MIMO-OTFS in High-Doppler Fading Channels:Signal Detection and Channel Estimation(1)

1.abstract

we focus on MIMO-OTFS which brings in the high spectral and energy efficiency benefits of MIMO and the robustness of OTFS in high-Doppler fading channels.
The OTFS channelsymbol coupling and the sparse delay-Doppler channel impulse response enable efficient MIMO channel estimation in high Doppler environments. ???
We present an iterative algorithm for signal detection based on message passing and a channel estimation scheme in the delay-Doppler domain suited for MIMO-OTFS. The proposed channel estimation scheme uses impulses in the delay-Doppler domain as pilots for estimation. We also compare the performance of MIMO-OTFS with that of MIMO-OFDM under high Doppler scenarios.
我们关注于OTFS的高谱效，高能量效率和鲁棒性，这篇paper对于信号检测提出了一个迭代算法和一个适合MIMO-OTFS的信道估计方案，比较了MIMO-OTFS和MIMO-OFDM在高多普勒场景下的表现。

2.introduction

我们直接看Contribution部分。
Our contributions can be summarized as follows. We first present a vectorized input-output formulation for the MIMO-OTFS system.Initially,we assume perfect channel knowledge at the receiver and employ an iterative algorithm based on message passing for signal detection. The algorithm has low complexity and it achieves very good performance. For example, in a 2 × 2 MIMO-OTFS system, a bit error rate (BER) of 10−5 is achieved at an SNR of about 14 dB for a Doppler of 1880 Hz (500 km/hr speed at 4 GHz). For the same system, MIMO-OFDM BER performance floors at a BER of 0.02. Next, we relax the perfect channel estimation assumption and present a channel estimation scheme in the delay-Doppler domain. The proposed scheme uses impulses in the delay-Doppler domain as pilots for MIMO-OTFS channel estimation. The proposed scheme is simple and effective in high-Doppler MIMO channels. For example, compared to the case of perfect channel knowledge, the proposed scheme loses performance only by less than a fraction of a dB.

3.OTFS Modulation

The received signal $y(t)$ is the sum of reflected copies of the transmitted signal $x(t)$.
$y(t)=\int_{v}\int_{\tau}h(\tau,v)x(t-\tau)e^{j2\pi v(t-\tau)}d\tau dv$

OTFS的调制过程如上图所示。
理解 $x[k,l],X[n,m]$的具体含义，这种表示方式之前没有了解过

3.1 Time-frequency modulation

• TF modulation/Heisenberg transform ???
  $x(t)=\sum_{n=0}^{N-1}\sum_{m=0}^{M-1}X[n,m]\varphi_{tx}(t-nT)e^{j2\pi m\Delta f(t-nT)}$
• TF demodulation/Winger transform ???
  $Y[n,m]=A_{\varphi_{rx,y}}(\tau,\nu)|_{\tau=nT,\nu=m\Delta f}$ $A_{\varphi_{rx,y}}(\tau,\nu)=\int\varphi_{rx}^*(t-\tau)y(t)e^{-j2\pi\nu(t-\tau)}dt$接下来还可以得到 $Y[n,m]=H[n,m]X[n,m]+V[n,m]$

明天将要阅读的部分：3.2 OTFS modulation，4 MIMO-OTFS Modulation 以及5 MIMO-OTFS Signal Detection的第一部分