Patent Application
20230231755
The present disclosure relates to a coding and modulation apparatus and method. Further, the present disclosure relates to a transmission apparatus and method. Still further, the present disclosure relates to a computer program and a non-transitory computer-readable recording medium.
Modern communications systems typically employ, among other elements, a coding and modulation apparatus (as part of a transmission apparatus) and a decoding and demodulation apparatus (as part of a receiving apparatus). The coding and modulation apparatus is often part of a so called BICM (Bit Interleaved Coded Modulation) apparatus, which generally comprises (at the transmitter side) a serial concatenation of a FEC (Forward Error Correction) encoder, a bit interleaver, and a modulator, which uses spectral efficient modulation such as multilevel PAM (Pulse Amplitude Modulation), PSK (Phase Shift Keying), or QAM (Quadrature Amplitude Modulation). It should be noted that hereinafter, whenever QAM is mentioned it should be understood as a generally term covering PAM, PSK and QAM.
BICM allows for good performance over both non-fading and fading channels due to the use of the interleaver and/or the FEC encoder. It has a reasonable decoding complexity as opposed to multilevel coding (MLC) coding schemes and is thus used frequently in communications systems, such as in all DVB systems, powerline communications (e.g., Homeplug AV, DAB, LTE, WiFi, etc.).
Generally, the coding and modulation capacity, such as the BICM capacity in systems using a BICM apparatus, is considered as a target function, and it is desired to find optimum constellation points such that this capacity is maximized, often subject to a power normalization, i.e., the average power of the constellation points should be normalized to e.g. 1.
The “background” description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventor(s), to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present disclosure.
It is an object to provide a coding and modulation apparatus and method providing an increased or even maximized coding and modulation capacity. It is a further object to provide a demodulation and decoding apparatus and method as well as a corresponding computer program for implementing said methods and a non-transitory computer-readable recording medium for implementing said methods.
According to an aspect there is provided a coding and modulation apparatus comprising
an encoder that encodes input data into cell words, and
a modulator that modulates said cell words into constellation values of a non-uniform constellation,
wherein said modulator is configured to use, based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, a non-uniform constellation from a group of constellations comprising one or more of the constellations defined by the constellation position vector u1 . . . v, wherein v=sqrt(M)/2−1, as described in detail in claim 1.
According to a further aspect there is provided a transmission apparatus comprising
a coding and modulation apparatus as proposed herein that encodes and modulates input data into constellation values,
a converter that converts said constellation values into one or more transmission streams to be transmitted, and
a transmitter that transmits said one or more transmission streams.
According to still further aspects corresponding methods, a computer program comprising program means for causing a computer to carry out the steps of the coding and modulation method disclosed herein, when said computer program is carried out on a computer, as well as a non-transitory computer-readable recording medium that stores therein a computer program product, which, when executed by a processor, causes the coding and modulation method disclosed herein to be performed are provided.
Preferred embodiments are defined in the dependent claims. It shall be understood that the claimed methods, the claimed computer program and the claimed computer-readable recording medium have similar and/or identical preferred embodiments as the claimed apparatus and as defined in the dependent claims.
One of the aspects of the disclosure is that the constellation points of the used constellations are not located on a regular grid with equidistant symbols, but rather on optimized locations, dependent on the channel characteristics, e.g., channel transition probabilities due to AWGN (Additive White Gaussian Noise), fading, etc. Further, the used constellation is selected dependent on the SNR (signal-to-noise ratio) and the desired total number of constellation points of the used constellation. A method how to find and optimize these non-uniform constellations (in the following called NUCs) will be explained below.
It should be noted that to every M-QAM, one can also think of the underlying sqrt(M)-PAM. Further, it should be noted that in other aspects the group of constellations defined in the claims comprises less constellations, e.g. only constellations for non-fading channels, only constellations for fading channels, only constellations for selected values of M, only constellation for M-QAM or sqrt(M)-PAM and/or constellations for less SNR values. In other words, less constellations may be contained in the group of constellations available for use by the modulator, i.e. the group of constellations available for use by the modulator may comprise one or more of the constellations defined in the claims. Accordingly, the present disclosure is also directed to a coding and modulation apparatus and method that have a smaller group of constellations available for used and use (as explained above) and/or where less constellations are available for a particular value of M.
It should further be noted that for some values of M there are two options of constellations for fading channels and two options of constellations for non-fading channels provided for the same selection parameters (e.g. for the same SNR value) among which the modulation can select. These two options (referred to as 1. option and 2. option) are the result of separate optimizations of the coding and modulation capacity. Hence, for instance based on the desired capacity the modulator may select a constellation from the constellations according to the 1. option or the 2. option, wherein the constellations according to the 2. option generally provide a slightly higher capacity.
However, the constellation points of the QAM constellations considered in this disclosure are not located on a regular grid with equidistant symbols, but rather on optimized locations, dependent on the channel characteristics, e.g., channel transition probabilities due to AWGN, fading, etc.
It is to be understood that both the foregoing general description of the disclosure and the following detailed description are exemplary, but are not restrictive, of the disclosure.
A more complete appreciation of the disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:
Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views,
In other embodiments of the coding and modulation apparatus 10 additional elements may be provided, such as a BCH encoder, an LCPC encoder, a bit interleaver and/or a demultiplexer (for demultiplexing bits of encoded data into the cell words). Some or all of these elements may separate elements or may be part of the encoder 11. For instance, a BICM device as conventionally used in the transmission apparatus of a DVB system may be used as coding and modulation apparatus 10.
In other embodiments of the transmission apparatus 20 addition elements may be provided, such as an input processing unit, a frame building unit and/or an OFDM generation unit as e.g. conventionally used in transmission apparatus of a DVB system.
A receiving apparatus 40 generally comprises a receiver 41 that receives one or more transmission streams, a deconverter 42 that deconverts the received one or more transmission streams into constellation values, and a demodulation and decoding apparatus 43 that demodulates and decodes said constellation values into output data. The demodulation and decoding apparatus 43 generally comprises a demodulator 44 for demodulating constellation values of a non-uniform constellation into cell words, and a decoder 45 for decoding cell words into output data words, wherein based on the total number M of constellation points of the constellation, the signal-to-noise ratio in dB and the channel characteristics, a non-uniform constellation is used from the group of constellations comprising the same predetermined constellations as used in the coding and modulation apparatus 10.
The preferred demodulation and decoding considers soft values as opposed to hard decided values (0 and 1). Soft values represent the continuously distributed received values (possibly after A/D conversion including quantization) by more than two states (as in the case of binary (hard) decision). The reason is that for hard decision, the NUCs are generally not optimal. Nowadays, BICM receivers typically are soft receivers anyway.
Generally, data (e.g. communications data, broadcast data, etc.) shall be transmitted from a transmission apparatus 20 to one or more of said receiving apparatus 40 over a transmission channel 50, 50′. The transmission channel 50, 50′ can be unicast channel, multicast channel, a broadcast channel and may be employed as one-directional or bi-directional channel (i.e. having a return channel from the receiving apparatus to the transmission apparatus).
In an embodiment the modulator 12 is configured to select and use a non-uniform constellation based on the total number M of constellation points of the constellation, the required signal-to-noise ratio SNR for error free decoding in dB and the channel characteristics. In broadcasting applications the constellation is generally not selected dependent on the SNR in the receiver, but dependent on the SNR that is required for error free decoding with a used channel code (if a code is used, for example LDPC codes in case of DVB 2nd generation transmission systems) for an expected channel characteristic, e.g., static reception or multipath fading.
The total number M of constellation points is generally selected according to the desired payload throughput jointly with the code rate of the FEC encoder. The SNR for error free decoding for typical channel characteristic is generally known, e.g. by simulation. In broadcasting the channel characteristics of the receivers are not known, i.e. a compromise is selected. For instance, in broadcasting for each code rate of the FEC encoder one non-uniform constellation is selected, optimized for an SNR that is a compromise for all channel characteristics.
The transmitter generally targets a certain scenario. For instance, a broadcast transmission over cable or satellite considers the channel to be just a non-fading AWGN (appropriate channel model), while a terrestrial broadcaster typically considers the channel to be a fading channel, e.g. with Rayleigh distribution, as several echoes are usually received.
In another embodiment the modulator 12 is configured to adaptively select and use a non-uniform constellation based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, wherein said signal-to-noise ratio SNR in dB and channel characteristics are received from a receiving device 40 to which data shall be transmitted. Such an adaptive selection of the constellation is generally only possible with a return channel in unicast environments. A non-uniform constellation may be adapted e.g. in time and/or frequency domain, e.g. for different OFDM subcarriers.
Depending on the SNR the optimum value for M and the code rate of the FEC encoder can be selected, which offers the highest throughput (equivalent to CB). In other words, for a large SNR a high value of M is selected leading to a high data throughput (and vice versa).
The channel characteristics describe the statistical properties of the channel, e.g., the extent of the multipath propagation of the transmission channel between transmitter and receiver. If the channel is characterized by no multipath propagation, corresponding to the AWGN channel, the required SNR for error free decoding is relatively low, i.e. the NUC has to be selected accordingly for optimum performance. If the transmission channel is characterized by strong multipath propagation, the required SNR for error free reception is larger compared to a channel without multipath propagation, i.e. a NUC optimized for higher SNR has to be used. Further, the NUCs should be optimized taking the fading characteristics into account, as will be discussed below.
As mentioned above, the number M of the constellation points of the constellations is selected according to the desired payload throughput. Larger values of M allow for higher data throughput, but require a larger SNR for error free reception. This is further influenced by the code rate of the FEC encoder, if any FEC encoder is used.
Another explanation (which is closely related to the optimization task of the present disclosure) is that for each SNR, optimized constellations are proposed for different M. The optimization target is the BICM capacity. For an expected SNR, say 15 dB of SNR should be guaranteed, M is chosen, for which the respective optimized NUC yields the largest BICM capacity. As a general rule it holds that for low SNR a low value of M should be selected and vice versa. But from a theoretical point of view, it turns out that high M is generally optimum, e.g., choosing M=4096 or M=1024 is preferred, because even for low SNR, the optimized NUC will “look (almost) like” a constellation with effectively smaller M, as several points will overlap. However, modulation and demodulation complexity increase with increasing M, so a tradeoff has to be considered.
As mentioned above known communications systems often employ among other blocks a so called BICM apparatus which may also be used as coding and modulation apparatus according to the present disclosure. The maximum possible capacity over a BICM apparatus is described by the BICM capacity CB:
where I denotes the i-th bit label of the constellation point, and m is the total number of bits/QAM symbol point. Altogether the QAM constellation consists of M=2m constellation points, each assigned a particular bit label (00 . . . 00, 00 . . . 01, . . . , 11 . . . 11). In (1), E[.] denotes expectation operator, p(rk) is the probability density function (pdf) of the received symbols, sk is the transmitted symbol according to a particular bit label, k is the discrete time (or subcarrier index in case of OFDM modulation), x1 is a particular symbol of the set of all constellation symbols, this set being denoted by (=symbol alphabet, with cardinality M=2m)
p(rk|sk=x1) is the likelihood function (transition probability—defined by the channel characteristics) that rk is received given the fact that sk=x1 was transmitted. The subset bi includes all symbols from
, where the i-th bit label is b (either b=0 or b=1).
As seen in (1), CB is a 2-dimensional integral. If only constellations are considered that can be split into two 1-dim. PAM constellations, it is easy to see that
C
B(2-dim.)=2×CB(1-dim.) (2)
All investigated channels here include AWGN (only or after the fading channel). This can be described by the signal-to-noise ratio SNR, typically in dB:
SNR=10*log10(Es/σ2), (3)
where Es is the average symbol power of the QAM constellation (typically normalized to 1), and σ2 is the variance (=power) of the additive white Gaussian noise (which is assumed to be of zero-mean).
In (2), the 1-dimensional consideration for CB (1-dim.) uses an N-PAM constellation, which has only half the symbol power, if just the projection on the in-phase or quadrature-phase, respectively, is taken. However, if again a power normalization to 1 is considered, the noise variance by a factor of 2 is increased. Thus, to be more precise, the target function for the optimization process considered according to the present disclosure is given by
C
B(2-dim. at SNR x)=2×CB(1-dim. at SNR x/2), (4)
where the 1-dimensional PAM has normalized power 1, thus just half the SNR (here, in absolute values, i.e. not in dB) as explained above. The 1-dimensional BICM capacity is also computed according to (1), where the 2-dimensional integral becomes a 1-dimensional integral with rk∈,
being the set of real numbers.
This equation (4) is optimized, given all degrees of freedom, namely the constellation points of the underlying 1-dim. constellation, subject to the power constraint, i.e.
For example, a regular 4-QAM consists of constellation points (ejπ/4, ej7π/4, e3π/4, ej5π/4), as can be seen in
The above example can be extended to higher order N2-QAMs, with M>2.
Then the underlying N-PAM describes for one component the 1st, 3rd, 5th and so on bit label, while for the other component it describes the 2nd, 4th, 6th and so on label.
Constellation shaping is generally known and has a long history. Only in recent years, constellations were investigated which maximize the BICM capacity CB. In [6], the authors propose an heuristic approach to maximize CB by forcing the underlying PAM to approach a Gauss-like form (as is well known from Shannon's capacity theorem, the optimum constellation over the AWGN channel should have a Gaussian distribution; note that this means that there is an infinite number of continuously distributed input signals, having a Gaussian distribution, i.e., symbols with small power should occur more frequently than symbols with large power). There is no proof that this maximizes CB, indeed those NUCs designed according to this method do not maximize CB. The resulting NUCs are in general no N2 NUCs, i.e., a 2-dimensional NUC was optimized, not the underlying PAM. However, in N. Muhammad, “Coding and modulation for spectral efficient transmission”, Ph.D. dissertation, Universität Stuttgart, Institut für Nachrichtenübertragung, Pfaffenwaldring 47, 70569 Stuttgart, Germany, June 2006, the first time constellations have been directly optimized with respect to the target function CB. For this method two differences to the current method occur:
As described above, two problems arise when solving the optimization:
a) improper integral: integration border selection; and
b) integrant.
With respect to problem a) (improper integral: integration border selection), as seen in eq. (1), the BICM capacity involves an integral from −infinity to +infinity (=improper integral). Any numerical solution of this integral has to consider finite integration borders such as from −b to +b, with b sufficiently large. Matlab provides several functions for numerical integration, even for improper integrals, such as the function “quad”, which internally optimizes the appropriate integration borders b. However, it has been observed that even these functions yield numerical instabilities and do not end up with the correct integral.
It can be observed that the integrant in (1) approaches 0 if the variable rk is sufficiently large (b→Inf). So a naïve approach would be to stepwise increase the variable rk, until the integrant falls below a certain threshold (say 10−300 or if it even becomes exactly 0) and chose this value for the integration border b. However, it has further been observed that the integrant can take on very small values even before it converges to 0 for large variables, as can be seen in the two examples depicted in
Note that for 30 dB, many very small integrant values occur in the interval [−2,2] and any optimized integration border would be misleading in this interval. Thus, it is proposed to find the optimum (=numerically correct) integration border b as follows:
i) start with a large positive value S, iteratively reduce the value by decrements D, compute the integrant with this value as variable rk, until the first non-zero value of the integrant is computed. If no non-zero integrant can be found before rk=0, start again with a larger initial value S (say 10 times larger than before) and reduce D (say by factor of 10) to have a larger search interval and a finer granularity.
ii) As this search is time consuming, it is proposed to adjust the initial value S and the decrement D according to the SNR. If σ2 is the noise variance of the 1-dimensional mapping (see eq. (3)), then as a good compromise S=4000*σ2 and D=50*σ2 has been chosen.
With respect to problem b) (integrant) it has further been observed that the integrant of the BICM capacity integral can cause numerical instabilities for large SNR values. As can be seen in eq. (1), the integrant consists of sums, including terms such as
x*log(x),x*log(1/x), or x*1/log(x).
The value of x is e.g. the transition probability p(rk|s_k=x1), or a pdf or includes parts thereof. The values of x become increasingly small (even approaching 0) if the SNR is very large, as the pdfs typically correspond to Gaussian distributions. Thus, the following limits might occur:
lim{x→0}x*log(x),lim{x→0}x*log(1/x), or lim{x→0}x*1/log(x)
Note that in theory, each limit converges to 0 (see l′Hospital's rule), but in a numerical computation, values such as + or −infinite or NaN (“not a number”) will occur. Thus, the following is proposed: during the computation of each element (i.e., each addend in the integrant of (1)), the value has to be checked if it is finite (otherwise infinite or NaN), and replace it by 0 in case it is not finite. Only this way, reliable integration results can be obtained.
With the above considerations, N2-NUCs have been optimized as one embodiment with N2 being 16, 64, 256, 1024 (1 k), 4 k, 16 k, 64 k, 256 k and 1024 k. This means, the target function CB of the underlying 1-dimensional PAM is used and the degrees of freedom (the real-valued constellation points of the PAM) are optimized. Note that the PAM has only N=sqrt(N2) degrees of freedom (e.g. a 64-NUC is based on an 8-PAM). Due to symmetry, the negative constellation values are the same as their positive counterparts, such that only N/2 degrees of freedom remain. Finally, one more degree of freedom is lost due to the power normalization (5). The 64-NUC can thus be optimized by considering only 3 degrees of freedom (“dof”, i.e., optimization variables).
The presented optimization is preferably based on the Matlab's fmincon function for constrained nonlinear optimization: the target function is the BICM capacity, the constraints are as follows:
The function fmincon requires an initial set of dof, where the values were taken from a regular, i.e. uniform constellation, but a random mutation was applied on them. It is to be noted that the resulting values should still be in increasing order, otherwise the Gray bit labeling is not fulfilled anymore. The NUCs will be described by their degrees of freedom, e.g., a 64-NUC optimized for the AWGN channel at SNR=11.5 dB yields the following values (optimized degrees of freedom):
This means that the positive constellation values are
As described before, the first entry (1.6405) corresponds to the bit label 000, the next one (1.0073) to 001 and so on. The 2-dim. 64-NUC is then obtained by symmetry, where both in-phase and quadrature-phase component of the NUC are based on the 8-PAM NUC.
The creation of the 2-dim. NUC based on the optimized degrees of freedom will be explained in more detail below.
Since the performance of NUCs depends on the SNR value they are optimized for, a thorough selection is preferably carried out depending on the (FEC) code rate to achieve optimum performance. If the channel characteristics are known, the required SNR value for FEC convergence can be determined by simulation. Then the NUC that has been optimized for this SNR value is chosen for best performance. If the SNR at the receiver is lower than this SNR decoding threshold, the constellation is not optimal. However, this is no drawback, since the BICM capacity is too low for successful decoding anyhow. On the other hand if the SNR at the receiver is clearly higher than the decoding threshold, a sufficient amount of BICM capacity for successful decoding is available, even though the NUC is suboptimal for this SNR range. Therefore, the NUC needs to be optimized for the SNR value at the waterfall region (i.e., decoding threshold for (quasi-) error free decoding) of the FEC. As the SNR value of the waterfall region depends on the code rate of the FEC, a different NUC is selected for each code rate.
The SNR value for (quasi-) error free decoding also depends on the channel characteristics of the receiver. For instance the required SNR for error free decoding of the DVB-T2 LDPC code in the AWGN channel is 0.8 dB, whereas 2.5 dB are required in the Rayleigh P1 multipath channel. The selected NUC for each code rate is thus not optimal in all channel environments and a tradeoff is necessary in a broadcasting environment that suits all (or most) users in the network. In a point-to-point network with return channel, the optimal NUC may be selected based on the measured channel characteristics in the receiver.
Currently, there exist no optimized constellations for fading channels. If the transmitter has no channel state information (CSI), but the receiver has perfect CSI (due to, e.g., pilot-based channel estimation), then the average BICM is the target function, which needs to be optimized for NUCs designed for fading channels. If the magnitude of the fading value for one QAM symbol is denoted as h (e.g. for a particular time instant and/or a particular subcarrier in case of OFDM), then the instantaneous BICM capacity is called CB(h) and given acc. to eq. (1). Note that the pdfs and transition probabilities in (1) are now different from the pure AWGN channel. E.g. in the AWGN case, the likelihood function p(rk|sk=x1) was given by a Gaussian distribution with zero-mean and variance σ2. Now, for fading with the value h, the distribution is still Gaussian with zero-mean, but with instantaneous variance σ2/h2.
A good model for the fading statistics is given by a Rayleigh distribution of the fading magnitude h. Thus, the pdf of h is:
p(h)=h/σh2*exp(−h2/(2*σh2)), (6)
where σh2 is the variance of the Rayleigh distribution. For a passive channel, i.e. one which on average neither attenuates nor magnifies the signal, σh2=½. This means, that the average SNR over a fading channel is the same as of a non-fading channel.
Now, the average BICM capacity over many channel realizations is given by
C
B=∫0∞p(h)*Cb(h)dh, (7)
i.e., the instantaneous BICM capacity as a function of h has to be multiplied by the pdf of h (see (6)) and integrated over all possible fading magnitudes (0 . . . infinity).
Again, an improper integral has to be solved. This time, the integrant of (7) converges to 0 due to the pdf of h. It was found that a sufficiently large upper limit for the integral in (7) is given by 38, independent of the instantaneous capacity CB(h). This enables faster optimization of (7) Results will be shown below for N2-NUCs, N2=16, 64, 256, 1024 (1 k), 4096 (4 k) and 16384 (16 k).
The same principle regarding the selection of the NUC that has been described for static channels also holds for receivers experiencing fading channels, e.g., portable or mobile receivers. But since in fading channels the SNR in the receiver is varying due to the fading effect of the channel, the NUC cannot always operate at the optimum SNR. In general, the NUCs optimized for the fading channel perform better compared to the NUCs optimized for the non-fading channel when used at SNR values for which they are initially not optimized for, i.e. they perform better over broader SNR regions. Moreover, it was found that the NUCs optimized for the Rayleigh fading channel are good for most fading channels, e.g., with Rice distribution, with more than one echo component (e.g. TU6 channel) or with time- and frequency-selective fading with correlation. This is because the optimization considers the average of several channel instances/realizations.
In the following some more explanation is provided regarding the definition of the non-uniform QAM constellations. Each input cell word (y0,q . . . ym-1,q) (i.e. provided to the modulator) shall be modulated using a non-uniform QAM constellation to give a constellation point zq prior to normalization, where m corresponds to the number of bits per QAM symbol m=log2(M). It should be noted that the parameter q used here for discrete time or subcarrier index corresponds to the parameter k as used in the above. The exact values of the real and imaginary components Re(zq) and Im(zq) for each combination of the relevant input bits y0 . . . m-1,q are given in the following tables for the various constellation sizes depending on the NUC position vector u1 . . . v, which defines the constellation point position of the non-uniform constellation. The length of the NUC position vector u is defined by
In one example, the corresponding constellation point zq for a 64-QAM NUC defined by the NUC position vector (u1 . . . 3)=(2,5,6) and the input cell word (y0,q . . . ym-1,q)=(100111) is Re(zq)=−u2=−5 and Im(zq)=u1=2. The complete constellation for this NUC position vector is shown in
The resulting constellation mapping (also called labeling) for the non-uniform constellations follows a binary reflected Gray-Mapping (labeling), i.e. neighboring constellation points differ in only one bit. The power of the constellation points zq is normalized such that the expectation value of the normalized constellation point fq equals 1, i.e. E(|fq|2)=1. For example, the normalized constellation value fq of a uniform 16-QAM constellation results by
The following tables define the constellation position vectors (prior to power normalization) as well as the bit labelling of the data cell words to the constellation points.
y10,q
y10,q
y10,q
y10,q
y11,q
y11,q
y11,q
y11,q
In the following the definition of the NUC position vectors obtained by use of the above described approach is provided. The signal-to-noise ratio (SNR) is always denoted in dB and corresponds to the average SNR in case of fading channels.
a1) 16-QAM or 4-PAM for a non-fading channel (1. option)
a2) 16-QAM or 4-PAM for a fading channel (1. option)
a3) 16-QAM/4-PAM for a non-fading channel (2. option)
a4) 16-QAM/4-PAM for a fading channel (2. option)
b1) 64-QAM or 8-PAM for a non-fading channel (1. option)
b2) 64-QAM or 8-PAM for a fading channel (1. option)
b3) 64-QAM/8-PAM for a non-fading channel (2. option)
b4) 64-QAM/8-PAM for a fading channel (2. option)
c1) 256-QAM or 16-PAM for a non-fading channel (1. option)
c2) 256-QAM or 16-PAM for a fading channel (1. option)
c3) 256-QAM/16-PAM for a non-fading channel (2. option)
c4) 256-QAM/16-PAM for the fading channel (2. option)
d1) 1024-QAM or 32-PAM for a non-fading channel (1. option)
d2) 1024-QAM or 32-PAM for a fading channel (1. option)
d3) 1024-QAM/32-PAM for a non-fading channel (2. option)
d4) 1024-QAM/32-PAM for a fading channel (2. option)
e1) 4096-QAM or 64-PAM for a non-fading channel (1. option)
e2) 4096-QAM or 64-PAM for a fading channel (1. option)
e3) 4096-QAM/64-PAM for a non-fading channel (2. option)
e4) 4096-QAM/64-PAM for a fading channel (2. option)
f1) 16384-QAM/128-PAM for a non-fading channel
f2) 16384-QAM/128-PAM for a fading channel
g) 65536-QAM/256-PAM for a non-fading channel
h) 262144-QAM/512-PAM for a non-fading channel
i) 1048576-QAM/1024-PAM for a non-fading channel
Obviously, numerous modifications and variations of the present disclosure are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the disclosure may be practiced otherwise than as specifically described herein(e.g., if the NUC position vectors are rounded to a smaller number of digits).
In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.
In so far as embodiments of the disclosure have been described as being implemented, at least in part, by software-controlled data processing apparatus, it will be appreciated that a non-transitory machine-readable medium carrying such software, such as an optical disk, a magnetic disk, semiconductor memory or the like, is also considered to represent an embodiment of the present disclosure. Further, such a software may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.
A circuit that may be used for implementing one or more of the elements of the claimed apparatus is a structural assemblage of electronic components including conventional circuit elements, integrated circuits including application specific integrated circuits, standard integrated circuits, application specific standard products, and field programmable gate arrays. Further a circuit includes central processing units, graphics processing units, and microprocessors which are programmed or configured according to software code. A circuit does not include pure software, although a circuit includes the above-described hardware executing software.
Any reference signs in the claims should not be construed as limiting the scope.
| Number | Date | Country | Kind |
|---|---|---|---|
| 12175587.0 | Jul 2012 | EP | regional |
| 13164169.8 | Apr 2013 | EP | regional |
This application is a continuation of U.S. application Ser. No. 16/020,554, filed on Jun. 27, 2018, which is a continuation of U.S. application Ser. No. 15/438,566, filed on Feb. 21, 2017, which is a continuation of U.S. application Ser. No. 14/412,265, filed on Dec. 31, 2014, which is a National Stage Application of International Application No. PCT/EP2013/063824, filed on Jul. 1, 2013, which claims the benefit of priority from EP Application No. 13164169.8, filed Apr. 17, 2013 and EP Application No. 12175587.0, filed Jul. 9, 2012. The entire contents of each of the above applications are incorporated herein by reference in their entirety.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 16844844 | Apr 2020 | US |
| Child | 17989023 | US | |
| Parent | 16020554 | Jun 2018 | US |
| Child | 16844844 | US | |
| Parent | 15438566 | Feb 2017 | US |
| Child | 16020554 | US | |
| Parent | 14412265 | Dec 2014 | US |
| Child | 15438566 | US |
