无线通信中的数字信号传输：克服衰落信道挑战

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"Digital Communications Over Fading Channels" 是一份由R. Clark Robertson和Nathan E. Beltz在2004年11月15日于美国海军研究生院发表的研究报告，该报告主要探讨了在多径衰落信道中进行数字通信的技术挑战和解决方案。在无线通信领域，"Fading Channels"（衰落信道）是常见的现象，它指的是由于信号在传播过程中遇到的多径效应，导致接收信号强度随时间快速变化。这种变化对通信系统的性能有很大影响，可能导致数据传输错误率增加、通信质量下降。因此，理解和处理衰落信道是无线通信系统设计的关键部分。报告详细讨论了以下知识点： 1. **衰落信道模型**：介绍了不同类型的衰落信道模型，如慢衰落（慢变信道）和快衰落（快变信道），以及它们的统计特性，如Rayleigh衰落、Rician衰落和 Nakagami衰落等。 2. **数字调制技术**：探讨了在衰落信道中使用的各种数字调制方式，如ASK（振幅键控）、FSK（频率键控）、PSK（相位键控）及其变种，以及它们对抗衰落性能的优劣。 3. **分集技术**：包括空间分集、时间分集、频率分集和极化分集等，这些技术通过从多个不同的信号路径或时间间隔获取信息来减少衰落的影响。 4. **均衡技术**：讨论了在接收端使用均衡器恢复信号的原理，如决定性均衡器和最小均方误差均衡器，以及它们如何抵消信道的影响。 5. **信道编码与交织**：详述了如何利用前向纠错编码（如Turbo码、LDPC码）和交织技术提高系统的抗干扰能力，以应对衰落信道中的错误。 6. **适应性传输**：介绍了根据信道条件动态调整传输参数（如编码速率、调制阶数）的策略，以优化系统性能。 7. **信道估计算法**：分析了用于获取信道状态信息的估计算法，如最小均方误差（MMSE）估计和最小二乘（LS）估计，这些信息对于实现高效的信道补偿至关重要。 8. **多天线技术（MIMO）**：阐述了多输入多输出系统如何利用多个天线来增强通信性能，尤其是在衰落信道中。这份报告不仅深入研究了理论概念，还可能涉及实际应用场景和实验结果，旨在为军事通信领域的Air Force Warfare Information Center提供有价值的指导。其内容对于理解无线通信系统在复杂环境下的性能和优化方法具有重要意义。

over time periods that are short compared to the duration of a symbol, and the channel is said to

be fast fading.

Channel frequency variations are characterized by the coherence bandwidth (∆f)

of the channel

[1]. The frequency components of a signal that are separated in frequency by more than (∆f)

are essentially uncorrelated and are aﬀected diﬀerently by the channel. Conversely, frequency

components of a signal that are separated in frequency by less than (∆f)

Hz are correlated to at

least some minimum deﬁned value and are aﬀected approximately the same by the channel. If the

noise equivalent bandwidth of the signal W>(∆f)

, then signiﬁcant distortion of the signal will

occur and the channel is said to be frequency-selective. On the other hand, if (∆f)

>W,thenall

frequency components of the signal are aﬀected equally by the channel, and the channel is said to

be frequency-nonselective.Thisisalsoreferredtoasﬂat fading.

Two widely used models for fading channels are the Rayleigh fading channel and the Ricean

fading channel, where the Rayleigh fading channel is actually a special case of the Ricean fading

channel. The Rayleigh model is used when there is no line-of-sight between transmitter and receiver,

and all of the received signal power is due to multipath. The Ricean model is used when there is

a line-of-sight between transmitter and receiver, but a substantial portion of the received signal

power is also due to multipath. When there is line-of-sight between transmitter and receiver and

virtually none of the received signal power is due to multipath, the non-fading channel model is

used.

A general representation of a passband signal is

s(t)=

√

cos [2πf

(t)t + θ(t)] (1)

For Ricean fading channels, a

is modeled as a Ricean random variable with probability density

function (pdf)

exp



−



+ α



2σ





αa



u(a

)(2)

where I

(•) is the zero

order modiﬁed Bessel function of the ﬁrst kind and u(•) is the unit

step function. Note that in this case σ

is not related to AWGN. This notational inconsistency

is unfortunate, but the notation used here is traditional. The average received signal power is

obtained from

(t)=a



∞

) da

(3)

which for Ricean fading can be evaluated to yield

(t)=a

= α

+2σ

(4)

For Ricean fading channels,

(γ

exp

⎡

⎣

−



+ α



2σ

⎤

⎦

⎛

⎝



⎞

⎠

u(γ

) (13)

(γ

2σ

exp



−



+ α



2σ



⎛

⎝



⎞

⎠

u(γ

) (14)

where σ

= N

Generally, we prefer to express our results in terms of the average energy per bit-to-noise power

spectral density ratio γ

. This is simply related to the average energy per symbol-to-noise power

spectral density ratio by

(15)

where M =2

and q is a positive integer.

2.1 Coherent Detection (BPSK, QPSK, MPSK, MQAM, GMSK)

In this subsection, the probability of bit error for binary phase-shift keying (BPSK), quadra-

ture phase-shift keying (QPSK), M-ary phase-shift keying (MPSK), M -ary quadrature amplitude

keying (M QAM), and Gaussian minimum-shift keying (GMSK) waveforms transmitted over slow,

ﬂat fading channels is derived. For each of these signaling techniques, the conditional probability

of bit error is of the form

(γ





bγ



(16)

where Q(•)istheQ-function and a, b,andq are constants that depend on the modulation type.

The constants a, b,andq for BPSK, QPSK, MPSK, MQAM, and GMSK are listed in Table 1. For

MQAM with q even, a square constellation is assumed, while for MQAM with q odd, a rectangular

constellation is assumed. In the case of BPSK and QPSK, (16) is exact, while for MPSK and

MQAM, (16) is an approximation that is obtained by using the lower bound P

)=1/k and

an upper bound on P

,whereP

is the probability of symbol error. Since P

= P

,the

use of a lower bound for P

) and an upper bound for P

oﬀset one another to produce a very

accurate approximation for P

. While it is possible to obtain exact expressions for P

for both

MPSK and MQAM, the exact expressions are both signiﬁcantly more complicated and impossible

to obtain for general values of M. In the case of GMSK, (16) is also an approximation where the

constant δ in Table 1 is determined by the 3 dB baseband bandwidth-bit duration product BT

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