Signal Detection and Channel Estimation in OTFS

doi:10.12142/ZTECOM.202104003

Abstract

Abstract:

Orthogonal time frequency space (OTFS) modulation is a recently proposed modulation scheme that exhibits robust performance in high-Doppler environments. It is a two-dimensional modulation scheme where information symbols are multiplexed in the delay-Doppler (DD) domain. Also, the channel is viewed in the DD domain where the channel response is sparse and time-invariant for a long time. This simplifies channel estimation in the DD domain. This paper presents an overview of the state-of-the-art approaches in OTFS signal detection and DD channel estimation. We classify the signal detection approaches into three categories, namely, low-complexity linear detection, approximate maximum a posteriori (MAP) detection, and deep neural network (DNN) based detection. Similarly, we classify the DD channel estimation approaches into three categories, namely, separate pilot approach, embedded pilot approach, and superimposed pilot approach. We compile and present an overview of some of the key algorithms under these categories and illustrate their performance and complexity attributes.

Key words: OTFS modulation, delay-Doppler domain, high-Doppler channels, signal detection, channel estimation

NAIKOTI Ashwitha, CHOCKALINGAM Ananthanarayanan. Signal Detection and Channel Estimation in OTFS[J]. ZTE Communications, 2021, 19(4): 16-33.

Figures/Tables 21

Figure 1 Multiplexing in delay-Doppler grid

Figure 2 Orthogonal time frequency space (OTFS) modulation scheme

Figure 3 Signal detection approaches in OTFS

Figure 4 Low complexity linear minimum mean squared error (LMMSE) equalization[23]

Figure 5 Message passing between variable nodes and check nodes

Figure 6 Full deep neural network (DNN) architecture for detection

Figure 7 Symbol DNN architecture for detection

Figure 8 BER performance of linear OTFS detectors for IEEE 802.11p WAVE channel model

Figure 9 Computational complexity of conventional MMSE and low-complexity MMSE detectors

Figure 10 BER performance of MMSE, message passing, and symbol-DNN based detectors

Table 1 Delay-Doppler profile considered in Figure 10

Path $(i)$	1	2	3	4	5	6	7	8
$τ i μ s$	0	4.16	8.32	12.48	16.64	20.8	24.96	29.12
$ν i m s$	0	0	938.5	938.5	938.5	1 875	1 875	1 875

Table 1 Delay-Doppler profile considered in Figure 10

Path $(i)$	1	2	3	4	5	6	7	8
$τ i μ s$	0	4.16	8.32	12.48	16.64	20.8	24.96	29.12
$ν i m s$	0	0	938.5	938.5	938.5	1 875	1 875	1 875

Table 2 Parameters of symbol-DNN detector in Figure 10

Parameters	Symbol-DNN
Number of input neurons	$2 M N ? = ? 512$
Number of output neurons	\| $A$ \| = 2
Number of hidden layers	1
Number of neurons in hidden layers	256
Hidden layer activation	ReLU
Output layer activation	Softmax
Optimization	Adam
Loss function	Binary cross entropy
Training SNR	10 dB
Number of training examples	50 000
Number of epochs	50

Table 2 Parameters of symbol-DNN detector in Figure 10

Parameters	Symbol-DNN
Number of input neurons	$2 M N ? = ? 512$
Number of output neurons	\| $A$ \| = 2
Number of hidden layers	1
Number of neurons in hidden layers	256
Hidden layer activation	ReLU
Output layer activation	Softmax
Optimization	Adam
Loss function	Binary cross entropy
Training SNR	10 dB
Number of training examples	50 000
Number of epochs	50

Figure 11 BER performance of ML detection and symbol-DNN based detection in 2×2 MIMO-OTFS with correlated noise

Figure 12 DD channel estimation approaches in OTFS

Figure 13 Transmit and receive symbol pattern for embedded pilot based channel estimation[27]

Figure 14 Transmit and receive symbol pattern for sparse Bayesian learning based channel estimation[29]

Figure 15 Transmit symbol pattern in superimposed pilot scheme in Ref. [35]

Figure 16 Transmit symbol pattern in superimposed pilot scheme in Ref. [36]

Table 3 Delay-Doppler profile for Figures 17 and 18

Path $(i)$	1	2	3	4	5
Delay $τ i$	$1 M Δ f$	$2 M Δ f$	$3 M Δ f$	$4 M Δ f$	$5 M Δ f$
Doppler $ν i$	0	$1 N T$	$2 N T$	$3 N T$	$4 N T$

Table 3 Delay-Doppler profile for Figures 17 and 18

Path $(i)$	1	2	3	4	5
Delay $τ i$	$1 M Δ f$	$2 M Δ f$	$3 M Δ f$	$4 M Δ f$	$5 M Δ f$
Doppler $ν i$	0	$1 N T$	$2 N T$	$3 N T$	$4 N T$

Figure 17 Mean squared error performance of delay-Doppler (DD) channel estimation methods

Figure 18 BER performance with estimated delay-Doppler (DD) channel at pilot SNR of 20 dB

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