex domain) Low pass filter Figure 4-6 Conventional I/Q generation with two analog demodulators of sub-carriers and high-order modulation (e.g., 64-QAM): i) due to imperfections in the RF components, it is difficult at moderate complexity to avoid a cross-talk between the I and Q signals and, hence, to maintain an accurate amplitude and phase matching between the I and Q components of the modulated carrier across the signal bandwidth. This imperfection may result in high received baseband signal degradation, i.e., interference, and ii) it requires two A/D converters. A low cost front-end may result in I/Q mismatching, emanating from the gain mismatch between the I and Q signals and from non-perfect quadrature generation. These problems can be solved in the digital domain. Digital FIR Filtering Method The second approach is based on employing digital techniques in order to shift the complex time domain signal up in frequency and produce a signal with no imaginary components which is fed to a single modulator. Similarly, the receiver requires a single demodulator. However, the A/D converter has to work at double sampling frequency (see Figure 4-7). The received analog signal can be written as r(t)= I(t)cos(πt /T samp ) + Q(t) sin(π t/T samp ), (4.12) where T samp is the sampling period of each I and Q component. By doubling the sampling rate to 2/T samp we get the sampled signal r(l)= I(l)cos(π l/2) + Q(l) sin(πl/2). (4.13) Low pass filter Delay N c -point FFT (complex domain) FIR Filter I Q (−1) l (−1) l Sampling frequency 2/T samp 1/T samp 1/T samp De- Mux r(2l +1) r(2l) Local oscillator f c −1/(2T samp ) A/D Figure 4-7 Digital I/Q generation using FIR filtering with single analog demodulator Synchronization 123 This stream can be separated into two sub-streams with rate 1/T samp by taking the even and odd samples r(2l) = I(2l)cos(πl) + Q(2l) sin(π l) r(2l + 1) = I(2l + 1) cos(π(2l + 1)/2) + Q(2l + 1) sin(π(2l + 1)/2) (4.14) It is straightforward to show that the desired output I and Q components are related to r(2l) and r(2l+1) by I(l)= (−1) l r(2l) (4.15) and the Q(l) outputs are obtained by delaying (−1) l r(2l + 1) by T samp /2, i.e., passing the (−1) l r(2l + 1) samples through an interpolator filter (FIR). The I(l) components have to be delayed as well to compensate the FIR filtering delay. In other words, at the transmission side this method consists (at the output of the complex digital IFFT processing) of filtering the Q channel with an FIR interpolator filter to implement a 1/2 sample time shift. Both I and Q streams are then oversampled by a factor of 2. By taking the even and odd components of each stream, only one digital stream at twice the sampling frequency is formed. This digital signal is converted to analog and used to modulate the RF carrier. At the reception side, the inverse operation is applied. The incoming analog signal is down-converted and centered on a frequency f samp /2, filtered and converted to digital by sampling at twice the sampling frequency (i.e., 2 f samp ).Itis de-multiplexed into the 2 streams r(2l) and r(2l + 1) at rate f samp = 1/T samp . The I and Q channels are multiplied by (−1) l to ensure transposition of the spectrum of the signal into baseband [1]. The Q channel is filtered using the same FIR interpolator filter as the transmitter while the I components are delayed by a corresponding amount so that the I and Q components can be delivered simultaneously to the digital FFT processing unit. 4.2 Synchronization Reliable receiver synchronization is one of the most important issues in multi-carrier communication systems, and is especially demanding in fading channels when coherent detection of high-order modulation schemes is employed. A general block diagram of a multi-carrier receiver synchronization unit is depicted in Figure 4-8. The incoming signal in the analog front end unit is first down-converted, performing the complex demodulation to baseband time domain digital I and Q signals of the received OFDM signal. The local oscillator(s) of the analog front end has/have to work with sufficient accuracy. Therefore, the local oscillator(s) is/are continuously adjusted by the frequency offset estimated in the synchronization unit. In addition, before the FFT operation a fine frequency offset correction signal might be required to reduce the ICI. Furthermore, the sampling rate of the A/D clock needs to be controlled by the time synchronization unit as well, in order to prevent any frequency shift after the FFT oper- ation that may result in an additional ICI. The correct positioning of the FFT window is another important task of the timing synchronization. The remaining task of the OFDM synchronization unit is to estimate the phase and amplitude distortion of each sub-carrier, where this function is performed by the channel estimation core (see Section 4.3). These estimated channel state information (CSI) values 124 Implementation Issues Channel decoder Channel Estimation Frequency Synchronization - Freq. offset correc. before FFT - Freq. offset correc. of the LO Receiver, Rx Channel state information (CSI) Rx Data Time Synchronization - FFT window positioning - Sampling clock control Sampling clock control FFT window control Freq. offset control References/Pilots References/Pilots Automatic gain control LO Frequency control Common phase error Complex valued data path De-mapper & De-interl. Despreader (only for MC-SS) De- framing FFT A/D (I/Q Gen.) Analog front end Figure 4-8 General block diagram of a multi-carrier synchronization unit are used to derive for each demodulated symbol reliability information that is directly applied for despreading and/or for channel decoding. An automatic gain control (AGC) of the incoming analog signal is also needed to adjust the gain of the received signal in its desired values. The performance of any synchronization and channel estimation algorithm is determined by the following parameters: — Minimum SNR under which the operation of synchronization is guaranteed, — Acquisition time and acquisition range (e.g., maximum tolerable deviation range of timing offset, local oscillator frequency), — Overhead in terms of reduced data rate or power excess, — Complexity, regarding implementation aspects, and — Robustness and accuracy in the presence of multipath and interference disturbances. In a wireless cellular system with a point-to-multi-point topology, the base station acts as a central control of the available resources among several terminal stations. Signal transmission from the base station towards the terminal station in the downlink is often done in a continuous manner. However, the uplink transmission from the terminal station towards the base station might be different and can be performed in a bursty manner. In case of a continuous downlink transmission, both acquisition and tracking algo- rithms for synchronization can be applied [22], where all fine adjustments to counteract time-dependent variations (e.g., local oscillator frequency offset, Doppler, timing drift, common phase error) are carried out in tracking mode. Furthermore, in case of a continu- ous transmission, non-pilot aided algorithms (blind synchronization) might be considered. However, the situation is different for a bursty transmission. All synchronization param- eters for each burst have to be derived with required accuracy within the limited time duration. Two ways exist to achieve simple and accurate burst synchronization: . Implementation Issues Spreader (only for MC- SS) Interleaver & Mapper OFDM D/A Analog front end Channel decoder Despreader (only for MC- SS) Demapper & Deinterl synchronization. After option- ally deinterleaving, despreading (only in the case of MC- SS) and demapping, the channel decoder corrects the channel errors to guarantee