Soft decision differential demodulator for radios in wireless networks supporting train control

Abstract

Improvements to demodulators in receivers of radios used for train communications t to receive a radio frequency (RF) signal transmitting a packet of data. A demodulator is configured to generate a soft decision for a decoder, the soft decision including reliability information determined by calculating for the bit position a logarithmic likelihood ratio (LLR). The demodulator is configured to correct a bias in the LLR calculation for any one of the bit positions resulting from a difference in the number symbols in the set of all possible symbols that could have a 0 value in the bit position and the set of all possible symbols that could have a 1 in the bit position.

Claims

1. A radio for communicating over a wireless network supporting train control, the radio comprising a receiver configured to receive a radio frequency (RF) signal transmitting a packet of data comprising a sequence of bits using a modulation scheme providing for at least 16 possible discrete symbols, each symbol comprising a group of at least 4 bits, each of the at least 4 bits occupying a predefined bit position in the symbol; the receiver comprising: a demodulator configured to demodulate the RF signal according to the modulation scheme and generate for each received symbol a soft decision of which of the at least 16 possible discrete symbols was received; and a decoder configured to decode the soft decisions to recover the data in the packet; wherein the demodulator is configured to generate a soft decision by generating for received symbol a bit value and reliability information reflecting a probability of the bit value being correct, the reliability information determined by calculating for the bit position a logarithmic likelihood ratio (LLR) of the probability of the bit value being 0 given the received symbol to the probability of the bit value being a 1 given the received symbol, the LLR being calculated on a basis of all possible symbols that could have a 0 value in the bit position and all possible symbols that could have a 1 value in the bit position; and wherein the demodulator is further configured to correct a bias in the LLR calculation for any one of the bit positions resulting from a difference in the number symbols in a first set of all possible symbols that could have a value of 0 in the bit position and a second set of all possible symbols that could have a value of 1 in the bit position.

2. The radio of claim 1, wherein demodulator is configured to correct the bias in the LLR calculation by mapping a first set of decision regions in a signal constellation for the modulation scheme into a second set of decision regions in the signal constellation according to a predetermined transformation; the first set of decision regions and the second set of decision regions containing a set of all possible symbols that contain the same bit value in the same position.

3. The radio of claim 2, wherein the demodulator is further configured to map a received symbol according to the predetermined transformation and calculating the LLR for each bit position according to the mapping.

4. The radio of claim 1, wherein the demodulator is configured to correct the bias in the LLR calculation by making the number symbols in the set of all possible symbols that could have a 0 value in the bit position equal to the set of all possible symbols that could have a 1 in the bit position by increasing the number of possible symbols in whichever of the first and second set of all possible symbols has a lower number of symbols before calculating the LLR for the bit position.

5. A method for communicating over a wireless network supporting train control, the method comprising: receiving a radio frequency (RF) signal transmitting a packet of data comprising a sequence of bits using a modulation scheme that provides for at least 16 possible discrete symbols, each symbol comprising a group of at least 4 bits, each of the at least 4 bits occupying a predefined bit position in the symbol; demodulating the RF signal according to the modulation scheme and generating for each received symbol a soft decision of which of the at least 16 possible discrete symbols was received; and decoding the soft decisions to recover the data in the packet; wherein demodulating comprises, generating for received symbol a bit value and reliability information reflecting a probability of the bit value being correct, the reliability information determined by calculating for the bit position a logarithmic likelihood ratio (LLR) of the probability of the bit value being 0 given the received symbol to the probability of the bit value being a 1 value given the received symbol, the LLR being calculated on a basis of all possible symbols that could have a 0 value in the bit position and all possible symbols that could have a 1 in the bit position; and correcting a bias in the LLR calculation for any one of the bit positions resulting from a difference in the number symbols in a first set of all possible symbols that could have a value of 0 in the bit position and a second set of all possible symbols that could have a value of 1 in the bit position.

6. The method of claim 5, wherein demodulating further comprises correcting the bias in the LLR calculation by mapping a first set of decision regions in a signal constellation for the modulation scheme into a second set of decision regions in the signal constellation according to a predetermined transformation; the first set of decision regions and the second set of decision regions containing a set of all possible symbols that contain the same bit value in the same position.

7. The method of claim 6, wherein demodulating further comprises mapping a received symbol according to the predetermined transformation and calculating the LLR for each bit position according to the mapping.

8. The method of claim 5, wherein demodulating further comprises correcting the bias in the LLR calculation by making the number symbols in the set of all possible symbols that could have a 0 value in the bit position equal to the set of all possible symbols that could have a 1 in the bit position by increasing the number of possible symbols in whichever of first or second set of all possible symbols has a lower number of symbols before calculating the LLR for the bit position.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a schematic diagram illustrating components of a train control system.

(2) FIG. 1B is a schematic drawing of a representative, non-limiting example of a digital transmitter and receiver.

(3) FIG. 2 is a schematic diagram of a 16-APSK transmitter and receiver.

(4) FIG. 3 is a table of transition values of differentially modulating a carrier signal using 16DAPSK.

(5) FIG. 4 is a signal constellation diagram for 16DAPSK with decision regions.

(6) FIG. 5A is an octant of a 16DAPSK signal constellation with decision regions.

(7) FIG. 5B is an octant of a 16DAPSK signal constellation with decision regions.

(8) FIG. 5C is an octant of a 16DAPSK signal constellation with decision regions.

(9) FIG. 5D is an octant of a 16DAPSK signal constellation with decision regions.

(10) FIG. 6A is a signal constellation diagram for 16DAPSK with altered decision regions for certain symbols with a most significant bit (MSB) value of 1.

(11) FIG. 6B is a flow diagram for a part of a demodulation method.

(12) FIG. 7 is a chart showing curves platting signal to noise ratio (SNR) in dB against packet error rates (PER) curves for MATLAB simulations of each of three different methods of a 16DAPSK demodulator generating soft decisions.

(13) FIG. 8 is a table listing the required SNR to achieve 5% PER with Rayleigh Fading at 3 different speeds using 16APSK and 16DAPSK modulation with different coding for each modulation scheme.

(14) FIGS. 9A-9B, 10A-10B, and 11A-11B show PER versus SNR curves for decoding with both hard- and soft-decision from 16DAPSK demodulator for different coding rates and under fading conditions with different vehicle speeds.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

(15) In the following description, like numbers refer to like elements.

(16) Because differential encoding is used, the difference or transition between the amplitude and phase between received between two consecutive symbols represents the symbol that is being sent. Tables 300 and 301 of FIG. 3 list, as a non-limiting example, the amplitude and phase transitions required in a 16DAPSK (8,8) modulation scheme to send one of the symbols along the top rows 302 and 306 after the symbol listed in the left columns 304 and 308 is sent assuming a ring ratio of =2. For example, to send symbol 10, which correspond to bits with binary values of 1010 (the left-most digit being the most significant bit (MSB), after sending symbol 6, which has bit values of 0110, the complex transition of the carrier wave to the next symbol state is 2<135. This means that the carrier signal must change in amplitude by a magnitude of 2 and change phase by 135 degrees.

(17) As it can be seen from the table of FIG. 3, the complex transitions have a magnitude of 1 when the MSB of the modulating symbol is 0 but can have varying magnitudes of either or 1/ when the MSB of the modulating symbol is 1.

(18) Referring to FIG. 4, a signal constellation chart 402 for 16DAPSK with a ring ratio of =2 is divided into oct MSB results in split decision regions indicated on constellation chart 402 for 16DAPSK (8,8). Decision region 404 contains 8 complex transitions with unit magnitude. These correspond to transitions in which the MSB of the modulating symbol is 0. Each symbol in this region is marked by a circle. Inner decision region 406 and outer decision region 408 contain a total of 16 possible complex transitions, each with an amplitude (region 408) or 1/ (region 406). Each of the possible symbols in these regions are marked by a plus sign.

(19) A boundary 410 between region 406 and region 404 represents a lower decision threshold for decision region 404, which is given by equation (6).

(20) $\begin{array}{cc}{}_L=\frac{2}{1+}& \mathrm{Equation}\left(6\right)\end{array}$

(21) A boundary 412 between region 404 and region 408 defines an upper threshold value for decision region 404, which is given equation (7).

(22) $\begin{array}{cc}{}_H=\frac{1+}{2}& \mathrm{Equation}\left(7\right)\end{array}$

(23) Having a split region in the decision for symbols sharing the same MSB, such as decision regions 406 and 408 in the illustrated example, creates a bias when calculating a logarithmic likelihood ratio (LLR) for the most significant bit (MSB) for a given received symbol. The reason is that for every complex transition corresponding to a transmitted bit with a logical value of 0 bit, there will be two complex transitions corresponding to a transmitted bit with logical value 1 bit. For bit b.sub.3 in the received 16APSK symbol r=b.sub.3b.sub.2b.sub.1b.sub.0 there are 8 symbols in the set S.sub.0 of all possible transitions or symbols with a MSB of 0 and there are 16 possible symbols in the set S.sub.1 of symbols for a received symbol with an MSB of 1. Thus, when calculating the LLR using equation (5) for bit b3, there will be a bias in the soft decision toward a b3 of 1. This bias has been confirmed using simulations. For the other bits b.sub.0 to b.sub.2, there are equal number of possible symbols (12) in S.sub.0 and S.sub.1. Thus, a split decision region for received symbols may result in a bias when calculating the LLR for a given bit position where the number of possible symbol values is unequal for a bit with a 0 value and a bit with a value of 1.

(24) To correct for this bias, the decision processes of a software implemented of a demodulator, such as demodulator 218 (FIG. 1B), are adapted and configured to implement one of the two methods described below when determining an LLR for the MSB of a received symbol transmitted using 16DAPSK. These methods may be similar situations arising in other modulations schemes, where the set of all possible transitions for each of the two possible values of a bit are not equal when calculating a LLR for a software decision.

(25) The first method will be referred to as the doubling method. In this method, the number of complex transitions corresponding to an MSB of 0 used in the calculation of LLRs are doubled. Thus, an equal number of complex transitions would be used in the numerator and the denominator of the LLR term in equation (5) for the MSB of a given received symbol. In other words, the number of symbols in sets S.sub.0 and S.sub.1 would be made the same for each received symbol r when calculating the LLR for the MSB.

(26) The second method will be referred to as the mapping method. In this method, the part of the inner decision region 406 within each octant 414 corresponding to a transmitted MSB of logical value 1 is mapped onto the outer decision region 408 within that octant corresponding to MSB of logical value 1. This effectively combines the split decision regions 404 and 408, which correspond to the symbols with an MSB value of 1 into one decision region. This makes the calculation of the LLR for soft decisions more straightforward and reduces the number of expressions used in the calculation of LLRs to 16 (8 in the numerator and denominator each) for all the bits in a received symbol. The mapping comprises scaling the inner region by a factor equal to followed by a reflection against the line tangent to the outer boundary 412 of the decision region 404 that corresponds to symbols with an MSB equal to 0 for each of the eight octants 414.

(27) FIGS. 5A to 5D demonstrates the mapping operation for one of the 8 octants 414 in the signal constellation of FIG. 4. FIG. 5A shows the decision regions 404, 406 and 408 for octant 1. FIG. 5B shows the same decision regions 404, 406, 408, plus a reflection line 502. FIG. 5C shows scaling of the inner decision region 406, resulting in a scaled decision region 504. In FIG. 5D, the scaled inner decision region 504 has been reflected against the reflection line 502, resulting in decision region 506.

(28) In general, it can be shown that the reflection of a point P with coordinates (p, q) against a given reflection line y=mx+b will be point R with coordinates (u, v), where the values of u and v are given by equations (8) and (9).

(29) $\begin{array}{cc}u=\frac{\left(1-m^2\right)p+2mq-2mb}{m^2+1}& \mathrm{Equation}\left(8\right)\\ v=\frac{\left(m^2-1\right)q+2mp+2b}{m^2+1}& \mathrm{Equation}\left(9\right)\end{array}$

(30) Thus, the parameters for the reflection line 502 can be rewritten as shown in equation (10), is the angle between the reflection line and the y coordinate.

(31) $\begin{array}{cc}m=-\cot ;b=\frac{+1}{2\sin }& \mathrm{Equation}\left(10\right)\end{array}$

(32) The new coordinates of a point (p, q) within the inner decision region 406 after scaling by a factor of and reflection against the line 502 can then be rewritten as shown in equations (11) and (12).
u=[(1+1/)cos p cos 2q sin 2]Equation (11)
v=[(1+1/)sin +q cos 2p sin 2]Equation (12)

(33) In general,

(34) 0$=n\frac{}{4},$
where n=0, . . . , 7 and is the octant number. For octant 1,

(35) $=/4,m=-1\mathrm{and}b=\frac{+1}{\sqrt{2}}.$

(36) Referring now also to FIG. 6A, an entire signal constellation 600 includes the new decision regions after mapping the inner decision region 406 for each octet into a new decision region 504, resulting in a different decision region for each symbol with an MSB of 1 and a magnitude of 1/. The decision regions of received symbols with a MSB of 1 now form one contiguous segment.

(37) The process of, for example, the demodulator 218 is modified to scale and reflect a sample of the received symbol having a magnitude and phase within the inner region 406 according to the transformation equations (11) and (12). This modified process is represented by a flow diagram 604 in FIG. 6B. In an implementation using, for example, MATLAB, the scaling and reflection step for a differentially demodulated symbol occurs when the magnitude of the differentially demodulated symbol falls below a lower threshold defined by equation (6), which is represented by boundary 410 in the figure. Received signal samples 606 are differentially demodulated at step 608 by the differential demodulator 218 to produce differentially demodulated symbols 610. As represented by decision step 612 and process step 614, if a differentially modulated symbol is less than the magnitude of the lower threshold value, it is scaled and reflected according to the transformation equations before the LLR is determined at step 616. If it is not below the lower threshold value, the symbol is not scaled and reflected prior to determination of the LLR. Thus, differentially demodulated symbols with magnitudes below the lower threshold defined in equation (6) are scaled and mapped to the outer decision region 408 for purposes of calculating an LLR that comprises a soft decision. Simulations demonstrate that removing the bias from the calculation results in better performance, a lower requirement for a signal to noise ratio (SNR) to achieve a given packet error rate (PER).

(38) FIG. 7 shows a comparison a simulated performance using a MATLAB simulation that includes models for fading channels, additive white Gaussian noise (AWGN) and forward error correction (FEC) in terms of PER versus SNR for a 16DAPSK soft-decision modulator as described above without the use of either the doubling method or the mapping method, which is labelled as original method, which is line 702, as compared to the performance of the 16DAPSK soft-decision modulator modified to use the doubling method, line 704, and the mapping method, line 706. The improvements of using the doubling method with the 16DAPSK soft-decision modulator and not using is improvement of 2 dB in terms of SNR required to achieve a 5% PER, which is indicated by dashed line 708. Using the mapping method improved performance by 4 dB. Furthermore, the simulation mapping method is the fastest. Computationally, the mapping method is also the fastest of all 3, requiring 570 seconds to process 10000 packets compared to 580 seconds for the original method and 590 seconds for the doubling method.

(39) The table of FIG. 8 lists the required SNR to achieve 5% PER with Rayleigh Fading at 3 different speeds using 16APSK and 16DAPSK modulation with no FEC coding, convolutional coding at rate, and convolutional coding at a rate for each modulation scheme. Depending on the example, the simulations demonstrate about 0.7 to 2 dB gain by using soft-decisions over hard-decisions for a decoder in a receiver.

(40) FIGS. 9A-9B, 10A-10B, and 11A-11B show the PER vs SNR curves from simulations that decode using hard-decisions (FIGS. 9A, 10A, and 11A) and soft-decisions (FIGS. 9B, 10B, and 11B) from 16DAPSK and 16APSK demodulators with the coding indicated in the table of FIG. 8 and speeds of 20 miles per hour (MPH) (FIGS. 9A-9B), 60 MPH (FIGS. 10A-10B), and 120 MPH (FIGS. 11A-11B). The PER target of 5% is also marked in these figures. The curves correspond to the demodulation and coding as set out in Table 1.

(41) TABLE-US-00001 TABLE 1 Curve 900 D16APSK with no forward error correction (FEC) Curve 902 16APSK with no FEC Curve 904 D16APSK with R = 7/8 Curve 906 D16APSK at R = 3/4 Curve 908 16APSK with R = 7/8 Curve 910 16APSK with R = 3/4

(42) Dashed line 912 represents the target PER.

(43) The foregoing description is of exemplary and preferred embodiments. The invention, as defined by the appended claims, is not limited to the described embodiments. Alterations and modifications to the disclosed embodiments may be made without departing from the invention. The meanings of the terms used in this specification are, unless expressly stated otherwise, intended to have ordinary and customary meaning and are not intended to be limited to the details of the illustrated or described structures or embodiments.