光无线散射通信的ISI信道估计与信号检测策略
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本文主要探讨了带符号间干扰（ISI）的光无线散射通信的信道估计与信号检测问题。在非视线（NLOS）的光学无线散射通信链路中，构建准确的统计信道模型是发展高效接收器侧数字信号处理技术的关键。研究者采用了源自分子通信领域的线性时不变（LTI）泊松信道模型，将这种模型应用于NLOS光学无线散射通信场景。
模型的核心在于通过概率延迟分布来刻画随机的ISI现象，这有助于理解信号传输过程中由于多径传播引起的前后符号相互影响。作者详细推导了接收信号的一阶和二阶统计特性，这对于理解和优化系统性能至关重要。他们提出了基于最小二乘法和相关性的信道估计策略，旨在精确估计延迟分布，评估了这两种方法的有效性。
信道估计部分是研究的重点，通过比较不同准则下的性能，展示了信道估计方案在处理ISI带来的复杂性时的作用。文中提到的两种信号检测方案——线性最小均方误差（LMMSE）接收机和最大似然序列检测（MLSD）——在考虑ISI的情况下进行了对比。LMMSE方法将ISI视为噪声来简化处理，而MLSD则更深入地考虑了ISI的影响，结果显示在存在ISI的信道条件下，MLSD展现出显著的优势。
这项工作为光无线散射通信，特别是那些发射功率高、符号率高的应用场景，提供了一种理论框架和有效的信道估计及信号检测方法。通过改进的模型和算法，有望提升NLOS光学无线通信系统的可靠性和效率，推动该领域的发展。
5328 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 14, NO. 10, OCTOBER 2015
diodes (LED). We consider a mu lti-path channel characterized
by the following channel outputs
y(τ ) =
D
d=0
h
d
x(τ − dT) + n(τ ), (1)
where T is the length of each symbol interval and n(τ ) is
background radiation intensity. Assume constant background
radiation in tensity, i.e, n(τ ) = N for a constant N. Note that the
energy received in interval [tT,(t + 1)T], denoted as X
t
,isthe
integration of the optical intensity in that slot, given by
X
t
=
(t+1)T
tT
y(τ )dτ
=
D
d=0
h
d
(t+1)T
tT
x(τ − dT)dt +
(t+1)T
tT
n(τ )dτ
=
D
d=0
h
d
P
t−d
T + NT, (2)
where P
t
denotes the transmission power in interval t.
Assume Poisson channel, with the constant ratio α between
the mean received signal photon number and the received signal
energy. Then from (2), the number of received signal photons
satisfies a Poisson distribution with the mean given by
αX
t
=
D
d=0
αh
d
P
t−d
T + αNT
=
D
d=0
α
d
P
t−d
+ λ, (3)
where α
d
= αh
d
T and λ
= αNT. From (3), it is seen that the
number o f received photons at slot t, d enoted as u
t
, can be
expressed as follows,
u
t
=
D
d=0
v
t−d,d
+ n
t
, (4)
where v
t−d,d
denotes the number o f received photons transmit-
ted at slots t − d satisfying the Poisson distribution with mean
α
d
P
t−d
;andn
t
denotes the number of r eceived background
noise photons satisfying Poisson distribution with mean λ.In
other words,
P(v
t−d,d
= n) =
(α
d
P
t−d
)
n
n!
e
−α
d
P
t−d
,
P(n
t
= n) =
λ
n
n!
e
−λ
. (5)
Such an LTI-Poisson channel model can be characterized as
follows.
1) Stochastic ISI Property: It is seen that the expectation of
u
t
is given as follows,
E[u
t
]=
D
d=0
E[v
t−d,d
]+E[n
t
]=
D
d=0
α
d
P
t−d
+ λ, (6)
which is the “convolution” between the transmission power
P
t
and the ratio as the average number of channel output
Fig. 2. Illustration of the stochastic ISI channel.
photons per slot power α
d
,for0≤ d ≤ D. The model (4)
can be treated as a stochastic ISI channel model,asshown
in Fig. 2. The term “stochastic” implies that the mean of the
signal component
D
d=0
v
t−d,d
of the received signal u
t
is
the convolution between the transmission power P
t
and the
ratio α
d
.
2) Statistical Independence of v
t,d
1
and v
t,d
2
for d
1
= d
2
: So
far we have modeled the channel taps v
t,d
as Poisson random
variables. We need to examine the statistical independence of
v
t,d
for different t and d. Due to the different transmission slots,
the independent assumption on v
t,d
for different t can be well
justified; and the statistical independence of v
t,d
1
and v
t,d
2
for
different d
1
and d
2
can be justified by the independent receiving
events in different time slots.
The statistical independence can also be justified based on
the binomial distribution which can be approximated by Pois-
son distribution. The readers can refer to Appendix VI-A for
details.
Therefore, we have the following stochastic properties on
Poisson approximation for the received signal u
t
in (4),
1) v
t−d,d
satisfies the Poisson distribution with mean value
α
d
P
t−d
;
2) for different t, v
t,d
are statistically independent of each
other; and for fixed t, v
t,d
for 0 ≤ d ≤ D are statistically
independent of each other.
III. P
ILOT-BASED CHANNEL PARAMETER ESTIMATION
Note that, according to the system block diagram shown in
Fig. 1, the channel estimation provides the estimated channel
state information to the subsequent processing blocks. The
channel parameters needed to be estimated are the ratio be-
tween the transmission power and mean value of Poisson dis-
tribution {α
d
}
D
d=0
for the LTI-Poisson channel. In this work, we
consider pilot-based channel estimation , wh ere the transmitter
sends known pilots to the receiver, and the receiver performs
channel estimation based on the number of received photons
in each slot. We adopt least-squares (LS) and correlation bank
(CB) estimation, for the parameters {α
d
}
D
d=0
.
We construct the pilots using a length-T “on and off” pi-
lot sequence with some pattern. In each slot 1 ≤ t ≤ T,the
transmitter either transmits certain number of particles N or
using a fixed power P (on), or it does not transmit (off).
Let z
t
∈{0, 1},1≤ t ≤ T, denote the indicator on whether the
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