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We investigate iterative trellis decoding techniques for DAB, with the objective of gaining from processing 2D-blocks in an OFDM scheme, that is, blocks based on the time and frequency dimension, and from trellis decomposition. Trellis-decomposition methods allow us to estimate the unknown channel phase since this phase relates to the sub-trellises. We will determine a-posteriori sub-trellis probabilities, and use these probabilities for weighting the a-posteriori symbol probabilities resulting from all the sub-trellises. Alternatively we can determine a dominant sub-trellis and use the a-posteriori symbol probabilities corresponding to this dominant sub-trellis. This dominant sub-trellis approach results in a significant complexity reduction. We will investigate both iterative and non-iterative methods.
The advantage of non-iterative methods is that their forwardbackward
procedures are extremely simple; however, also their
gain of 0.7 dB, relative to two-symbol differential detection
(2SDD) at a BER of

Digital audio broadcasting (DAB) systems, DAB+ systems, and terrestrial-digital multimedia broadcasting (T-DMB) systems use orthogonal frequency division multiplexing (OFDM), for which every OFDM-subcarrier is modulated by

Commonly used

If MSDD is combined with iterative (turbo) processing (parallel concatenated systems were first described by Berrou et al. [

We focus in the present paper on 2D processing, that is, in both the frequency and time domains. We will propose methods based on iteratively demodulating and decoding blocks of received symbols in a DAB-transmission stream. First we will; however, summarize other 2D approaches that are relevant to our work.

The work of ten Brink et al. in [

To obtain a posteriori probabilities of the information symbols in a 2D setting, May, Rohling, and Haase in [

To reduce complexity we accept a small performance loss due to channel-phase discretization (see, e.g., Peleg et al. [

Franceschini et al. [

In this paper, we will focus both on iterative and noniterative decoding techniques for DAB-like systems. In the next section, we will give a short outline of the DAB system. In Section

Terrestrial digital broadcasting systems like DAB, DAB+, and T-DMB, all members of the “DAB family,’’ comprise a combination of convolutional coding (CC), interleaving,

DAB convolutional encoder, interleaver, differential encoders, and multicarrier modulator with an inverse fast Fourier transform (IFFT).

Three services mapped onto consecutive OFDM symbols. Note that there is an overlap between the service since differential modulation is used.

Note, that due to this “idle time,’’ the mix-metric techniques of [

In the following subsections we will describe the transmit processes (convolutional encoding, differential modulation, and OFDM) in more detail.

The convolutional code that is used within DAB has basic code-rate

For each subcarrier,

OFDM in DAB is realized using a

We assume that the channel is slowly varying with an impulse response shorter than the cyclic-prefix length. Moreover, we assume that the channel coherence bandwidth and coherence time span multiple OFDM subcarriers and multiple OFDM symbols. Therefore, the channel-phase and gain might be assumed to be fixed for a number of adjacent subcarriers and consecutive symbols. This is the assumption on which we base our investigations. The channel phase and gain are assumed constant (yet unknown to the receiver) over a

A 2D block of symbols out of an OFDM stream. We are interested in

The receiver, in the case of perfect synchronization, removes the (received version of the) cyclic prefix, and then applies a

In the next subsection, we focus on a single subcarrier.

The sequence

Accepting a small performance loss as in, for example, Peleg et al. [

It is well known and straightforward to show that the

We will start by considering the single-carrier case. For some single subcarrier, we will discuss DE-QPSK modulation with incoherent reception. Based on trellis decoding techniques, we will determine the a posteriori symbol probabilities under the assumption that the (quantized) channel phase is uniform and unknown to the receiver. We also assume the transmitted symbols to be independent of each other and uniform.

In this section, we will focus on noniterative detection. We start our analysis by noting that if we define

Trellis representation of the states

If we would use the standard BCJR algorithm for computing the a posteriori symbol probabilities in the trellis in Figure

An important observation for our investigations is that the trellis can be seen to consist of eight subtrellises

Subtrellis

Note that for the likelihood

In this subsection, we would like to focus on computing the a posteriori symbol probabilities

In our forward pass, we focus on subtrellis

If for

Our proof is based on induction. Clearly for

Also in the backward pass we first focus only on subtrellis

Based on definition of

Again our proof is based on induction. Note first that for

To determine the a posteriori symbol probability for symbol value

The demodulator that operates according to (

Equation (

We use in our simulations, just like Peleg et al. [

The demodulator calculates, for each OFDM-subcarrier, the a posteriori probability given by (

Figure

Bit-error performance for LLRs computed as in (

We will compare the performance of this demodulator with that of two well-known procedures described in the literature: firstly, to “classical’’ DQPSK [

The simulation results, which are shown in Figure

Next, in Figure

Bit-error performance for LLRs computed as in (

Our simulations demonstrate that for trellis length

With a trellis length of

After having concluded that we cannot make

We have seen that the trellis-length

Now we assume that in each subcarrier

Just like in the single carrier case, we can determine the a posteriori subtrellis probabilities:

Now the a posteriori symbol probability for

This suggests that the demodulator first determines the a posteriori subtrellis probabilities (weighting coefficients) using (

Equation (

In the previous section, we analyzed and simulated the single subcarrier approach. Here we will discuss the simulations corresponding to the multi-carrier method. We will again study the coded BER versus the signal-to-noise ratio

Bit-error performance with ideal LLRs for a decomposed multi-carrier trellis for different values of

From Figure

We do not show the results of the dominant subtrellis approach for the multi-carrier case here, since these results are identical to the corresponding results for the single-carrier case shown in Figure

Our investigations for the noniterative 2D-case show that we are very close to the performance of coherent detection of DE-QPSK even for small values of the trellis length

In the following two sections, we consider iterative decoding procedures. Peleg and Shamai [

In the current section, we will investigate iterative decoding procedures for DAB-like systems, which are based on convolutional encoding, interleaving, and DE-QPSK modulation. If we consider DE-QPSK modulation as the inner coding method and convolutional encoding as the outer code, then it is obvious that we can apply techniques developed for serially concatenated coding systems here, see Figure

Structure of the receiver.

We will start in this section by considering the single carrier case and our aim is again to find out what we can gain from decomposing the trellis used in the demodulator into a part that corresponds to the channel phase and a part that relates to differential encoding. In the section that follows, we will consider the multi-carrier setting.

In this subsection, we investigate the forward backward procedures where we drop the assumption that the symbols

Just like Peleg et al. [

Again starting from

To determine the a posteriori symbol probability for symbol value

Using the standard BCJR algorithm for computing the extrinsic symbol probabilities in the trellis in Figure

Here we investigate whether we can decompose the entire trellis for the case where the a priori probabilities are nonuniform. We are interested in decomposing (

It can be shown that

To achieve a complexity reduction, we investigate a method that is based on finding, at the start of a new iteration, the dominant subtrellis first and then do the forward-backward processing for demodulation only in this dominant subtrellis.

Finding the dominant subtrellis for an iteration is done based on the a posteriori subtrellis probabilities

A second approach involves choosing the dominant subtrellis only once, before starting with the iterations. Since before starting the iterations the a priori probabilities

We simulated the Peleg method described in [

Bit error performance of the Peleg method for trellis length

To see how the performance in the iterative case depends on the trellis length

Bit-error performance for the Peleg method for different values of

Finally, we compared for

Bit-error performance with dominant subtrellis approach for different values

Just like in the noniterative multicarrier case, we do the processing based on trellis decomposition and focus on the computation of the a posteriori subtrellis probabilities:

Now the a posteriori symbol probability for

This suggests that, for each iteration, the demodulator first determines the a posteriori subtrellis probabilities using (

Using the weighting coefficients, the convex combination in (

Equation (

If we compute the dominant subtrellis only before the start of the iteration process, we obtain a significant complexity reduction since the analysis in Section

We have seen before that in the noniterative multi-carrier case the performance was more or less determined by the size

Bit-error performance for the multi-carrier case for different values

Finally, we compare for

Bit-error performance with dominant subtrellis approach for different values

So far we have used AWGN channels with unknown channel phase and fixed (unit) gain in our analysis and simulations. To investigate the performance in practise, we have used the TU-6 (Typical Urban 6 taps) channel model defined in [

We use our methods for DAB transmission in Mode-I, where the inverse subcarrier spacing

Now, with these settings, the

Note that to prevent ISI in an OFDM-scheme, the delay differences on separate propagation paths need to be less than the cyclic-prefix period [

The channel gain representative for a 2D block, where it is assumed to be constant, is estimated similar to (

The results of our simulations with the TU-6 model are shown in Figure

Bit error performance for the TU-6 COST-207 channel with the solid lines for

The value for

It can be concluded from Figure

We have investigated decoding procedures for DAB-like systems, focussing on trellis decoding and iterative techniques, with a special focus on obtaining an advantage from considering 2D blocks and trellis decomposition. These 2D blocks consist of the intersection of a number of subsequent OFDM symbols and a number of adjacent subcarriers. The idea to focus on blocks was motivated by the fact that the channel coherence time is typically limited to a small number of OFDM symbols, but also since per service symbol processing is used which limits the number of OFDM symbols in a codeword.

We have used trellis decomposition methods that allows us to estimate the unknown channel-phase modulo

We have first investigated noniterative methods. The advantage of these methods is that forward-backward procedures turned out to be extremely simple since we could use Colavolpe processing [

Simulations for the noniterative AWGN case show that (a) trellis-lengths of

For the iterative AWGN case with

On the other hand, iterative simulations for a practical setting (i.e., the TU-6 model) show that (a) with trellis-length

The authors would like to acknowledge Professor J. W. M. Bergmans, the management and the technical staff of Catena Radio Design B. V., and NXP-Research Eindhoven for their support to accomplish this work. Moreover, They thank the anonymous reviewers for their comments and valuable suggestions.