US RE42884 E1 Abstract An nth root transformation is used for generating near Gaussian metrics from non-Gaussian metrics for input into a conventional turbo decoder that is based on the assumption that the input sequence to the decoder has a Gaussian distribution. The nth root transformation transforms channel non-Gaussian statistics to near Gaussian statistics for use with conventional turbo decoding for improved noncoherent communications over a non-Gaussian channel, such as a fading channel. For a differential coherent PSK waveform, where the channel statistics of a demodulator are non-Gaussian, for example, in the presence of fading, the nth root transformation is used to transform the non-Gaussian statistics to near Gaussian statistics for generating near Gaussian metrics, for improved PSK communications.
Claims(27) 1. A turbo decoding communication system for communicating a data signal over a communication channel, the system comprising,
a turbo encoder for encoding the data signal into an encoded signal,
a modulator for generating a modulated signal from the encoded signal, the modulated signal being communicated over the communication channel,
a demodulator for demodulating the modulated signal into a demodulated signal providing non-Gaussian metrics,
a transformer for transforming the non-Gaussian metrics into near Gaussian metrics,
a turbo decoder for decoding the near Gaussian metrics into the data signal, the turbo decoder decoding the near Gaussian metrics into the data signal using a Gaussian characterization for characterizingof the communication channel, and
a decoder reference for providing a Gaussian mean and a Gaussian standard deviation to the turbo decoder for decoding the near Gaussian metrics into the data signal, the Gaussian mean and Gaussian standard deviation being the Gaussian characterization.
2. The system of
a channel interleaver for interleaving the encoded signal, and
a channel deinterleaver for deinterleaving the demodulated signal.
3. The system of
the demodulator is a noncoherent demodulator.
4. The system of
the communication channel is a non-Gaussian communication channel.
5. The system of
the data signal is communicated over the communication channel using phase shift keying signaling.
6. The system of
the Gaussian characterization is an Eb/No signal-to-noise ratio.
7. A turbo decoding communication system for communicating a data signal using phase shift keying (PSK) signaling over a non-Gaussian communication channel, the system comprising,
a turbo encoder for encoding the data signal into an encoded signal,
a PSK modulator for generating a PSK modulated signal from the encoded signal, the PSK modulated signal being communicated over the non-Gaussian communication channel,
a PSK demodulator for demodulating the PSK modulated signal into a PSK demodulated signal providing non-Gaussian metrics,
an nth root transformer for transforming the non-Gaussian metrics into near Gaussian metrics where n does not equal one nor equal infinity,
a turbo decoder for decoding the near Gaussian metrics into the data signal, the turbo decoder decoding the near Gaussian metrics into the data signal using a Gaussian characterization for characterizingof the communication channel, and
a decoder reference for providing a Gaussian mean and a Gaussian standard deviation to the turbo decoder for decoding the near Gaussian metrics into the data signal, the Gaussian mean and Gaussian standard being the Gaussian characterization.
8. The system of
a channel interleaver for interleaving the encoded signal, and
a channel deinterleaver for deinterleaving the demodulated signal.
9. The system of
10. The system of
11. The system of
12. The system of
n defines the root of the nth root transformer, and
n is a positive integer greater than one.
13. A turbo decoding communication system for communicating a data signal using differential coherent phase shift keying (DPSK) signaling over a non-Gaussian communication channel, the system comprising,
a turbo encoder for encoding the data signal into an encoded signal,
a DPSK modulator for generating a DPSK modulated signal from the encoded signal, the DPSK modulated signal being communicated over the non-Gaussian communication channel,
a DPSK demodulator for demodulating the DPSK modulated signal into a DPSK demodulated signal providing non-Gaussian metrics, and a square root transformer for transforming the non-Gaussian metrics into near Gaussian metrics where n does not equal one nor equal infinity,
a turbo decoder for decoding the Gaussian metrics into the data signal, the turbo decoder decoding the near Gaussian metrics into the data signal using a Gaussian characterization for characterizingof the communication channel, and
a decoder reference for providing a Gaussian mean and a Gaussian standard deviation to the turbo decoder for decoding the near Gaussian metrics into the data signal, the Gaussian mean and Gaussian standard deviation being the Suasion characterization.
14. The system of
a channel interleaver for interleaving the encoded signal, and
a channel deinterleaver for deinterleaving the demodulated signal.
15. The system of
16. A method for turbo decoding communication system for communicating a data signal over a communication channel, the method comprising:
encoding the data signal into an encoded signal with a turbo encoder; generating a modulated signal from the encoded signal; demodulating the modulated signal into a demodulated signal providing non-Gaussian metrics; transforming the non-Gaussian metrics into near Gaussian metrics; decoding the near Gaussian metrics into the data signal; decoding the near Gaussian metrics into the data signal with a turbo decoder using a Gaussian characterization of the communication channel; and providing a Gaussian mean and a Gaussian standard deviation with a decoder reference to the turbo decoder for decoding the near Gaussian metrics into the data signal, wherein the Gaussian mean and Gaussian standard deviation being the Gaussian characterization. 17. The method of claim 16, wherein the method further comprises:
interleaving the encoded signal; and deinterleaving the demodulated signal. 18. The method of claim 16, wherein the Gaussian characterization is an E
_{b}/N_{o }signal-to-noise ratio.19. A method for turbo decoding a data signal using phase shift keying (PSK) signaling over a non-Gaussian communication channel, the method comprising:
encoding the data signal into an encoded signal; generating a PSK modulated signal from the encoded signal; demodulating the PSK modulated signal into a PSK demodulated signal providing non-Gaussian metrics; transforming the non-Gaussian metrics into near Gaussian metrics with an nth root transformer, where n does not equal one nor equal infinity; decoding the near Gaussian metrics into the data signal using a Gaussian characterization of the communication channel; and providing a Gaussian mean and a Gaussian standard deviation for decoding the near Gaussian metrics into the data signal, wherein the Gaussian mean and Gaussian standard being the Gaussian characterization. 20. The method of claim 19, wherein the method further comprises:
interleaving the encoded signal; and deinterleaving the demodulated signal. 21. The method of claim 19, wherein the nth root transformer is a square root transformer.
22. The method of claim 19, wherein the PSK signaling is binary PSK signaling.
23. The method of claim 19, wherein the PSK is differential coherent PSK signaling.
24. The method of claim 19, wherein, n defines the root of the nth root transformer, and n is a positive integer greater than one.
25. A method for turbo decoding a data signal using differential coherent phase shift keying (DPSK) signaling over a non-Gaussian communication channel, the method comprising,
encoding the data signal into an encoded signal; generating a DPSK modulated signal from the encoded signal; demodulating the DPSK modulated signal into a DPSK demodulated signal; providing non-Gaussian metrics from the DPSK demodulated signal and a square root transformer for transforming the non-Gaussian metrics into near Gaussian metrics where n does not equal one nor equal infinity; decoding the Gaussian metrics into the data signal; decoding the near Gaussian metrics into the data signal using a Gaussian characterization of the communication channel; and providing a Gaussian mean and a Gaussian standard deviation with a decoder reference, wherein the Gaussian mean and Gaussian standard deviation being the Gaussian characterization. 26. The method of claim 25, further comprising:
interleaving the encoded signal; and deinterleaving the demodulated signal. 27. The method of claim 25, wherein the non-Gaussian communication channel fades the DPSK modulated signal over the non-Gaussian communication channel.
Description The invention was made with Government support under contract No. F04701-00-C-0009 by the Department of the Air Force. The Government has certain rights in the invention. The invention relates to the field of turbo decoding communication systems. More particularly, the present invention relates to soft metric formulations in turbo decoding systems for improved performance for non-Gaussian communications channels. Turbo decoding in a receiving communication system is based on the concept of maximum a posteriori probability of bit decisions made on blocks of channel symbols communicated over a communication channel from a turbo encoding transmitting communication system. Conventional turbo-decoding algorithms are based on the assumption that the input sequence to the turbo decoder has been disturbed by a noise process that has a Gaussian distribution. Conventional turbo-decoding algorithms are optimized for Gaussian channels for reducing the bit-error-rate (BER). Conventional turbo decoders are equipped with a decoder reference for providing a mean and a standard deviation as an estimate of the assumed Gaussian channel statistics. However, when the actual channel statistics of the input sequence to the decoder varies significantly from the Gaussian distribution assumption, the turbo decoder performance will degrade. Hence, the conventional turbo-decoding algorithm incorrectly assumes a Gaussian channel in all cases. A coherently demodulated signal will preserve channel statistics in a turbo decoding system. When the channel is non-Gaussian, the conventional turbo-decoding algorithm suffers degraded performance with a reduced BER. Often, the input sequences to the turbo decoder exhibits non-Gaussian statistics, such that, there will be a mismatch between likelihood values assumed by the decoder and the actual likelihood values presented by non-Gaussian channels. This mismatch produces degradation when using decoding from metrics generated from noncoherently demodulated signals, such as with differentially coherent phase shift keying (DPSK) signals. The performance degradation will also occur from channel disturbances with channel memory, such as from fading, regardless of the demodulation method. Hence, the turbo decoding performance suffers with a reduced BER in the presence of a mismatch between the assumed Gaussian channel without fading and a non-Gaussian channel, such as, a Gaussian channel with fading. For DPSK signaling, the output statistics of a differentially coherent demodulator is non-Gaussian. When a metric sequence from a differentially coherent demodulator is fed directly into a conventional turbo decoder, particularly under a fading environment, the mismatch between decoder algorithm assumptions and actual input statistics can result in significant decoder performance degradation. Referring to prior art Although optimum decoder performance for a non-Gaussian channel can be achieved by modifying the decoder reference based on the actual input statistics to the turbo decoder for various respective channel statistics, such modifications would only be effective for channel statistics having a Gaussian distribution. To correctly match non-Gaussian channel statistics, the turbo decoder algorithm would need to be modified to match metric processing to the non-Gaussian distribution. Such a redevelopment would only be effective during predetermined fading and predetermined noncoherent demodulation methods, and may not be suitable for a steady state Gaussian channel or other non-Gaussian channels. These and other disadvantages are solved or reduced using the invention. An object of the invention is to provide improved communications over non-Gaussian communication channels. Another object of the invention is to provide an nth root metric transformation in a turbo decoding system. Yet another object of the invention is to provide an nth root metric transformation in a turbo decoding system for matching non-Gaussian channel statistics to Gaussian metric processing of a turbo decoder. Still another object of the invention is to provide an nth root metric transformation in a turbo decoding system for matching non-Gaussian channel statistics to Gaussian metric processing in a turbo decoder system demodulating phase shift keying (PSK) received signals. A further object of the invention is to provide an nth root metric transformation in a turbo decoding system for matching non-Gaussian channel statistics to Gaussian metric processing in a turbo decoder system demodulating differential phase shift keying (DPSK) received signals. Yet a further object of the invention is to provide an nth root metric transformation in a turbo decoding system for matching non-Gaussian channel statistics to Gaussian metric processing in a turbo decoder system demodulating binary phase shift keying (BPSK) received signals. The invention is directed to turbo decoding communication systems for matching non-Gaussian statistics to turbo decoding Gaussian metric processing by an nth root transformation of the non-Gaussian metric inputs into Gaussian metrics inputs prior to turbo decoding. The nth root transformation of the non-Gaussian metrics effectively shifts the probability histogram functions to near Gaussian metrics for use in a conventional turbo decoder Gaussian metric processing algorithm for improved performance in the presence of non-Gaussian channel statistics, such as those resulting from fading and multipath. The nth root transformation is applied independent of the turbo decoding and hence can be retrofitted into existing turbo decoding systems. The nth root transformation transforms non-Gaussian statistics into near Gaussian that largely resembles a true Gaussian distribution. The near Gaussian distribution would have a different mean, different standard deviation, and a slightly different shape, but in the general appearance of a bell shaped distribution. The decoder reference has side channel information indicating the standard deviation and mean that are modified to match the near Gaussian distribution generated by the nth root transformation of the non-Gaussian statistics. In this manner, an improvement in turbo decoder performance, and hence an improvement in the bit error rate (BER) performance, can be achieved in the presence of non-Gaussian channel statistics using a conventional turbo decoder and using an effective biased Gaussian distribution as indicated by the channel side information. Conventional turbo decoding can now be used to communicate over a fading channel communicating DPSK signals. In a receiver, the DPSK demodulator output statistics would still exhibit a large deviation from a Gaussian distribution. The non-Gaussian distribution is effectively transformed for improved decoder performance in fading channels by altering the statistics of the demodulated sequence, through nth root signal transformation, so that the channels then appears to be near Gaussian for subsequent conventional turbo decoding with biased side information. That is, the nth root transformation provides near Gaussian turbo decoding metrics for conventional turbo decoding. By using the transformed metric inputs, with quantized input soft metric values, to the conventional turbo decoder, the BER performance in fading conditions is improved. These and other advantages will become more apparent from the following detailed description of the preferred embodiment. An embodiment of the invention is described with reference to the figures using reference designations as shown in the figures. Referring to The transmission signal is fed through a communication channel that may be a non-Gaussian channel. The Gaussian channel noise can be modeled by n Referring to Decoder performance degradation occurs any time that there exists a mismatch between the likelihood values assumed by the decoder based on the Gaussian decoder reference Referring to all of the Figures, and more particularly to The invention is directed to metric transformations, such as nth root transformations, of metrics in a noncoherent demodulating turbo decoding communication system, such as a PSK demodulating system, for matching non-Gaussian channel statistics to near Gaussian channel statistics by transforming the metrics inputs to the turbo decoder. In order to improve the robustness of the communication system against fading and multipath, the metric transformation operates on a non-Gaussian metric sequence originating from a noncoherent demodulator. Although this metric transformation can slightly degrade the BER performance in a benign Gaussian channel environment, an improvement is had in the most critical scenario, when the channel is faded. While the preferred form uses a square root transformation, other types of root transformations can be used, excepting the trivial cases of n=1 and n=∞ root transformations. Other non-root metric transformations could be used as well, such as logarithmic, exponential, and algebraic metric transformations. Those skilled in the art can make enhancements, improvements, and modifications to the invention, and these enhancements, improvements, and modifications may nonetheless fall within the spirit and scope of the following claims. Patent Citations
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