A TCM OFDM Software Transceiver
Ping-han Chiang, Ying-tzu Huang, Tsai-wen Chen, I-hsueh Lin, and Kwang-cheng Chen
Department of Electrical Engineering
National Taiwan University
Abstract — Orthogonal Frequency Division Multiplexing (OFDM), a multicarrier technique, is capable of coping with highly dispersive channels. In this paper, we adopt advanced Trellis Coded Modulation (TCM)-OFDM, instead of Convolutional Code (CC)-OFDM adopted by HIPERLAN/2 and IEEE 802.11a, to enhance the SNR requirement. A sophisticated OFDM transceiver is designed, including synchronizers in every aspect and the data-aided (DA) equalizer. We focus on the design and simulation of the high-speed OFDM system suitable for Wireless Local Area Network (WLAN) applications with the cons ideration of software radio implementation.
I. Introduction
OFDM is a promising technique that is able to cope with multipath channels, especially high speed wireless data communications. An OFDM system divides the available spectrum into several subchannels. The frequency responses of the subchannels are overlapping and orthogonal to each other, hence is named OFDM. When the subchannels are narrowband, they experience almost flat fading, and equalization is relatively simple. In addition, we further pioneerly adopt TCM, a breakthrough of combining modulation and coding by Gottfried Ungerboeck, to enhance link performance than state-of-the-art standard, such as IEEE 802.11a and ETSI HIPERLAN/2.
One improvement that distinguishes OFDM from ordinary FDM systems is the use of Discrete Fourier Transform (DFT)[1], which can be executed more quickly by Fast Fourier Transform (FFT) algorithm instead of oscillators to send the signals to high frequencies. Practical application of the OFDM system lies in the use of the cyclic prefix (CP)[2]. Traditionally, a
preceding guard interval (GI) can help reduce the intersymbol interference (ISI). However, to prevent the received signals from intercarrier interference (ICI), barely a GI is not enough. To maintain the orthogo nality required to avoid ICI, the CP, which is a copy of the last part of the OFDM symbol, is introduced. The use of CP not only makes the transmitted signals periodic, but also reduces ISI and ICI in a constructive way.
Owing to the irreducible error floor in an uncoded OFDM system[3], the adoption of coding is therefore inevitable. According to the comparison made in [3], a Turbo-coded OFDM in spite of tremendous coding delay works the best among all the coding schemes, while it is also the most complicated one in algorithm and implementation. The TCM-OFDM system has the next best performance and is better than CC-OFDM adopted by HIPERLAN/2 and IEEE 802.11a with near complexity. Consequently, TCM-OFDM strikes the best compromise between performance and complexity.
II. Principle
Compared with regular single carrier systems, the complexity of equalization in an OFDM system does not grow exponentially with higher data rates. However, constructing OFDM systems is not simple owing to its high sensitivity to synchronization errors. Since orthogonality maintains only when the transmitter and receiver use exactly the same frequencies, frequency synchronization is thus critical to the performance of an OFDM system. Besides, timing offsets lead to unsatisfied performance in interpolation-type channel estimation[4], which affects the equalization simultaneously. Therefore, how to develop effective synchronization algorithms of satisfactory performance and
complexity has been an important issue. Due to the inevitable adverse effects in the wireless environment, the transmitted signal is bound to be distorted under such channels. Therefore, to acquire the original desired signals, proper procedures must be taken, such as channel estimation, a characteristic way in coherent detection. Although differential detection needs no channel estimation in contrast to
coherent detection, it has several drawbacks: the relatively poor performance, smaller tolerance of delay spread[5], and the difficulty in handling amplitude- modula ted systems. Therefore, coherent detection is adopted in our design. We use DA interpolation-type channel estimation, which uses only the pilot subcarriers to acquire the sampled channel frequency response. To compensate the channel effects by zero forcing, simply multiply the signal by the reciprocal of the interpolated channel frequency response.
In the design of an OFDM receiver, at least three synchronization problems must be considered. The first is the frame timing synchronization problem, which can be solved by a careful design of the preamble. The second problem is frequency synchronization, which can be estimated and then compensated by exploiting information contained in the received preambles, pilot subcarriers, guard band, and CP. The last problem is about symbol timing and sample clock synchronization, which can be estimated by us ing pilot subcarriers and CP.
III. System Model
The block diagram of our design is shown in Fig. 1. The OFDM baseband signal of IFFT output using N subcarriers is[6]
∑
− = = 1 0 2 ) ( 1 ) ( N k kn j k n X j e N j x π (1)where Xk(j) is the modulated complex data of the
k-th subcarriers in the j-th OFDM symbol, and n
is the sample time. The transmitted OFDM symbol with CP is
∑
− − = = 1 ( ) ) ( N G n n n j x j s (2)where G is the length of guard interva l and the received n-th sample in the j-th OFDM symbol is[6]
∑
− = ⋅ = 1 0 2 ) ( 1 ) ( N k k N kn j k n X j e H N j y π (3) ) ( ~ 2 ) ( 2 2 0 s sym fT T j t k T T k j nT jT n e sym u u d + + ∆ + + ∆ +π φ π πwhere Hk is the channel frequency response at the
k-th subcarrier, and Td, ∆t(j), φ0, and ∆f are
symbol timing offset, sample timing offset, phase offset, and frequency offset in the j-th OFDM
symbol, respectively. Tu, Ts, and Tsym are the
useful data duration, sample interval and the OFDM symbol duration, respectively. The FFT output for the k-th subcarriers in the j-th OFDM symbol is k k fT T j t k T T k j k k k j X j H e I N Y u u sym d + + = ∆ + + ∆ +π φ π π 2 ( ) 2 2 0 ) ( ) ( (4)
where Ik is ICI from carrier frequency offset and
Nk is noise for the k-th subcarrier. Thus the phase
rotation at the k-th subcarrier of the j-th OFDM symbol from synchronization error is[6]
sym u d k k fT T j t T j = π +∆ +φ + π∆ φ ( ) 2 ( ) 0 2 (5) IV. Design 4-1 Parameters
The parameters set in our system are listed
Serial to Parallel TCM . . . . . . IFFT Parallel to Serial . . . Cyclic Prefix Insertion DAC LPF Channel ADC LPF Cyclic Prefix Removal Serial to Parallel . . . FFT . . . Viterbi . . . Parallel to Serial
in Table 1. Since a radix-4 FFT is the least complex and the most efficient one in algorithm, we choose the number of FFT points as 64 here. The CP interval is assumed 1/4 long as the useful data duration. In this design, the accuracy of the carrier center frequency is within +62.5 ppm at 5GHz. Therefore, the range is set +50 ppm here to be on the safe side. Besides, The first subcarrier, namely the dc term, is set zero in order to facilitate the ADC/DAC. The outer subcarriers are set null to serve as the guard band
in using a filter. The pilots are allocated at +8th,
-8th, +24th, and -24th, respectively.
Table 1. System Parameters
Data rate 12Mbps
Modulation QPSK
Coding 1/2 TCM
FFT point 64
Sample rate 20Msample/sec
Sample interval 0.05μs
OFDM Symbol
Interval 4μs
Useful Data Duration 3.2μs
CP period 0.8μs Data subcarriers 48 Subcarrier spacing 0.3125MHz Pilot subcarrier 4 Pilot spacing 4.375MHz Carrier center frequency 5GHz (Accuracy +50ppm) Occupied bandwidth 16.6MHz
4-2 Frame Timing and Carrier Frequency Synchronization
We adopt the Minimum Mean Square Error (MMSE) algorithm for frame timing in our system because of its performance advantage over Maximum Correlation (MC) algorithm and lower complexity than Maximum Likelihood (ML) algorithm[7]. Since our system is designed for burst-mode or packet-type transmission, certain form of power detecting wake-up
algorithm must be implemented. A long preamble can get a more accurate frequency offset estimate but the lock-in range is comparatively small. On the contrary, a shorter preamble can get a larger acquisition range, but accuracy is not as good. To meet the requirement of our system, we use short preambles first, which are used for coarse frequency synchronization, followed by long preambles, which are for frame timing and fine frequency synchronization, to get the best performance.
The structure of the preambles in our system is shown in Fig. 2. The first 32 samples are for wake-up use. Then, two identical 16 samples are used as short preambles, specified in IEEE 802.11a[8], to do coarse and wide range frequency offset estimation. Afterwards, we use 144 samples as long preambles to do fine frequency offset estimation and accurate frame timing estimation. The long preambles, specified in IEEE 802.11a[8], contain two identical 64-sample OFDM symbols. The usage of the 8-sample inverse cyclic prefix in the front of the long preambles and inverse cyclic postfix at the end of the long preambles will be discussed shortly.
The MMSE frame timing and carrier frequency synchronization algorithm is stated as follows. The received power sum and the
complex correlation inside a frame of Ds received
samples are[7] 2 1
∑
− + = =k Ds k m m k y P (6)∑
− + = + = 1* s s D k k m D m m k y y S (7)In our system, Ds=64 for long preambles and
Ds=16 for short preambles. The receiver
continuously monitors the power sum in the receiving window, once the energy reaches a
Long preamble Short preamble
16 pts 16 pts 8 64 pts 64 pts 8
Fig. 2. Structure of data frame preambles
×-1 ×-1
16 pts 16 pts Wake -up preamble
threshold value obtained by simulation, the receiver is waked up to perform frame synchronization algorithm. With MMSE criterion, the frame starting position is indicated as the
metric Mk =2Sk −Pk −Pk+Ds reaches its
maximum value. That is, the first sample of the two identical OFDM symbols in the preambles
should be at k
k
M
Kˆ=argmax . In the process of
finding the starting position, we store the maximum amplitude of M, the corresponding correlation S and the counter value[9]. If the incoming amplitude of M is larger than the stored maximum amplitude of M, the new values are updated and the counter value is reset. When the searching range the counter records reaches certain optimal value obtained by simulation, we take the stored maximum as the desired value. After the frame starting position Kˆ is found, we can use it to estimate the normalized frequency
offset ξ by the following equation
) ( 2 ˆ ˆ k S angle Ds D π ξ= (8)
where D is the length of an IFFT/FFT window in
the data frame, i.e. D=64 in our system. ξ is
defined as the frequency offset ∆f divided by
OFDM subcarrier frequency spacing ∆fsub, i.e.
sub f f ∆ ∆ =
ξ . Thus we can get the accurate frame
timing and fine frequency offset estimation. The expectation of power sum P, absolute value of complex correlation S, and metrics M in the interval of receiving long preamble are illustrated in Fig. 3.
We can see that apart from ξˆ , any
s D D n + =ξ ξ ˆ , with n∈Z , is a possible
normalized frequency offset estimate. Hence the normalized frequency offset must be confined in a range smaller than
Ds D
before we do the fine frequency offset estimation. Since a short
preamble has smaller Ds, it can find frequency
offset in a larger range.
The 8-sample inverse cyclic prefix and inverse cyclic postfix mentioned above are constructed to improve timing estimation accuracy. As the correlation window aligns with the two identical OFDM symbols in the preambles, i.e. at the frame starting position, the metric M reaches its maximum value. In order to avoid possible ambiguity, M is expected to decrease as quickly as possible when the window moves slightly away from the frame starting position. Consider the situation that the receiving window is one sample before the aligned position,
that is, k =kˆ−1. Since the sample just before
the identical OFDM symbols in our long preamble is the inverse of the last sample in the
OFDM symbol, the Sk-1 in our design with the
inverse cyclic prefix and inverse cyclic postfix
will be smaller than the Sk-1 with the ordinary
cyclic prefix, while Pk-1 remains the same. This
will make the metrics M using such preamble
change more sharply than those using
conventional two identical symbol preambles. The improvement of such design is shown in Fig. 4.
Besides, when coarse frequency synchronization is working, we store necessary information in the buffer beforehand for the following frame timing and fine frequency synchronization to compute the summatio n recursively and reduce the complexity of track-back. After getting the coarse frequency offset estimation, we compensate the correlation values S of the incoming samples and the stored
values by multiplying with e−j2πξ inferred from
Eq.(7).
4-3 Symbol Timing Synchronization
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 0 1 2 E ( P ) 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 0 0 . 5 1 E ( S ) 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 - 1 . 5 -1 - 0 . 5 0 E ( M ) S N R = 1 0 d B Power wake up threshold Wake up by power sum Frame start position
The pilots, originally used for channel
estimation, simultaneously carry some
information about timing. Besides the pilots, the CP of each transmitted OFDM symbol[10] with ML algorithm can also help in the symbol timing syncronization. The metrics from CP and pilot are 2 1 2 1 * 2 n D L k k n n L k k n D n n cp k y y y y + − + = − + = +
∑
∑
− + = Λ ρ (9)∑
∑
+=− + − − + = − + − + = Λ 1 * 1 ) ( ) 1 ( L k k n k n D n n D k k n k n n p k ρ y m ρ y y m (10)where L is the length of CP, mk is the OFDM
symbol containing purely pilots in the time domain, and fixed
1 + = SNR SNR ρ is determined
by simulation to circumvent the SNR estimation. The OFDM symbol starting position is indicated
as the joint metric p
k cp
k
k = Λ + − Λ
Λ ρ (1 ρ)
reaches its maximum value. The expectation of
Λp
, Λcp and Λ is illustrated in Fig. 5. The Λp term
increases the sharpness of Λ, hence the accuracy
of the symbol timing estimation. The computing complexity can be reduced by calculating and
comparing the Λ of only a few points around the
80th point. The beginning of the next symbol is
thus set at the point of the maximum Λ. Such
method can surely improve the computation efficiency significantly. Besides the integer sample offset of symbol timing synchronization error, there is the fractional sample offset of sample clock synchronization error. That the phase rotation of sample timing offset is negligible can be seen from Eq.(5). Therefore, the
sample clock synchronization is excluded here.
4-4 Equalization
In our design, channel estimation is achieved by the known pilots, since the decision-directed approach is not applicable in fast fading channels and is vulnerable to error propagation[11]. Therefore, interpolation is needed. The optimal interpolation filter is based on MMSE; however, due to significant computation complexity, a suboptimal approach based on Least Square (LS) and DFT that is not sensitive to the channel statistics[11] is adopted instead. As mentioned above, the use of FFT in place of DFT also helps reduce the time needed to complete the channel estimation. Firstly, the pilots are extracted and compared with the receiver-known ones, while the polarity of the previously known pilots depends on the cyclic extension of the 127 elements sequence, defined in IEEE 802.11a[8], and each of the elements is used for an OFDM symbol. In other words, the extracted pilots are divided by the known pilots to get a first estimate of the channel. Since the pilot pattern in our design is 1 or –1, we can use multiplication rather than division to ease the computing load. The four pilots are allocated uniformly along the 64 subcarriers, so we send the results through 4-point IFFT to the time domain. Afterwards, the outputs of the 4-point IFFT along with phase rotation and padded zeros, which are for interpolation use in the frequency domain, are sent to the 64-point FFT. The equalization coefficient is then acquired and equalization is done by multiplying the signal by its reciprocal. 220 230 240 250 260 270 280 290 300 310 320 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 Conventional preamble Our improved preamble Frame start position
Fig.4 Expectation of M near frame start position
0 10 20 30 40 50 60 70 80 -0.1 0 0.1 E(Λp) 0 10 20 30 40 50 60 70 80 -0.2 -0.1 0 0.1 E(Λcp) 0 10 20 30 40 50 60 70 80 -0.1 0 0.1 E(Λ)
Fig.5 Symbol Timing Synchronization Symbol start
4-5 TCM and Interleaving
We choose the generator polynomial of TCM with the popular convolutional encoder, used by Global System of Mobile
Communication (GSM), as (23,33)8[12]. The
coding rate, constraint length, and the number of states are 1/2, 5, and 16, respectively. The mapper of Quadratic Phase Shift Keying (QPSK) is generated by set-partitioning, not conventional Gray mapping. The soft-decision Viterbi decoder is implemented without track-back steps to reduce complexity[13]. Although the decode length should be determined by simulation, it is taken as the number of data subcarires for its suitability in our OFDM system. In addition, interleaving is used to overcome burst errors due to deep fading. Because the subchannel gains of OFDM system are the continuous channel frequency responses, the adjacent subchannels experience similar fading. To avoid the poor performance around the notches in frequency dispersive channels the Maximum Likelihood Sequential Estimation (MLSE) algorithm, namely Viterbi algorithm, may suffer, the periodic interleaving, which maps consecutive coded symbols apart from each other, is used to improve the performance [14].
V. Simulations
The overall block diagram of our design is shown in Fig.6. The three types of channels taken in our simulation are listed in Table 2 [15]. Because the influence of Doppler shift is comparatively small in portable applications, it is not included in the simulation. The uniform random frequency offset is set within +1.5
subcarriers spacing, while the uniform random
phase offset is set between +π. The power gain of
the channel is assumed one here.
Table 2. Power Profile of Simulating Channels
Type Power Profile(dB)
AWGN N/A
Rician
Rayleigh 0,-5,-11,-17,-22,-28
The relationship of BER v.s. SNR is as plotted in Fig. 7. As the simulation results justify, the performance of our system is satisfactory as expected.
VI. Conclusion
OFDM is a recently-emphasized technique. Because it enjoys many advantages suitable for the high-speed networks, it is regarded as the best approach to transmit data on the high-speed networks. Owing to its transmission with overlapping orthogonal signals in parallel, it can save the bandwidth in an efficient way. Furthermore, the complexity of the OFDM system does not grow exponentially as the bit rate increases. Therefore, it surely has considerable potential in practical applications. As our simulation results prove, under carefully-chosen algorithms, a TCM-OFDM system can perform quite well over 5 GHz. Not only the multipath problem, but also the frequency offset and the timing offset difficulties can be solved simultaneously. The distortion of channel effects can also be compensated by relatively simple
Fig. 7. The Simulation Results
Input Convolutional
Encoding Interleaving Mapping TCM
Subcarrier Allocation & Pilots Insertion IFFT
Digital Reversal & CP Insertion Wakeup Detecting Channel Simulator Coarse Frequency Synchronization Frame Timing & Fine
Frequency Synchronization
Coarse Frequency Compensation
Symbol Timing & Carrier Frequency Synchronization Carrier Frequency Compensation CP Removal & FFT Pilot Extraction Channel Estimation Equalization Subcarrier Reallocation & Deinterleaving Digit Reversal Viterbi Decoding Output Error Counting Preamble
equalization scheme. Therefore, the future development on software environment, such as DSP, is promising. By exploiting the fixed-point architecture and the code optimization of a fixed-point DSP, the complexity of algorithms and computation can be eased. In conclusion, the future development of such a system is worth anticipating.
VII. Acknowledgement
The authors wish to express their grateful acknowledgement to Prof. Chen Kwang-cheng for his instruc tion in this paper. Furthermore, the authors are thankful for Liao Yi-ching, Liu Pei-chun, Chiu Wei-chen, and Chou Chia-tai for the fruitful discussions.
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