NHK Laboratories Note No. 476

A Study on Adaptive Soft-Decision Decoding
for QPSK-OFDM on Multipath Channels

YIM Zungkon*, Naohiko IAI,Kenichi TSUCHIDA, and Shigeki MORIYAMA
(Digital Broadcasting Networks Division)
* A visiting researcher from KBS (Korean Broadcasting System)

  This paper describes an adaptive soft-decision Viterbi decoding technique for QPSK-OFDM transmission on multipath channels. An OFDM signal that employs multi-carrier modulation can be demodulated coherently by using pilot signals under a multipath environment. Because an equalizer compensates not only the corrupted signal but also the noise components, the characteristic of noise varies with the carrier position in an OFDM signal. Conventional Viterbi decoders are designed to correct received signals having an invariable noise characteristic. This paper proposes a noise estimation method to determine a variable noise characteristic with the carrier position and an adaptive soft-decision technique that adjusts the metric step size to the result of the estimation process. The simulation results show that the adaptive soft-decision decoding technique described in this paper is useful for designing QPSK-OFDM receivers.

1. Introduction
  Many countries around the world are investigating digital broadcasting systems. For digital sound broadcasting in particular, the majority of the new systems utilize orthogonal frequency division multiplexing (OFDM) methods. Some examples are the Eureka-147 DAB (Digital Audio Broadcasting) system of Europe, the IBOC (In-Band on-Channel) system of the USA, and the ISDB-T (Integrated Services Digital Broadcasting - Terrestrial) system in Japan.
  In terrestrial transmission systems for mobile reception, quadrature phase shift keying (QPSK)-OFDM or differential QPSK (DQPSK)-OFDM methods are valued for their good reception characteristics and robustness to burst errors. The QPSK-OFDM method's advantage is that a smaller necessary electric field strength delivers better bit error rate (BER) characteristics compared to existing analog modulation methods.
  In this paper, we propose an adaptive soft-decision decoding technique employing variable soft-decision metric step size according to the estimated noise power spectral density for each carrier in an OFDM signal. The estimation technique to determine noise power spectral densities for each carrier is also presented. In addition, we show how to draw the soft-decision metric step size using the channel frequency response.

2. OFDM signal with multipath interference

  In the OFDM method, pilot signals and guard interval signals are usually inserted within the data signals. By compensating the amplitude and phase of a complex vector signal, ideal demodulation can be achieved. In such a case, there is no distortion in amplitude and phase of the complex vector signal [1].
  In reality, because of multipath signals, ripples occur in the transmission spectrum. But if the multipath signals are located within the guard interval duration, almost all of the original signals can be recovered by compensating the amplitude and phase according to the channel frequency response. When there is not a multipath signal, the OFDM signal   s(t)  can be obtained by


where  ,    is the central frequency of the OFDM signal,    is the frequency spacing between each carrier,  m  is the number of carriers between    ,and  C (m)  is the complex data vector for the mth carrier.
Under a multipath environment with one echo signal, when the amplitude of the undesired echo signal is   , the delay time is    within the guard interval duration and the phase difference is   , the resultant composite signal  g (t)  can be represented as equation (2):


  From equation (2), the amplitude  A (m)  of the transfer function is derived as the following equation (3) [2]:


  The frequency characteristics of the composite signal with an echo signal are changed by the parameters of   , , or   . The simplified concept is shown in Figure 1.

(a) Spectrum of OFDM signal (no echo)       (b) Spectrum of OFDM signal (one echo)
Figure 1. Transmission model of OFDM signal with one echo signal

3. CNR variation by amplitude compensation
      If the echo signals are added to the desired signals on the additive white Gaussian noise (AWGN) channel, ripples occur in the transmission band and the carrier-to-noise ratio (CNR) varies widely (see Figure 2 (a)). According to the CNR of each carrier, the BER characteristic of each carrier is also caused to varying. Applying an equalization process using pilot signals as scattered pilots (SPs), the transmission characteristics can be determined by only the CNR of each carrier.
  The noise power spectral density  N0(m)  of each carrier can be obtained by equation (4) for the noise power spectral density  N0 , which is added to OFDM signals. The simplified results are plotted in Figure 2 (b).


(a) Received spectrum (AWGN, one echo) (b) Compensated spectrum
Figure 2. Noise power density variation for the compensated OFDM carriers

4. Estimation of Noise Power Density

  The noise power spectral density  N0  is not given in a real case, so this paper proposes an estimation method of  N0  added to transmission signals. As shown in Figure 3, assuming a set of four OFDM symbols, all the pilot carriers are extracted and the data carrier positions are interpolated by the data '0'. After extracting the pilot carriers, the pilot carrier set is transformed with an inverse fast Fourier transform (IFFT). Almost all the energy is concentrated in the main lobes, as shown in Figure 4.

Figure 3. Arrangement of pilot signals

Figure 4. IFFT result of one set of pilot carriers (no AWGN)

  In contrast, because of the inherent nature of AWGN, the noise components are evenly distributed over the transmission band. The noise components can be obtained from the part of the time domain that is not in the main lobes, and are used to calculate the value of   , the estimated noise power spectral density (see Figure 5).

Figure 5. IFFT result for one set of pilot carriers (CNR = 24 dB)

  The transfer function of the transmission channel corrupted by multipath signals and AWGN can be obtained by using the SPs. By using a coherent equalizer [3] for the amplitude and phase compensated signals, we can presume that the variation of noise power spectrum density  (m)  for the mth carrier is in inverse proportion to the estimated amplitude   (m)  of the transfer function as shown in equation (5):


5. Soft-Decision Decoding

5.1 Soft-decision for Viterbi decoder.

  The binary phase shift keying (BPSK) and QPSK demodulators generate analog signals that require conversion to a digitized format before the Viterbi decoder process. Figure 6 shows a diagram of a PSK demodulator with the Viterbi decoder. The use of two-level quantization by a 1-bit analogue-digital converter (ADC) is commonly referred as "hard-decision" decoding. When the quantization level of the ADC is greater than two, the decoding is called "soft-decision" decoding.

Figure 6. PSK series demodulator quantizer with Viterbi decoder

5.2 Uniform quantizer

  In Figure 7, a characteristic of a uniform quantizer for 3-bit soft-decision is shown. The horizontal axis shows the analog or high-precision digital input signal level. The value in the horizontal axis indicates the decision metric step size. The vertical axis shows the quantized output level.

Figure 7. Uniform quantizer

5.3 Adaptive quantizer

  Assuming that the channel is modeled using AWGN with a spectral density  N0/2 , the mean value  r  and variance    of the received signal with energy  E s are given by equation (6):


  The 3-bit soft-decision quantizer performs better if the decision metric step size  D  is given by equation (7)


  where the  q  value should be in range of  0.45 to 0.7 [4][5][6]. Using equation (6) for    and 0.5 for  q , the step size results in equation (8):


  Each carrier has an independent noise spectral density since it has been amplitude and phase compensated. We can obtain the soft-decision metric step size  D (m)  for the mth carrier by:


6. Simulation

6.1 Simulation conditions

  Transmission parameters for the computer simulation are given in Table 1. The channel frequency response was estimated and equalization was performed. The pilot signals used to estimate transmission characteristics are referred to as SPs and were inserted in the signal every third interval in the carrier direction and every fourth interval in the time direction. These SPs were modulated by BPSK, and their amplitude was boosted to 4/3 that of QPSK average amplitude [7]. The multipath conditions and the Viterbi decoder parameters are respectively shown in Table 2 and Table 3.

Table 1. Transmission parameters for computer simulation

Transmission Method ISDB-T OFDM
Mode 1
Number of Segments 13
Number of Carriers 1405
Carrier Spacing 3.97 kHz
Useful Symbol Duration 252   sec
Guard Interval 31.5   sec
Modulation QPSK
Inner Code Punctured Convolution CodeCoding Rates = 1/2, 2/3, and 3/4
Outer Code No
Interleaving Inter-segment Interleaving

Table 2. Multipath conditionran

Multipath Delay Signal
Number of Delayed Waves 1
Delayed Time 14.8887   sec
DUR 3, 6, 9, 12, 15 dB

Table 3. Viterbi decoder parameters

Viterbi Decoder
Number of Quantization Level 8 (3 bits)
Constraints Length 7
Number of Memory Depth 70

6.2 Simulation results

  Figures 8 and 9 show the BER performances of convolutional coded QPSK-OFDM under the multipath conditions of the adaptive technique and those of the conventional uniform technique. Figure 8 is the result for a fixed convolutional code rate of 1/2, in which the desired-to-undesired ratio (DUR) ranges from 3 dB to 15 dB. Figure 9 shows the result of a fixed DUR at 3 dB for code rates of 1/2, 2/3, and 3/4.
  Focusing our attention on the proposed soft-decision decoding with an adaptive quantizer, we can see that for all code rates, the adaptive technique has better performance.

Figure 8. Result of adaptive soft-decision decoding
(fixed code rate of 1/2, varying DUR)

Figure 9. Result of adaptive soft-decision decoding
(fixed DUR of 3 dB and varying code rates of 1/2, 2/3, and 3/4)

  Figure 10 shows the improvement in CNR by the adaptive technique compared to the conventional uniform quantizer at the BER of    . We can see that the adaptive technique can achieve a 0.41.4 dB improvement in CNR characteristics under certain conditions.

Figure 10. Improvement in CNR

7. Conclusion

  The adaptive soft-decision decoding technique for OFDM receivers using scattered pilot signals improves reception performance under multipath distortion. The proposed technique first estimates channel noise spectral density and the channel frequency response, then calculates the soft-decision metric step size for each QPSK-OFDM carrier. The results of a computer simulation reveal that the soft-decision decoding technique can significantly improve characteristics compared to the conventional technique that employs a uniform quantizer.


[1] S. Nakahara, M. Okano, M. Takada, and T. Kuroda, "Digital Transmission Scheme for ISDB-T and Reception Characteristics of Digital Terrestrial Television Broadcasting System in Japan", IEEE Transactions on Consumer Electronics, Vol. 45, No. 3, pp. 563-570, August 1999.
[2] S. Nakahara, M. Okano, M. Takada, and T. Kuroda, "Digital Transmission Scheme for ISDB-T and Reception Characteristics of Digital Terrestrial Television Broadcasting System in Japan", IEEE Transactions on Consumer Electronics, Vol. 45, No. 3, pp. 563-570, August 1999.
[3] M. Yamashita, M. Kuwabara, M. Itami, H. Ohta, and K. Itoh, "A Study on Equalization of OFDM using a Pilot Symbol", ITE Technical Report Vol. 22. No. 25, pp.13-18, May, 1998.
[4] AHA Application Note ANRS07-0795, "Soft Decision Thresholds and Effects on Viterbi Performance".
[5] A.J. Viterbi, "Error Bounds for Convolutional Codes and An Asymptotically Optimum Decoding Algorithm," IEEE Transactions on Information Theory, vol. IT-13, April, 1967, pp. 260-269
[6] Qualcomm Application Note AN1650-2, "Setting Soft-Decision Thresholds for Viterbi Decoder Code Words from PSK Modems".
[7] S. Nakahara, M. Takada, K. Tsuchida, and T. Kuroda, "A Study on soft decision decoding of 64QAM modulated OFDM signals under multi path distortion", ITE Technical Report Vol. 22, No. 34. pp. 1-6, June, 1998.

Tanaka Yim Zungkon
Yim Zungkon received the B. Eng. and M. Eng. degrees in electronic engineering from Inha University, Inchon, Korea, in 1994 and 1996 respectively. He joined Korean Broadcasting System (KBS) in 1996. Since 1996, he has been with KBS Technical Research Institute, where has been engaged in the research on digital broadcasting system. From 2000 to 2001 he stayed at NHK Science and Technical Research Laboratories as a visiting researcher of NHK Research Award for invitation of researchers from organizations participating in ABU(Asia-Pacific Broadcasting Union).
Inoue Naohiko Iai
Naohiko Iai received the B. Eng. and M. Eng. degrees in Department of Applied Physics from Osaka University, Suita, Japan. He joined NHK in 1993. Since then he has been with NHK Science and Technical Research Laboratories, where he has been engaged in research on millimeter-wave circuits, digital transmission technique, digital terrestrial broadcasting systems and their applications to intelligent transport systems.
Tanaka Kenichi Tsuchida
Kenichi Tsuchida received the B. Eng. and M. Eng. degrees in information engineering from Tohoku University, Sendai, Japan, in 1988 and 1990 respectively. He joined NHK in 1990. Since 1992 he has been with NHK Science and Technical Research Laboratories, where he has been engaged in research on digital terrestrial broadcasting systems and digital outside broadcasting link.
Inoue Shigeki Moriyama
Shigeki Moriyama received the B. Eng. and M. Eng. degrees in electronic engineering from Toyohashi University of Technology in 1981 and 1983 respectively. He received Dr. Eng. in electronic engineering from University of Tokyo in 1999. He joined the NHK in 1983. Since 1986 he has been with NHK Science and Technical Research Laboratories, where he has engaged in research on satellite broadcasting systems, data multiplexing broadcasting systems, digital outside broadcasting links and digital terrestrial broadcasting systems.

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