Demodulation and decoding
10097382 ยท 2018-10-09
Assignee
Inventors
Cpc classification
H04L25/03171
ELECTRICITY
H04L1/005
ELECTRICITY
H04L25/067
ELECTRICITY
H04L1/0054
ELECTRICITY
International classification
H03M13/29
ELECTRICITY
H04L25/03
ELECTRICITY
H04L1/00
ELECTRICITY
H04L25/06
ELECTRICITY
Abstract
A receiver for a modulated signal of a communication system is disclosed. The receiver includes a demodulator to demodulate the received modulated symbols of a received signal into received soft-bits. The receiver also includes a hard-decision decoder that is configured to decode the received soft-bits into decoded bits. A feedback loop is included to provide feedback from the hard decision decoder to the demodulator. The feedback loop is configured to re-encode the decoded bits from the hard-decision decoder into re-encoded bits. The demodulator is further configured to iteratively demodulate the received modulated signal using an output of the feedback loop.
Claims
1. A receiver for a modulated signal of a communication system, comprising: a demodulator arranged and configured to demodulate the received modulated symbols of a received signal into received soft-bits; a hard-decision decoder arranged and configured to decode the received soft-bits into decoded bits; a feedback loop arranged to provide feedback from the hard decision decoder to the demodulator, the feedback loop being configured to re-encode the decoded bits from the hard-decision decoder into re-encoded bits and to modulate the re-encoded bits into estimated modulated symbols, and wherein the demodulator is further arranged and configured to iteratively demodulate the received modulated signal using an output of the feedback loop.
2. The receiver as claimed in claim 1, wherein the output of the feedback loop is the re-encoded bits or interleaved re-encoded bits.
3. The receiver as claimed in claim 1, wherein the modulated signal is a differentially modulated signal.
4. The receiver of claim 3, and further comprising a noise suppression circuit arranged and configured to combine the estimated modulated symbols and the received modulated symbols and wherein the demodulator is further arranged and configured to iteratively demodulate the received signal using the combined estimated modulated symbols and the received modulated symbols.
5. The receiver as claimed in claim 4, wherein the noise suppression circuit is configured to combine the estimated modulated symbols and the received modulated symbols as a weighted sum.
6. The receiver as claimed in claim 1, wherein the demodulator is a coherent demodulator and wherein the receiver further comprises a channel estimator configured and arranged to supply an estimate of a communications channel over which the modulated signal was received to the coherent demodulator.
7. The receiver as claimed in claim 6, wherein the channel estimator is configured and arranged to receive and process the received modulated symbols or the channel estimator is configured and arranged to receive and process estimated modulated symbols and the received modulated symbols.
8. The receiver as claimed in claim 1, wherein the receiver includes a further demodulator, and wherein the further demodulator is arranged to receive the received modulated symbols and wherein soft-bits output by the demodulator and further soft-bits output by the further demodulator are combined by a combiner before being supplied to the hard-decision decoder.
9. The receiver as claimed in claim 1, and further comprising a channel change estimator and compensator arranged to receive the received modulated symbols and/or estimated modulated symbols and configured to estimate changes in a communications channel over which the modulated signal was sent and to compensate for those changes to improve the received modulated symbols and/or the estimated modulated symbols.
10. The receiver as claimed in claim 1, and further comprising a symbol buffer arranged to receive the received modulated symbols and buffer the received modulated symbols while the feedback loop generates the output.
11. The receiver as claimed in claim 10, wherein the symbol buffer is further configured to randomly select received modulated symbols for buffering and iterative demodulation.
12. The receiver as claimed in claim 10, wherein the symbol buffer is further configured to select received modulated symbols for buffering based on the strength of the communications channel over which the received modulated symbols were transmitted.
13. The receiver as claimed in claim 12, and further comprising a channel strength estimator arranged to receive the received modulated symbols and configured to estimate the strength of the communications channels over which the received modulated symbols were transmitted and determine which received modulated symbols were received over channels having a moderate strength between an upper channel strength limit and a lower channel strength limit.
14. A package including an integrated circuit, wherein the integrated circuit is configured to provide the receiver of claim 1.
15. A method of iteratively demodulating a modulated signal of a communication system, the method comprising: demodulating received modulated symbols into soft-bits using a demodulator; hard-decision decoding the soft-bits into decoded bits using a hard-decision decoder; re-encoding the decoded bits output by the hard-decision decoder into re-encoded bits; modulating the re-encoded bits into estimated modulated symbols; feeding back the re-encoded bits or the estimated modulated symbols to the demodulator; and iteratively demodulating the modulated signal using the re-encoded bits or the estimated modulated symbols.
Description
(1) Embodiments of the invention will now be described in detail, by way of example only, and with reference to the accompanying drawings, in which:
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(19) Similar items in the different Figures share like reference signs unless indicated otherwise.
(20) Apparatus and methods for demodulating and decoding transmitted data will be described below. In the following, the example system of a Digital Audio Broadcasting (DAB) system will be used but it will be appreciated that the approach can be applied to other communications systems as well, e.g., DAB+, T-DMB, WiFi standards, optical communication systems, cable communication systems and satellite communication systems.
(21) Generally speaking the apparatus and methods can be applied to both coherent modulation systems and differential modulation systems. For differential modulation then either differential or coherent demodulation may be used. For coherent modulation then coherent demodulation may be used.
(22) With reference to
(23) The transmitting device includes a main system 112 including one or more data processing devices and which acts as a source of digital data for transmission. The details of the main system are conventional and will be understood by a person of ordinary skill in the art and therefore are not described herein in detail. The bits of digital data are passed to a transmitter 114 which drives a transmission antenna 116 to transmit a wireless signal.
(24) The receiving device 120, which may be a radio or other audio device, includes a receiving antenna 122 for receiving the transmitted wireless signal and a receiver 124 which demodulates and decodes the received signal and outputs bits of digital data to a main system 126. The main system 126 includes one or more data processing devices and which acts as a sink of the received digital data. The details of the main system 126 are conventional and will be understood by a person of ordinary skill in the art and therefore are not described herein in detail.
(25) The DAB standard uses phase modulation and in particular differential quadrature phase-shift keying (DQPSK) modulation of an orthogonal frequency-division multiplexing (OFDM) signal. Differential phase modulation techniques compare the phase shift between consecutive transmitted symbols, which can be consecutive in time or frequency.
(26) In the example DAB system 100, the data is modulated with differential modulation in the time domain and transmitted over parallel subcarriers of an OFDM symbol as described below with reference to
(27) As noted above, in other embodiments, coherent modulation can be used instead of differential modulation. Various forms of coherent modulation may be used such as phase modulation or amplitude modulation. Coherent modulation and demodulation techniques are based on comparing the received symbol with a received reference signal. In the following only a differential phase modulation transmitter is described, but the construction and operation of a suitable coherent modulation transmitter will be apparent to a person of ordinary skill in the art.
(28) As noted above, differential modulation is a modulation technique which can be demodulated with a non-coherent receiver, i.e., a conventional differential demodulator can demodulate the symbols without using any channel estimation or equalization processes at the receiver which simplifies the receiver structure. Due to this property, differential modulation has been chosen as the modulation scheme in several wireless standards, e.g., DAB, TDMB etc. On the other hand, this simplifying property also brings some performance degradation compared to coherent reception schemes where coherently modulated symbols are used with pre-determined training sequences or pilots in the transmitted signal. In this case, demodulation requires channel state information which can be obtained by using the training sequences or pilots in the signal. A drawback of differential modulation and demodulation arises from the encoding of the data in two successive symbols. This will lead to two noise sources affecting the demodulation process even if the channel is static and leading to approximately 3 dB performance loss.
(29) Nonetheless the various receivers described herein can give rise to benefits for differential modulation and coherent modulation. The use of iterative demodulation in the receiver can be applied to differential modulation and coherent modulation and can give the receiver flexibility in terms of complexity compared to performance. Also, for differential modulation, improved noise suppression can be achieved.
(30) With reference to
(31) The transmitter 200 carries out a conventional differential modulation in which complex symbols are modulated onto orthogonal subcarriers by using OFDM signalling. After forward-error-correction (FEC) encoding by block 202 and interleaving by block 204, bits are mapped to complex data symbols by blocks 206 and 208. For example, pair of bits, e.g. (x.sub.1, x.sub.2), are mapped by modulator block 206 to a differential quadrature phase-shift keying (D-QPSK) symbol d.sub.k=exp (j.sub.k) with .sub.k{/4, 3/4, 5/4, 7/4} by using Gray labelling in the DAB standard, i.e., d.sub.k=1/2[(121)+j(122)], and differential modulation is applied by differential modulator block 208 on these complex symbols as:
s.sub.k+1=s.sub.kd.sub.k
.sub.k+1=.sub.k+.sub.k
where s.sub.k=exp(j.sub.k) represents the complex symbol value transmitted over the kth symbol and {s0} is defined in the DAB standard as reference symbol. As described above, s.sub.k is modulated using a /4-shift in D-QPSK, and .sub.k can be in either the set A={/4, 3/4, 5/4, 7/4} or the set A={0, /2, , 3/2} depending on the index of the symbol of the OFDM symbol and which is known at both the transmitter and receiver side.
(32) In differential modulated OFDM systems, the modulation is done for every subcarrier in parallel and independent of each other. This discussion focusses only a single subcarrier for the sake of simplicity of explanation of the approach. After an IFFT and insertion of a cyclic prefix by 212, an analog signal is output by 214 to drive antenna 116 to transmit the wireless signal over a time varying multipath wireless communication channel.
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(34) Generally speaking, a demodulator 310 receives the received modulated symbols, or IQ samples, from the data extractor 308 and outputs soft-bits or LLRs (described below). The hard decision decoder 314, then decodes soft-bits from the demodulator into decoded bits which can eventually be output. The decoded bits are also fed back by a feedback loop to the demodulator. The feedback loop includes an encoder 316, which re-encodes the bits output by decoder 314 to generate re-encoded bits. The re-encoded bits are then interleaved by interleaver 318. In some embodiments, a noise suppression circuit 332 may also be provided in which case a modulator 320 is also included in the feedback loop to output estimates of the modulated symbols.
(35) In other embodiments of the receiver, for example receiver 350 as shown in
(36) Furthermore, the interleaver 318 may also be omitted from the feedback loop in some embodiments of the receivers described herein. In such embodiments, the de-interleaver block 312 may also be omitted. Hence, in some systems, interleavers are not used and so there is no need to interleave and/or de-interleave in the receivers. For example in some systems, the system may include only a symbol interleaver. Additionally or alternatively, if the received modulated signals are already de-interleaved, and stored like that, then there is no need to interleave the re-encoded bits in the feedback loop.
(37) Returning to
(38) In some embodiments, all the received modulated symbols can be iteratively demodulated using feedback. In other embodiments only some of the received modulated symbols are iteratively demodulated using feedback. Hence, either a full iterative demodulation or a partial iterative demodulation can be carried out.
(39) The baseband received signal at the kth OFDM symbol for the intended subcarrier, r.sub.k, is
r.sub.k=H.sub.ks.sub.k+n.sub.k,
where H.sub.k is the channel frequency response of the subcarrier at kth OFDM symbol, and n.sub.k is the additive white Gaussian noise (AWGN) at the kth OFDM symbol with variance .sup.2 noise at the intended subcarrier. Similarly, the received signal at the (k+1)th OFDM symbol, r.sub.k+1, is
r.sub.k+1=H.sub.k+1s.sub.k+1+n.sub.k+1.
(40) The channel frequency response can be assumed to be constant, i.e., H.sub.k+1=H.sub.k, for fixed reception as well as in the case of a low mobility receiver.
(41) Generally speaking, the demodulator 310 estimates the bit pair (x.sub.1,x.sub.2) by using r.sub.k and r.sub.k+1.
(42) The log-likelihood of the first bit, x.sub.1, is:
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and similarly for the second bit, x.sub.2, is:
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(45) Following de-interleaving by de-interleaver, 312, these values can be used as the input to a forward error correction (FEC) decoder 314, such as a Viterbi decoder as used in the example DAB system, to correct for any errors in the received data due to the transmission channel and noise.
(46) The receiver 300 uses feedback from the hard decision decoder 314 to iteratively demodulate and decode to improve the performance of the receiver 300.
(47) This approach is preferable to iterative solutions which use more complex demodulators, such as a trellis demodulator, in order to be able to use feedback from a decoder. Such decoders need to provide soft feedback and hence would require a soft-decision decoder rather than a hard-decision decoder.
(48) The approach embodied by the receivers described herein provides the receiver performance benefits of iterative demodulation and decoding, but with much simpler processing blocks, i.e., avoiding the use of complex soft decision demodulators and decoders, e.g., trellis demodulators and BCJR decoders. Instead of using a soft decision decoder, the output of a hard decision decoder 314, e.g. Viterbi decoder for DAB receivers, is used. The hard decision decoded bits are encoded 316, interleaved 318 and modulated 320 by a feedback loop and this information, an estimate of the differentially transmitted symbol, i.e. an estimate of d.sub.k, is provided to an iterative demodulation stage 310. The encoding block 316 can be implemented relatively simply, for example using only shift registers and XOR operations for convolutional coding. The modulation block 320 maps bit pairs to a complex value.
(49) Error correction inserts redundancy in the transmitted signal. This redundancy helps to recover errors, but is only available at the decoding stage. This redundancy information is carried to earlier blocks such as the demodulation block to help them to generate better more reliable values.
(50) The iterative nature of the operation of the receiver 300 will now be described. For 4 successive received signals, i.e., r.sub.k1, r.sub.k, r.sub.k+1, r.sub.k+2, the receiver 300 would like to compute the reliability of bits transmitted in d.sub.k where s.sub.k=s.sub.k1 d.sub.k1, s.sub.k+1=s.sub.k d.sub.k, s.sub.k+2=s.sub.k+1 d.sub.k+1. The received signals are r.sub.k1=H.sub.k1 s.sub.k1+n.sub.k1, r.sub.k=H.sub.k s.sub.k+n.sub.k, r.sub.k+1=H.sub.k+1 s.sub.k+1+n.sub.k+1, r.sub.k+2=H.sub.k+2 s.sub.k+2+n.sub.k+2.
(51) If it is assumed that the transmission channel is varying slowly, then it can be assumed that that H.sub.k1=H.sub.k=H.sub.k+1=H.sub.k+2. The output from the FEC decoder 314 is feedback, encoded by 316, interleaved by 318 and modulated by 320 which provides information about d.sub.k1 and d.sub.k+1, i.e., estimated values for d.sub.k1 and d.sub.k+1, namely d.sub.est k1 and d.sub.est k+1. This information is used to improve the demodulation of d.sub.k, by using the estimates d.sub.est k1 and d.sub.est k+1 to get estimates of r.sub.k and r.sub.k+1 to suppress noise in the received signals.
(52) When D-QPSK modulation is used, r.sub.est,k=d.sub.k1 r.sub.k1 and r.sub.est,k+1=d*.sub.k+1 r.sub.k+2. An estimate of the received signals is provided by the hard decision feedback loop to noise suppression block 322 together with the original received signal, and a weighted sum of the two values is calculated by the noise suppression block 322 to provide a better estimate of the received signals having less noise. The noise suppressed version of the kth and (k+1)th received signals output by the noise suppression black 322 are r.sub.ns,k=w.sub.1 r.sub.est,k+w.sub.2 r.sub.k and r.sub.ns,k+1=w.sub.1 r.sub.est,k+1+w.sub.2 r.sub.k+1, where w.sub.1 and w.sub.2 are weightings.
(53) The values of the weights w.sub.1 and w.sub.2 can be chosen according to the reliability of the feedback from the hard decision decoder 314. If the feedback has higher reliability, then weighting values of w.sub.1=w.sub.2=1 can be used so that the original received signals and estimated values have equal weights in the weighted sum. If the feedback has lower reliability, then weighting values of w.sub.1=1 and w.sub.2=2 can be used so that the original value of the received signals have a higher weight.
(54) The weighted sum of the estimated received signal and the received signal, is then used by the differential demodulator 310 for demodulation of the differential modulated symbols. The functionality of the differential demodulator 310 is the same, but its input is now more refined due to noise suppression.
(55) In other embodiments, noise suppression circuit 322 does not need to be used as a standalone block but can be combined with the demodulator. In that case, rather than supplying the weighted sums to the input of the differential demodulator the estimates of the symbols are supplied as its inputs instead.
(56) Noise suppression circuit 322 may optionally be included in receivers for differentially modulated signals irrespective of whether a coherent demodulation or differential demodulation is used.
(57) In the preceding example, four successive values of r are used. Another approach is to use other received signals and feedback from other symbols. For example estimated values of the kth and (k+1)th received signals can be calculated using r.sub.est2,k=d.sub.k2 d.sub.k1 r.sub.k2 and r.sub.est2,k+1=d*.sub.k+1 d*.sub.k+2 r.sub.k+3. The noise suppressed values of the kth and (k+1)th signals can then be obtained by the noise suppression block calculating the weighted sums r.sub.ns,k=w.sub.1 r.sub.est,k+w.sub.2 r.sub.k+w.sub.3 r.sub.est2,k and r.sub.ns,k+1=w.sub.1 r.sub.est,k+1+w.sub.2 r.sub.k+1+w.sub.3 r.sub.est2,k+1, in which w.sub.1, w.sub.2 and w.sub.3 are weightings. In this example, six successive values of r are usedduring a steady state of demodulation and decoding operation of the receiver 300.
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(59) Receiver 400 uses the same general principle of operation of receiver 300 in that it uses a hard decision decoder 314 and feedback of the output of the hard decision decoder in order to generate a better estimate of the value of the received signal to the coherent demodulator 402. However, the coherent demodulator 402 needs information about the channel and so the received signal is also supplied to the channel estimator block which is configured to estimate the channel magnitude and phase using pilots symbols and/or using blind methods. In some embodiments, the channel estimator block 404 may be a blind channel estimator block similar to that described in Blind channel estimation assisted coherent demodulation of DPSK modulated OFDM systems, S. Serbetli, IEEE Global Communications Conference (GLOBECOM) 2014, Dec. 2014.
(60) In other embodiments of the receiver, for example receiver 360 as shown in
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(63) The first demodulator 422 receives the original received signals, r, at its input and outputs a first pair of log-likelihoods LLR.sub.1 and LLR.sub.2 using r.sub.k and r.sub.k+1 for a bit pair (x.sub.1, x.sub.2). The second demodulator 424 receives the noise suppressed values for r.sub.ns, k and r.sub.ns, k+1, from the noise suppression block 322 at its input and outputs a second pair of log-likelihoods LLR.sub.1 and LLR.sub.2 using r.sub.ns, k and r.sub.ns, k+1 for the bit pair (x.sub.1, x.sub.2). The two pairs of log-likelihood values from the first and second demodulators are then combined as a weighted sum using weightings w.sub.1 and w.sub.2 in a manner similar to that described above.
(64) In cases in which the communications channel varies more rapidly, for example mobile receivers (such as receivers in vehicles, such as cars, trains, etc.) the assumption of the channel staying the same may not be valid and may decrease the performance of the receiver. When H.sub.k1=H.sub.k=H.sub.k+1=H.sub.k+2 is less valid, then the noise suppression by using a weighted sum of the estimated and original signals may not be as effective owing to changes in the channel. In such scenarios, the receiver can be configured to estimate the channel changes and compensate for channel changes, using either blind channel change estimation or channel change estimation using the hard decision feedback as illustrated in
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(66) In another embodiment, the channel change estimation and compensation block 432 receives the estimated values of the received signals, r.sub.est, on line 436 from the modulator 320 of the feedback loop. The channel change estimation and compensation block 432 is configured to estimate the channel changes, and compensate these changes in the received signal and feed this processed received signals to the noise suppression block 438. However, differently to the previous embodiment, block 432 can also be configured to use the feedback 436 from the decoder to estimate the channel changes more reliably. The functionality of noise suppression 438 does not change, but its input is better compensated for channel changes by block 432.
(67) The above described iterative demodulation using hard decision feedback provides the benefits of iterative decoding without requiring complex demodulators and soft decision decoders, such as a Trellis demodulator and BCJR decoder for the FEC decoder. However, the above described receivers may increase the memory footprint since the received signals need to be stored while waiting for the bits to be decoded in the FEC decoder 314 and then encoded 316 and modulated 320 again. This may increase the memory requirement as illustrated by
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(69) In applications in which memory consumption if a more important factor a partial iterative demodulation and decoding approach may be used, in which some of the received symbols are decoded and demodulated iteratively and the rest are decoded and demodulated only once. Various approaches may be taken to selecting which symbols are iteratively demodulated and which are demodulated non-iteratively, i.e. in an open-loop manner.
(70) A first approach is based on random selection of symbols. In this approach, as illustrated by
(71) A second approach is based on selection of symbols depending on the channel the received signals are going through. This approach is based on the consideration that when the channel is of good quality, the demodulator 310 will work well, and will not make any mistake with a high probability. Also if the channel is in deep fade, there is a higher chance that the feedback signal is in error and so iterative demodulation may not be that beneficial. Thus, it is reasonable to use iterative demodulation on moderate channels rather than very weak or very good channels.
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(73) The channel strength estimation block 462 may be configured to define some thresholds T1 and T2 for channel strengths, with T1>T2. If the estimated channel strength of a channel over which a symbol was received is larger than T1, these symbols may be characterized, based on the channel strength information, as highly reliable symbols, if less than T2, then these symbols may be characterized as non-reliable symbols, and the symbols in between may be characterized as moderately reliable symbols.
(74) The channel strength estimation block 462 may be configured to choose not to apply second iteration demodulation on highly reliable symbols, by not storing them in channel dependent symbol buffer 464, since they are already of good quality. In the same way, the channel strength estimation block 462 may be configured to choose not to apply second iteration demodulation for non-reliable symbols, by not storing them in channel dependent symbol buffer 464, since they are noisy. So these two groups of symbols may not be stored at all for second iteration demodulation, but only moderately reliable symbols are stored for second iteration demodulation in channel dependent symbol buffer 464, thereby leading to less memory requirement for the second iteration demodulation stage. It will be appreciated that in other embodiments, a greater number of thresholds may be used to define more than 3 groups to characterize the symbols.
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(76) More specifically receiver 510 includes a receiver filter and analog-to-digital conversion block 512, a synchronisation block 514 a CP removal and Fast Fourier Transform (FFT) block 516, a data extraction block 518, a coherent demodulation block 520, a de-interleaver block 522 and an FEC decoder block 524 which outputs digital data bits. A pilot signal extraction block 526 is configured to extract pilot signals from the received signals and to co-operate with a channel estimator block 528 which is configured to generate channel estimates which are supplied to the coherent demodulator 520. A feedback loop 530 includes an FEC encoder 532 and an interleaver 534. Interleaver 534 outputs encoded bits which are fed back to the coherent demodulator 520 for use in demodulating the received modulated symbols. A symbol buffer 536 is also provided and is configured to receive and buffer all the extracted received modulated symbols from data extractor 518 in a manner similar to that described above with reference to
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(82) As illustrated in
(83) Any of the above described receivers may further be modified so that for some of the time iterative demodulation is carried out by the demodulator using feedback and at other times, the demodulator does not iteratively demodulate using feedback, but simply demodulates without feedback. For example, the decoder may be configured to determine the error rate in the decoded data and when the error rate is low, then the receiver may be configured not to use feedback and iterative demodulation, but to demodulate non-iteratively without using feedback. When the error rate is sufficiently high, then the receiver may be configured to use feedback and iterative demodulation. Hence at certain times the receiver may be configure to provide iterative demodulation with feedback and at other times the receiver may be configured to provide non-iterative demodulation without feedback.
(84) The receivers described herein may be beneficial in communication and broadcasting systems using various differential modulation schemes, such as, but not limited to, the DAB family of standards, and in communication and broadcasting systems using coherent modulation and iterative demodulation. The receivers may significantly improve the required signal strength to achieve a certain BER target and/or reduce the BER for a given signal strength.
(85) The receivers may have much lower complexity compare to other iterative demodulation and decoding methods for differential or coherent modulated symbols, owing to the use of hard decision feedback instead of using soft decision decoding and demodulation.
(86) Furthermore, the memory requirement can be reduced by using partial iterative demodulation and decoding, for example by random symbol selection or exploiting channel strength information to select the symbols for iterative processing for both differential and coherent modulated symbols.
(87) In this specification, example embodiments have been presented in terms of a selected set of details. However, a person of ordinary skill in the art would understand that many other example embodiments may be practiced which include a different selected set of these details. It is intended that the following claims cover all possible example embodiments.
(88) Any instructions and/or flowchart steps can be executed in any order, unless a specific order is explicitly stated. Also, those skilled in the art will recognize that while one example set of instructions/method has been discussed, the material in this specification can be combined in a variety of ways to yield other examples as well, and are to be understood within a context provided by this detailed description.
(89) While the disclosure is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and described in detail. It should be understood, however, that other embodiments, beyond the particular embodiments described, are possible as well. All modifications, equivalents, and alternative embodiments falling within the scope of the appended claims are covered as well.