Common OFDM system contains redundancy necessary to mitigate interblock interference and allows computationally effective single-tap frequency domain equalization in receiver. Assuming the system implements an outer error correcting code and channel state information is available in the receiver, we show that it is possible to understand the cyclic prefix insertion as a weak inner ECC encoding and exploit the introduced redundancy to slightly improve error performance of such a system. In this paper, an easy way to implement modification to an existing SDR OFDM receiver is presented. This modification enables the utilization of prefix redundancy, while preserving full compatibility with existing OFDM-based communication standards.

Thanks to their flexibility, SDR platforms enable relatively easy modifications to the communication system subblocks, which could bring advantages or gains to existing system. It is even possible sometimes to exploit already standardized protocols in an unexpected new way. In this paper, this future will be illustrated on an example of the standard OFDM transmission technique.

In current standards, for example, IEEE
802.16e, the OFDM system uses a cyclic prefix (CP) to mitigate the effects of
channel impairment. For each transmitted OFDM symbol, the length of the prefix
is a fraction of useful symbol length. The main purpose of using cyclic prefix
is protection against intersymbol interference (ISI), or more precisely interblock
interference (IBI), in connection with simple equalization in frequency domain.
Most of current receivers throw the cyclic prefix away or use it only for
channel estimation. In this paper, we present a method for exploiting the
redundancy introduced by the cyclic prefix, by means of decoding two serially
concatenated codes. To be more precise, we understand the prefix insertion as
an inner repetition coding, where only a part of the samples is repeated. With
code rate

In the next section, we give a short description of current OFDM systems along with a brief overview of recent methods for exploiting of cyclic prefix. The third section refreshes the principle of concatenated coding and depicts the possible OFDM error performance improvement using a simulation with real-life settings. The fourth section is devoted to description of the received prefix processing, which is necessary for successful extraction of repetition data. The last section describes the whole modified OFDM receiver and then presents simulation results showing the actual error performance improvement in a multipath environment.

Figure

Standard
OFDM system model: ECC, outer error correcting code encoder; CM, constellation mapping; (I) DFT, (inverse) discrete Fourier transform;

OFDM
processing begins with blocks of ECC encoded binary data that are first
digitally modulated in frequency domain (CM Block), then transformed to time domain by IDFT. A
cyclic prefix is attached in the CPI block. The OFDM symbol (or time domain block) consisting of many (1024 and more) samples travels through multipath
environment, which can be modeled by a convolution with channel impulse
response

The channel estimation and symbol
detection blocks are omitted from Figure

The first one is reducing of the CP size to less than the
channel delay spread and overcoming the resulting IBI by modifying the
iterative ECC decoder to work over two consecutive OFDM symbols so that it is
able to fix errors resulting from IBI that occurs in case of insufficient CP
size [

A different approach is exploiting of
the CP (of size greater than the channel delay spread) to improve the channel
estimation [

The residual intersymbol interference
cancellation (RISIC) is presented in [

A more general method of turbo frequency
domain equalization (turbo FDE) is presented in [

Finally, the third concept is based on
the observation that cyclic prefix size defined in

The principle of serial concatenation of
codes is well known. As shown in Figure

Serial concatenated encoding.

The situation in the receiver is more
complicated; usually two SISO decoders cooperate in an iterative manner, exchanging
extrinsic information as described in [

In today’s systems, OFDM is always used
along with a powerful error correcting code such as turbo or LDPC code as shown
in Figure

In Figure

Iterative decoding of serially concatenated codes.

Modified OFDM decoder principle.

Before actual prefix redundancy
extraction efforts, simplified simulation experiments were done, primarily with
the goal to give us a proof of concept. The first round of simulations used a
simplified OFDM system model. In the simulations, we used the inner partial
repetition code of rate

BER after
1st, 3rd, and 7th decoder iterations for UMTS turbo code with (

Prolonging of blocks in multipath channel results in interblock interference; currently the redundant CP samples are all discarded.

The resulting 0.25 dB improvement can be interpreted as a rough estimate or an upper bound to the actual improvement that can be achieved in real systems. The significant difference between the simplified model and the real system is corruption of the second copy of data used in repetition decoder. This corruption is caused by IBI and cannot be fully remedied. Two differently successful solutions addressing this problem are described in the following sections.

The following section consists of three parts. First, the principle of prefix insertion (CPI) and removal (CPR) for the purpose of simple frequency domain equalization in context of OFDM multipath-environment transmission is reviewed. Second, a more formal matrix-based description of channel and CPI/CPR processes is presented. Finally, the process of extraction of redundant information from cyclic prefix (CP) is described, based on the formal matrix representation.

The propagation of a signal through a
multipath channel with ISI is usually described by convolution with the channel
impulse response

Structure of
channel convolution matrix

One possible way of coping with IBI is
to send an all-zero
guard prefix. Another way, used in OFDM, is to use a cyclic prefix—part of the
samples from the end of the transmitted block is copied and prepended before
the beginning of the block. In the receiver, only the appropriate subblock of
the received sequence is selected, redundant samples of the prefix are
discarded. The motivation for CP insertion and removal is that these operations
allow us to understand the channel convolution matrix as a circulant matrix. More
precisely a submatrix

Theoretical background for
equalization: selecting the correct submatrix

The goal of prefix extraction is to process the currently discarded received CP subblock to obtain a second copy of the data bits, more specifically a second set of channel LLR values for the data bits, in order to use these values in a repetition decoder and in that way fortify the successive error correcting soft-input decoder.

To completely understand the process, a
more formal description of transmission based on (

Conforming to Figure

However, if matrices

However,

The reconstruction of the transmitter
output in receiver is straightforward (as shown in Figure

The first obstacle here is the fact that
the time domain samples

This can be done by concatenation

A serious drawback of
this procedure is the fact that the inversion of channel response submatrix

The

As the standard branch of processing depends on the circulant property which is a consequence of cyclic prefix insertion in transmitter and appropriate subblock selection in receiver, in case of the 2nd copy extraction, the circulant property will be provided by a correction done in the receiver. The result will be a second copy of frequency domain samples that originates from the otherwise ignored prefix samples.

In Figure

The
circulant matrix

Modified OFDM receiver.

Standard (

As apparent in Figure

In Figure

As indicated earlier, all of the functional blocks are implemented in software. The key property of the modified branch is that it is built using exactly the same components as the standard processing branch with one exception—the spectral shift block that is implemented as a simple scalar complex multiplication. The development and inclusion of the modification is very straightforward in an SDR receiver. Furthermore, the additional processing can be turned off and on adaptively, depending on the transmission quality requirements and available processing time.

We simulated a coded OFDM system with an
outer RSC turbo code of rate

The error performance of the new system
is only slightly better (approx. 0.1 dB) than the basic system. The improvement
is most visible in the error floor area (below

We have shown that it is possible to exploit the redundancy in a cyclic prefix of OFDM. The modified receiver is fully backward compatible with any existing OFDM-based protocol. The computational complexity is approximately double compared to the standard OFDM receiver. Simulations for specified parameters have shown that a relatively small improvement of 0.1 dB in bit error rate could be achieved thanks to exploitation of the prefix redundancy. Because the modification reuses most of the functional blocks already present in the system, it can be implemented very rapidly in an SDR system using a high-level programming language.

This work was supported by Scientific Grant Agency of Ministry of Education of Slovak Republic and Slovak Academy of Sciences under contract VEGA 1/0376/09, 2009–2012.