This can be attributed to the fact that the HOC values of the QPSK and 8-PSK variant signals are ambiguous. OQPSK, QPSK, π4-QPSK, 8-PSK and 16-QAM using RA-AMC technique for different SNR values.
Introduction to Automatic Modulation Classification (AMC)
AMC for MIMO Systems
The modulation classifier should be resistant to such noise and high classification accuracy under different noise levels. In some applications such as CR and software-defined radio (SDR), the modulation classifier must determine the modulation candidate from a pool of limited number of modulation types.
LB Approach
ALRT Approach
Under hypothesis HM, the likelihood function of the received signal using ALRT can be written as [28]. The probability function of the received signal with respect to HM can be expressed as [17].
HLRT Approach
FB Approach
Moments
Cumulants
Existing Works on the AMC of MIMO Signals
The algorithm uses fourth-order cumulants as the AMC functions and the likelihood ratio test (LRT) for decision making. The algorithm uses the HOMs and HOCs of the received signal as the AMC features and the J48 decision tree as a classifier.
Motivation and Problem Formulation
Thesis Organization
The proposed method uses a centralized cooperative classification framework with forward-level fusion to distinguish between BPSK, OQPSK, QPSK, π4-QPSK, 8-PSK,16-QAM and 64-QAM modulation types. In the second step, it uses a cumulant feature vector derived from the equalized signal to distinguish the modulation types iQ1.
Summary
In the first step, the method uses a cumulant feature vector derived directly from the received signal to distinguish BPSK, OQPSK and the subpool Q1 = {QPS K,π4 − QPS K,8− PS K,16− QAM} as a whole. This cumulative function resists noise amplification that occurs in a correlated AF relay system.
Cumulants
- Moment and Moment Generating Function
- Cumulant and Cumulant Generating Function
- Relationship between Moments and Cumulants
- Properties of Cumulants
- Additive Property
- Scaling Property
- Cumulants of Normal Random Variables
- Multivariate Cumulants
For example, the first four moments can be expressed in terms of the cumulant axis. 2.12) Similarly, the first four cumulants can be expressed in terms of the moments as. The additive property of cumulants states that the cumulant of sum of two independent random variables is equal to the sum of the cumulants of the individual random variables.
Summary
This chapter deals with AMC for QPSK variants and 8-PSK over spatially correlated MIMO channels. The 4th order cumulants of the QPSK variants and the 8-PSK signals are discussed in Section 3.4.
MIMO System Model
Rayleigh Fading
Rician Fading
Spatial Correlation
Channel Equalization
ZF Equalization
The ZF equalizer premultiplies the signal received by the Moore-Penrose pseudo inverse H+ofH.
JADE Equalization
The i, jth entry of a matrix given by a transformation, say Fi,j, can be defined as There is a special structure of the cumulant tensor z that can be observed in the eigenvalue decomposition. Furthermore, all other eigenvalues of the tensor can be shown to be zero.
The probability measure function (PMF) of RV x1 representing the QPSK constellation is given by.
Proposed Cumulant Features
In the following sections, we discuss the proposed cumulant features to classify the QPSK, OQPSK, π. Suppose xe4(k) and xe4(k) denote the sequences of the odd and even symbols respectively. 3.46) The PMF of random variables xo4enxe4 is then given by Based on the discussion above, we propose a distinct cumulant feature vectorvM to distinguish four modulation types, namely QPSK, OQPSK, π.
Proposed AMC Method
Extracting Cumulant Features
Combining Cumulant Features
It is reported in [19, 35] that a better classification result can be achieved by combining these cumulative estimates in an efficient way. In this work, we apply the MRC technique to combine the cumulative features. The estimates affected by high noise are weighted less and estimates affected by low noise are weighted higher [35].
Classification Rule
Simulation Results and Discussion
AMC Performance over Rayleigh Flat Fading Channel
- Effect of Sample Length and SNR
- Effect of Antenna Correlation
A number of experiments were conducted to study the performance of the proposed method by varying the sampling length, NT and antenna correlation values. One can also note that the performance of the JADE-MC technique is close to that of the ZF-MC technique. It is observed that there is a decrease in PC with an increase in the antenna correlation value.
The decrease in PC with increasing antenna correlation is attributed to the fact that channel correlation amplifies the noise at the equalizer output [18].
AMC Performance over the Rician Flat Fading Channel
The decrease in PC with an increase in K is attributed to the fact that with the increase in the Rician factor, the scattered component disappears, resulting in a highly correlated channel.
Summary
In the previous chapter, we addressed the AMC of MIMO signals in a single multi-antenna receiver situation. It was observed that the spatial blurring and the spatial correlation affect the AMC performance. The emergence of wireless sensor networks (WSN) and cognitive radio (CR) networks makes cooperative classification an attractive strategy to improve the AMC performance.
A better statistical estimate can be obtained by combining signals from multiple sensors, thus improving the AMC performance.
System Model
Let ρT and ρR denote the correlation coefficient of two adjacent antennas of the transmitter and the receiver, respectively.
Proposed CAMC Method
Feature Selection
M can distinguish QPSK and OQPSK and f3M can distinguish π4-QPSK and 8-PSK. Based on the above discussions, we select the f1M, f2M, f3M, and f4M features to distinguish the modulation types in Q. By concatenating f1M, f2M, f3M and f4M we get the feature vector.
Cooperative Classification
The next step is to combine these estimates at FC in an efficient way. 35] used the MRC technique to combine the decision statistics in the FB framework, while Ref. In the FB framework, the HOC features are obtained as the weighted sum of those estimated from the equalized signals [35].
We use the MRC technique to combine similar cumulant features obtained from different sensors.
Simulation Results and Discussion
Summary
The spatial MIMO channel changes the statistical properties of the modulated signal, making AMC a challenging task. It is observed in the literature that most of the existing MIMO blind channel estimation techniques, such as JADE [31] and the constant modulus algorithm (CMA) require the channel matrix to be of full rank. The majority of the AMC algorithms for MIMO systems have considered the rich scattering environment, that offers a full channel matrix.
The opacity of building walls to the signal transmitted by the user device allows most of the signal energy to pass through keyholes such as windows, doors etc [14].
System Model
MIMO Keyhole Channel
Investigation of the Fourth-Order Zero-Conjugate Cumulant based AMC tech-
Effect of a Keyhole on Channel Equalization
The JADE technique also fails to equalize the received signal, as it requires the channel matrix to be of rank one for TH.
Proposed AMC Method
We analyze this relationship for 4th-order and 6th-order cumulants for BPSK, QPSK, OQPSK, and 16-QAM modulation types. It can be seen from the table that this relationship exists for zero conjugate of the 4th order, two conjugates of the 4th order, one conjugate of the 6th order and three conjugate cumulants of the 6th order. 6th order triconjugate cumulant and 4th order biconjugate cumulant of RVs x1 (associated with transmitted data sequence x1(k)) TH.
For an OQPSK signal x3(k), the 6th-order three-conjugate cumulant and the 4th-order two-conjugate cumulant of RVsx3(associated with transmitted data sequence x3(k)) and ∇x3 (associated with data sequence ∇ x3(k) )) are given by. 5.33) Now record the above cumulant values in Eq.
Simulation Results and Discussion
Performance Comparison of the DMR Technique and the JADE-FZC
5.7-5.9 show the effect of antenna correlation on the DMR technique over a Rayleigh channel and Figs. It can be observed that with an increase in the antenna correlation value, there is a decrease in PC. The decrease in PC with an increase in the antenna correlation value is attributed to the reduced diversity gain since a correlated low-rank channel model yields only receiver array gain.
The increase in PC with increasing SNR and is attributed to the fact that the accurate estimation of cumulants depends on SNR and N.
Summary
In the previous chapter, we discussed that MIMO systems can operate in an insufficient dispersion environment, which can lead to a ranking deficiency. It is necessary to cancel the channel mixing effect before AMC, since the spatial MIMO channel changes the statistical properties of the modulated signal. A keyhole channel makes AMC a challenging task, as the existing blind channel equalization techniques such as the JADE algorithm [ 31 ] and the constant modulus algorithm (CMA) [ 29 , 30 ] require the channel matrix to be of full rank.
This cumulative function resists noise amplification that occurs in a correlated AF relay system.
AF- Relay Assisted MIMO System
We assume that the gain of each CR is constant and is normalized to the number of CRsNC. In the absence of relay noise and antenna correlation, the equivalent channel matrix H can be written as
Proposed AMC Algorithm over AF-Relay Fading Channel
Feature Selection for Distinguishing the Modulation Types in Q 1
The following points are considered for the selection of the features to distinguish the modulation types inQ1: . 1) Consider the 4th-order cuualnt characteristics f1M = C40(x(k)) and f2M = C42(x(k)) [4]. Note that vM cannot be obtained directly from the received signal, as the channel affects the cumulant values. Based on the above discussion, we propose an AMC method, namely RA-AMC, for an AF relay fading channel with uMandvMas feature vectors.
In MRC, the cumulant properties are obtained as the weighted sum of the cumulants estimated from NT equalized signals [35].
Simulation Results and Discussion
Classification Performance of the DMR technique and the JADE-FZC
Effect of Number of Relays
Effect of Antenna Correlation
The decrease in PC with an increase in the antenna correlation value is attributed to the reduced diversity gain since a correlated low-rank channel model yields only receiver array gain. 6.12-6.14 show PC versus SNR in the case of classification of QPSK, π4-QPSK, 8-PSK and 16-QAM using the feature vector vM over an AF relay fading channel for different antenna correlation values. The decrease in Pc with an increase in the antenna correlation value is contributed by the noise gain at the equalizer output.
The decrease in PC with an increase in the antenna correlation is due to the reduced diversity gain and the noise amplification at the equalizer output.
Summary
Scope for Future Work
Yun, “A novel automatic modulation classification using cumulant functions for multipath communications,” IEEE Transactions on Wireless Communications, vol. Berbineau, “Blind digital modulation identification for spatially correlated MIMO systems,” IEEE Transactions on Wireless Communications, vol. Oien, “On the Amount of Fading in MIMO Diversity Systems,” IEEE Transactions on Wireless Communications, vol.
Heath, "Cooperative Algorithms for MIMO and Forward Relay Networks," IEEE Transactions on Signal Processing, vol.
A MIMO system with keyhole
PDFs of Rayleigh and Double-Rayleigh Channel Amplitude
P C versus SNR for JADE-FZC and DMR over a Rician channel with N = 2000,
P C versus SNR for the DMR technique in a correlated Rayleigh channel with
P C versus SNR for the DMR technique in a correlated Rayleigh channel with
P C versus SNR for the DMR technique in a correlated Rayleigh channel with
