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Trellis-Coded Quadrature Amplitude Modulation

Profile image of Matthias PätzoldMatthias Pätzold

2016

https://doi.org/10.1109/25.790523
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22 pages

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Abstract

Trellis-coded quadrature amplitude modulation with 2N-dimensional constellations mobile radio channels

Figures (17)
CORRESPONDENCE BETWEEN Z/,Z0, AND THE FOUR 2-D SUBSETS TABLE I
CORRESPONDENCE BETWEEN Z/,Z0, AND THE FOUR 2-D SUBSETS TABLE I
PARTITION OF THE 128-POINT 4-D SIGNAL SET INTO 16 SUBSETS S; (k = O, J,...,15
PARTITION OF THE 128-POINT 4-D SIGNAL SET INTO 16 SUBSETS S; (k = O, J,...,15
bed? A bit converter (see Fig. 2) converts the four bits YO,, I/,, I2,,,and I3,,,into two pairs of selection bits Z0,Z1, and ZOn+1Z1n+1, which are used to select the pair of 2-D subsets corresponding to the 4-D type. With the correspondence between the bit pair ZO,Z1, and the 2-D subsets A, B, C, and D as shown in Table I, the operation of the bit converter for the Partition I is as shown in Table TV
bed? A bit converter (see Fig. 2) converts the four bits YO,, I/,, I2,,,and I3,,,into two pairs of selection bits Z0,Z1, and ZOn+1Z1n+1, which are used to select the pair of 2-D subsets corresponding to the 4-D type. With the correspondence between the bit pair ZO,Z1, and the 2-D subsets A, B, C, and D as shown in Table I, the operation of the bit converter for the Partition I is as shown in Table TV
We will design now two convolutional encoders which fit in the general diagram shown in Fig. 2. Note that every one of the sixteen 4-D subsets contains eight 4-D points which are different from each other in both the first and the second 2-D component. Therefore, the intraset Hamming distance of the 16 subsets is maximized to dy = 2. However, the interset Hamming distance only equals 1. Recall that our aim is not to maximize the Euclidean distance between allowed sequences, but the Hamming distance. A 4-D block encoder then takes three input information bits /2, , J3, , and //,4; and generates two pairs of selection bits, Z2,Z3, and Z2n4;Z3n+41 , in accordance with Table V. Each of the bit pairs can assume any of the values given in Table IJ, but they cannot both assume the value 10 which corresponds to the outer ring R2.
We will design now two convolutional encoders which fit in the general diagram shown in Fig. 2. Note that every one of the sixteen 4-D subsets contains eight 4-D points which are different from each other in both the first and the second 2-D component. Therefore, the intraset Hamming distance of the 16 subsets is maximized to dy = 2. However, the interset Hamming distance only equals 1. Recall that our aim is not to maximize the Euclidean distance between allowed sequences, but the Hamming distance. A 4-D block encoder then takes three input information bits /2, , J3, , and //,4; and generates two pairs of selection bits, Z2,Z3, and Z2n4;Z3n+41 , in accordance with Table V. Each of the bit pairs can assume any of the values given in Table IJ, but they cannot both assume the value 10 which corresponds to the outer ring R2.
There are 16 parallel transitions between any current state i and a successive state j. Therefore, in this case also, the shortest event path has a length equal to one transition. However, the multiplicity of two transitions error event path is only half of that for the 16-state convolutional encoder. The association of 4-D subsets with the state transitions satisfies the Rule 2 as given for the case b = 3. The logical diagram of the convolutional encoder is shown in Fig. 7(b). The authors have also designed 4-D trellis codes for transmitting b = 5 bits per signaling interval and 6-D trellis codes based on signal constellations partitioned such that the Hamming distance between the points within a subset equals 3. These codes have not been included in this paper by considerations of typographical space. The interested readers are kindly invited to contact the authors.
There are 16 parallel transitions between any current state i and a successive state j. Therefore, in this case also, the shortest event path has a length equal to one transition. However, the multiplicity of two transitions error event path is only half of that for the 16-state convolutional encoder. The association of 4-D subsets with the state transitions satisfies the Rule 2 as given for the case b = 3. The logical diagram of the convolutional encoder is shown in Fig. 7(b). The authors have also designed 4-D trellis codes for transmitting b = 5 bits per signaling interval and 6-D trellis codes based on signal constellations partitioned such that the Hamming distance between the points within a subset equals 3. These codes have not been included in this paper by considerations of typographical space. The interested readers are kindly invited to contact the authors.
= sl CU eee eee eee ee eee The transmitted signal is impaired first by a complex multiplicative stochastic process describing the fading behavior of the frequency-nonselective mobile radio channel and second by a complex additive white Gaussian noise (AWGN) process. In the receiver, the received signal is demodulated and deinterleaved before feeding into the trellis decoder. The trellis decoder is based on the maximum likelihood sequence decoding principle by using the classical Viterbi algorithm. It is well-known that the performance of the trellis decoder can be considerably improved if channel state information (CSI) is available. To obtain CSI from the received signal a channel estimator is required in the receiver.
= sl CU eee eee eee ee eee The transmitted signal is impaired first by a complex multiplicative stochastic process describing the fading behavior of the frequency-nonselective mobile radio channel and second by a complex additive white Gaussian noise (AWGN) process. In the receiver, the received signal is demodulated and deinterleaved before feeding into the trellis decoder. The trellis decoder is based on the maximum likelihood sequence decoding principle by using the classical Viterbi algorithm. It is well-known that the performance of the trellis decoder can be considerably improved if channel state information (CSI) is available. To obtain CSI from the received signal a channel estimator is required in the receiver.
OPTIMIZED PARAMETERS OF THE EXTENDED SUZUKI CHANNEL MODEL [15] TABLE VUI The above described extended Suzuki process N(t) is an analytical (mathematical) model that cannot be implemented exactly on a computer. In order to enable the simulation of such processes, an efficient simulation model was also derived in [15] (see Fig. 9) by applying the concept of deterministic channel modeling (e.g. [18], [19]). The parameters 9, 03, m3, and fp appearing in Fig. 9 are obtained directly from Table VIII, whereas the remaining parameters of the simulation model (fins Cin> @,,,) have to be determined according to the procedure described in [15].
OPTIMIZED PARAMETERS OF THE EXTENDED SUZUKI CHANNEL MODEL [15] TABLE VUI The above described extended Suzuki process N(t) is an analytical (mathematical) model that cannot be implemented exactly on a computer. In order to enable the simulation of such processes, an efficient simulation model was also derived in [15] (see Fig. 9) by applying the concept of deterministic channel modeling (e.g. [18], [19]). The parameters 9, 03, m3, and fp appearing in Fig. 9 are obtained directly from Table VIII, whereas the remaining parameters of the simulation model (fins Cin> @,,,) have to be determined according to the procedure described in [15].
Rice process with cross-correlated components
Rice process with cross-correlated components
A profound insight into the performance of the proposed scheme is obtained by comparing the BER of our b=3 4-D TCM system with the BER of an appropriate reference system. As system we used an uncoded 8-PSK system which has the same information bit rate as the trellis-coded 12-QAM transmission system with b=3 bits per signaling interval. The resu of the reference system is also depicted in Fig. 10. The presented results show us that t reference proposed ting BER he coding gain ranges from 2.0 dB (AWGN) up to 5.4 dB (heavy shadowing) at a BER of 10°. No proposed TCM scheme has especially been designed for fading channels, what explains th the achieved coding gain is higher for the heavy shadowing condition than for the AWGN te that the e fact that channel.
A profound insight into the performance of the proposed scheme is obtained by comparing the BER of our b=3 4-D TCM system with the BER of an appropriate reference system. As system we used an uncoded 8-PSK system which has the same information bit rate as the trellis-coded 12-QAM transmission system with b=3 bits per signaling interval. The resu of the reference system is also depicted in Fig. 10. The presented results show us that t reference proposed ting BER he coding gain ranges from 2.0 dB (AWGN) up to 5.4 dB (heavy shadowing) at a BER of 10°. No proposed TCM scheme has especially been designed for fading channels, what explains th the achieved coding gain is higher for the heavy shadowing condition than for the AWGN te that the e fact that channel.

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Related topics

  • Engineering
  • Mathematics
  • Technology
  • Mobile Radio Channel Estimation
  • Fading Channel
  • Trellis Coded Modulation
  • Quadrature Amplitude Modulation
  • Additive White Gaussian Noise
  • Set partitions
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