Chapter 2 System Model
2.2 Received Signal
Fig. 2.3: The OFDM demodulator at the jth receive antenna
For simplification, we assume that the synchronization and channel estimation at the receivers are perfect and the maximum multipath delay spread is fewer than
T
g, so receivers can obtain the accurate channel information and be ISI-free.The signals of all L transmitters propagate through the multipath channel and are received by M receivers. At the jth receiver, we obtain baseband signals on N subcarriers from an
OFDM demodulator in Fig. 2.3. After GI deletion and FFT operation, the received signal of the jth receiver is the superposition of the signals fromL transmitters plus the complex additive white Gaussian noise, given by
, frequency response matrix (N×N ) between lth transmitter and jth receiver. It is defined by
At the multipath environment, the channel matrix can be written as , ,
1 number of the paths. The N elements of N are the complex additive white Gaussian j noise with zero mean and variance σ .n2
Chapter 3
Iterative Multi-Layered Detection Methods for MIMO MC-CDMA Systems
In this MIMO system, each transmitter is used to transmit different data stream that induces the layered antenna interference (LAI). The received signals which are described in Eq.(2.2) contain LAI. The data stream for individual transmitter must be detected from signals at M receivers. Each layer is considered in turn to be the desired signal, and the remainder is treated as interference. In Section 3.1, we describe the adaptive MMSE equalization for each receiver is used to suppress LAI and noise. After the equalizing and dispreading, the signals of M receivers are combined to obtain the receiver diversity, and a decision on the desired signal is made. Afterward the decision results can be used to reconstruct and cancel the received interferers from the received signals.
After several iterations, the decision data is accurate enough, so we can apply the MPIC to suppress inter-code interference which results from the loss of orthogonality between spreading codes. The details of above are included in Section 3.2. By exploiting MMSE
equalizer and MPIC combined with layered antenna interference cancellation (LAIC) by turn, the LAI and MPI can be reduced iteration by iteration. In Section 3.3, we present different interference cancellation orders, and the performance results are showed in section 3.4.
3.1 Adaptive MMSE Equalizer and
Iterative Layered-antenna Interference Cancellation
After process in Fig. 2.3, the MMSE equalizer for the Qth layer is applied to suppress the other layered interferers and noise at jth receiver as Fig.3.1. For the first iteration, the equalizer factor gij Q, is derived by minimize the mean square error between the transmitted symbol dQk and the equalized signal gij Q, rij on the ith subcarrier [18], and it can be
After the equalization, dispreading and scrambling, the signals of all M receivers is combined, then the signal of the uth spread code for the Qth layer can be expressed as
( )
Layered Antenna Interference Enhanced Noise
M L K M N through multiple carriers over the frequency selective channel that causes the equivalent channel gain which equals gij Q, hij Q, is not the same on N chips and the orthogonality between spreading codes is destroyed. Hence, the inter-code interference (ICI) is induced. In addition to ICI, layered antenna interference and enhanced noise are also the reasons for the performance degradation.
After the decision is made on zuQ, the decision results ˆdlk are delivered to the next iteration. The layered antenna interference cancellation scheme which combines with MMSE
equalization is illustrated in Fig. 3.2. The decision result ˆdkl passes through spreading, scrambling and multiplying channel gain hij l, to reconstruct the interference from other
transmitters. The LAI is subtracted from the received signal
r
j, then we have, ,
Fig.3.1:The first iteration of multilayered detection method
where I includes the transmitter index which we want to cancel, and Q is not included.
Because some LAI are cancelled from
r
j, the coefficient of MMSE equalizer in Eq.(3.1) isadjusted to 2 2 ,
= +
∑
, and the signal before decision can be expressed as follows:where the residual LAI is due to the decision errors for other layers. If the decision result ˆdlk is correct, the residual LAI from the lth transmitter will be cancelled, such that the decision for Q th layer becomes more accurate and some decision errors made before will be corrected. Theoretically, the LAI cancelled in later iteration will be more accurate than the former, and this system is finally free of LAI. In practice, however, the error propagation may occur between layers because the interference is so serious at first that decision results have (3.4)
too many errors.
3.2 Multipath Interference Cancellation
As described in Eq.(3.2), inter-code interference which comes from the loss of orthogonality between spreading codes is one of the reasons for the performance degradation.
If each path is matched individually, the frequency response will become flat to avoid ICI, and the multipath diversity can be obtained additionally. Thus when the decision data is accurate enough, we use the multipath interference cancellation (MPIC) scheme following MMSE equalization as Fig. 3.2.
The details of the MPIC block are illustrated in Fig. 3.3. For the qth path, the interferers from other paths ( 1~ ,p= P p≠q) for the Qth layer are reconstructed and cancelled from
Afterward maximum ratio combining is exploited to get multipath diversity gain. rqj Q, is matched by the complex conjugate of the channel frequency response for the qth path, and the sum of all matched signals is descrambled and despread. After receiver diversity
Fig. 3.2: The second and su bsequent iterations of mu ltilayered iteration method
combining, we have
After several iterations, the LAI is almost cleared and the MMSE equalization can’t improve performance any more, so we remove the MMSE equalization and only apply MPIC at subsequent iterations.
Fig. 3.3: The Multipath interference cancellation block
3.3 Successive and Parallel Interference Cancellation
The successive interference cancellation (SIC) scheme, as its name, detects L layers successively. The decision results from the former layers are exploited to cancel LAI or MPI for the later. Hence, for the first iteration, LAIC has been employed as shown in Fig. 3.2, and
the set of recostructed layers
I
for the Qth layer in Eq.(3.3) includes Q-1 layers which have been detected before. For the later layer detection, signals will have less interference and more accurate decision results. Thus the iteration denotes that all layers finish detecting sequentially. After the second iteration, the setI
includes all layers except the Qth layer.In contrast, the parallel interference cancellation (PIC) scheme detects all layers simultaneously. The set I is null for the first iteration, and includes all layers except the
Qth layer for the following iterations. For the PIC architecture, the iteration denotes that all layers finish detecting simultaneously. Thus LAI has never been deleted from received signals will make more decision errors than SIC, then incorrect LAI cancellation for the following iteration is induced by these errors that degrades the performance, and even serious error propagation occurs between layers. Although PIC spends less time for each iteration, SIC may obtain better performance finally. The performance comparison of these methods is illustrated and discussed in Section 3.4.1.
3.4 Performance Results
We compare the performance of iterative multi-layered detection methods with different interference cancellation architectures and different numbers of spread code used in this section. Additionally, these methods are also compared with VBLAST at their performance and computation complexity.
The simulation parameters are listed in Table 3.1. We apply the Walsh code to spread symbols and a pseudo random code generator to produce the scrambling codes. It is assumed that synchronization and channel estimation are perfect, and the noise power is known at the
Modulation QPSK
Number of subcarriers (N) 256
Length of Walsh codes (N) 256
Number of total Walsh codes (K) 256
Carrier frequency 2 GHz
Total bandwidth 5.12 MHz
Guard interval (Tg) 12.5 μs
number of resolvable paths (P) 2
Table 3.1:Simulation parameters
receive end. The equivalent baseband impulse response of the multipath fading channel multipath component. P denotes the number of resolvable paths and ( )δ • is the unit impulse function. In our simulations, τ is uniformly distributed between 0 spj l, μ to 12.5 sμ , apj l, is generated by complex Gaussian random variable, and for the two-path channel model, the power ratio of paths is 0:0 (dB). Furthermore, the fading patterns of each path between each transmitter and receiver are generated independently.
Throughout this chapter, the process procedure is presented in Table 3.2.
Table 3.2: The process procedure
3.4.1 The Performance Comparison with Different Interference Cancellation Architectures
The BER performance of the MIMO system with four transmitters and four receivers using successive interference cancellation is showed in Fig. 3.4. At early iterations, we observe that the layer detected later always has better performance. However, when the information of all layers is propagated adequately at later iterations, all layers will have the
iteration 1st 2nd~4th 5th~9th
process MMSE MMSE and MPIC MPIC
same performance. We can find the BER at high Eb/N0 is close to the performance with perfect LAIC and MPIC, the bound of diversity order equals to 8. By exploiting this detection method with SIC in MIMO system, the spectral efficiency becomes eight times in SISO system.
Fig. 3.4: BER performance of the MIMO MC-CDMA system with SIC for all four layers in a two-path channel at iteration 1, 3, 5 and 9. (Tx = 4, Rx = 4, K = 256)
Fig. 3.5: BER performance of the MIMO MC-CDMA system with PIC in a two-path channel. (Tx = 3, Rx = 4, K = 256)
From the simulation results of the system (Tx = 4, Rx = 4) with PIC architecture, we find that the error propagation occurs, so the iterative interference cancellation can’t improve the performance. Fig. 3.5 shows the performance of the system which decreases the number of transmitter to three. We observe that the speed of convergence is almost the same as that of the system with SIC. Hence, the spectral efficiency of the PIC architecture is three-fourths of SIC. But the former spends lesser process time than the later.
3.4.2 Effect of the Number of Walsh Codes Used
The number of Walsh codes used (K) will affect the LAI, ICI and spectral efficiency. Fig.
3.6 shows the effect of the number of Walsh codes used. In this MIMO MC-CDMA system (Tx = 4, Rx = 4) using PIC, We can find that more Walsh codes are used, more LAI and ICI occur to received signals. Thus, the performance of the system which uses fewer Walsh codes is more close to the theoretical performance, but its spectral efficiency is lower. We compare it with the system using PIC described in section 3.4.1, the highest spectral efficiency of these workable systems, 5 bits/sec/Hz, is still lower slightly than that of the system with PIC using three transmitters, 6 bits/sec/Hz.
Fig. 3.6: BER performance of the MIMO MC-CDMA system with PIC versus the number of Walsh codes used in a two-path channel. (Tx = 4, Rx = 4)
3.4.3 The Performance Comparison between V-BLAST and the Proposed Systems
Fig. 3.7 shows the BER performance comparison between VBLAST and the proposed systems. The system parameters are showed in Table 3.3.
System VBLAST Table 3.3: The system parameters of VBLAST and the proposed systems.
Here we use the VBLAST with the MMSE detector and successive interference cancellation in OFDM system to compare with our proposed methods. The performance of VBLAST is far away from the theoretical bound and our systems. In the Multipath channel, the frequency selective effect will make the symbols on some carriers fade seriously in the OFDM system. If the symbols are spread to all subcarriers, as in MC-CDMA, the effect will be mitigated. Our proposed methods exploit MC-CDMA system to increase frequency diversity and resist the frequency selective fading. MPIC is applied to combine the multipath diversity gain that VBLAST can’t obtain. Our proposed systems can achieve the performance of perfect LAIC and MPIC. But the system with parallel interference cancellation has lower spectral efficiency than the other systems.
The complexity comparison between them is presented in Table 3.4. Most complexity of our proposed systems is used on spreading and despreading process. The complexity of the PIC is lower than SIC in the first iteration, and both of them are much higher than V-BLAST.
We can compare PIC architecture with the layered space-time (LST) technique mentioned in [4]. Although the LST technique combines layered space time scheme and turbo coding, the performance are still worse than our proposed systems.
Fig. 3.7: BER performance comparison between VBLAST and the proposed systems in a two-path fading channel.
Table 3.4: The complexity comparison of multi-layered detection methods
( measured by the number of the real multiplier, N=256, K=256 , P=2. ).
Architecture Each layer at each receiver each layer at all
receivers
LAIC 2 'L NK+6NL' 2 'L NK +6NL' 4NML'
MMSE 8N+2KN+2 4 (2N ML'2+L' )3
MPIC 8NP+2 (N K+ 1) 0
All L layers at M receivers / the average for each layer at M receivers
1st iteration 3721248 / 930312 1597464 / 532488 360448 / 90112 LAIC+MMSE
+MPIC iteration
6422560 / 1605640 4816920 / 1605640
LAIC+MPIC iteration
4292608 / 1073152 3219456 / 1073152
802816 / 200704 (for the other
iterations)
Chapter 4
Parallel Iterative Multi-Layered
Detection Method for Bit-Interleaved Coded Modulation in MIMO
MC-CDMA Systems
Here we describe a parallel iterative multi-layered detection method which combines soft interference cancellation, adaptive MMSE detector and bit-interleaved coded modulation (BICM). By exploiting soft information from output of the soft-in soft-out decoder at receive end, the interference reconstruction is more reliable, so the situation of the error propagation is reduced. The bits which are affected by the same channel gain or correlate with each other are spread by the bit interleavers to resist bursty errors induced by the correlated fading and maximize the diversity order.
In the Section 4.1, we present the BICM scheme proposed in [15]. Our proposed method is presented in the Section 4.2, and the simulation results are included in the last section.
4.1 Bit-Interleaved Coded Modulation
4.1.1 The Transmitter
Fig. 4.1: The transmitter block diagram of the 8PSK bit-interleaved coded modulation.
The BICM transmitter is showed in Fig. 4.1, where t is the time index. The BICM transmitter is a serial concatenation of the convolutional encoder, the interleaver and the 8-PSK modulator. Here we use a rate-2/3 convolutional encoder, a group of independent bit interleavers and an 8-PSK modulator. By applying 8-PSK modulation, the bandwidth efficiency is not lost on coding.
At first two data bits bt =[b ,b ]0t 1t are encoded to three bits Ct=[C ,C ,C ]0t 1t 2t , and C t passes through the interleaver which is the combination of three bit interleavers. In order to mitigate bursty errors and maximize the diversity order, the interleaver design can follow some rules below :
z Using three independent interleavers to ensure the coded bits with different protection
keep their different positions at the symbol labeling.
z The interleaved coded bits Vt=[V , V ,V ]t0 t1 t2 modulated to the same symbol must come from C which are at a distance larger than the code constraint length from each other. it
z The coded bits close to each other at code trellis will be modulated to symbols which apart from each other or suffer uncorrelated channel gains.
After interleaving, V is mapped to a 8-PSK symbol by a mapping operator t μ. The symbol d belongs to t Ω , the 8-PSK constellation, and is transmitted.
4.1.2 The Receiver
Fig. 4.2: The receiver block diagram of the 8PSK bit-interleaved coded modulation.
The receive signal can be presented as y = H d + nt × t , where H is the channel gain and n is the complex additive white Gaussian noise. The BICM receiver block diagram is showed in
0 1 2
t t t t t
d = ([V ,V ,V ]) , dμ ∈Ω (4.1)
Fig. 4.2. Here we use the suboptimal method with separate steps, demapper and decoder. They are separated by bit interleavers used to return the coded bit information to original sequence.
The details of the demapper and soft-in soft-out decoder are described below:
a. Demapper
This block is used to demodulate channel symbol and obtain bit information for decoding.
The bit information is computed by using the maximum a-posterior probability criterion. The a-posteriori probability of coded bit can be calculated as
i t c= 0 or 1 and w is a 8-PSK symbol. For the fading channel, the conditional probability of
received signal can be presented as the complex Gaussian distribution
t 2
We use the log likelihood ratio (LLR) to deal with the bit information. The a-posterior LLR of coded bit is defined as
(V 0 | )
Substituting Eq.(4.2) into Eq.(4.4) and assuming independent bits (using the random enough
interleavers), we have
Substituting Eq.(4.3) and Eq (4.7) into Eq.(4.5), we have
t t 2 2 i' i'
The a-posterior LLR of the coded bit can also be written as
i
The extrinsic information term output by the demapper is
After the first decoding, the extrinsic information of coded bits Λex(C )it is delivered by the decoder to the interleaver and becomes Λa(V )ti , the a-prior probability of the demapper.
The process to exchange information between demapper and decoder is continued, and the final decoding output is the a-posteriori information of data bits Λex(b )it , i = 0 or 1.
a. Gray Labeling
b. Set-Partitioning Labeling
Fig. 4.3: Two signal labeling schemes, the bits from left to right are V , t0 V and t1 V . t2
The improvement of iterative demapping is much-correlated with the signal labeling. Two general signal labeling schemes are showed in Fig. 4.3. For the ith bit, the subset Ω 1i includes the symbols in the shadow regions, and the other symbols are included in Ω are in 0i the white regions. In the figure of the ith bit, the pair of symbols which have the same bits except the ith bit is connected by a line. When we use the a-prior information of the other bits (≠Vti) from interleaver to help demap V , one of four pairs is chosen and 8-PSK mapping is ti
translated to binary modulation. Because of the reduction of the nearest neighbor symbols, the distance between the symbols in the pair becomes larger and the extrinsic information of the ith bit Λex(V )ti is more reliable. Thus the improvement of iterative detection is much relative to the signal labeling scheme used.
Comparing two signal labeling schemes, the average distance of all pairs of symbols in set-partition labeling is larger than Gray labeling, so set-partition labeling has better improvement with iterative decoding. However, Gray labeling have fewer nearest neighbor symbols in the beginning because the neighbor symbols for every symbol are only different in one bit. Hence it will provide more reliable soft information for the first iteration than set-partition labeling. For the MIMO systems, layered antenna interference is so serious that if the set-partition labeling scheme is used, the extrinsic information of the demapper for the first iteration will be unreliable. The terrible information is passed between the demapper and decoder for the following iterations and error propagation occurs. That is the reason why we use Gray labeling scheme for our proposed iterative multi-layered method presented in this chapter.
B. Soft-in soft-out decoder
After deinterleaving the output of the demapper, Λa(C )it is utilized to decode. Here we
use the soft-in soft-out decoder which applies the modification of BCJR algorithm suggested by [17]. This algorithm defines the forward and backward recursions as follows:
2 i' i' backward probability for the state s at time t. The probability of the state transition ( , ')s s at time t, γt( , ')s s , is substituted by the product of the probability of the coded bits which come from the demapping output.
For simplification, we use the natural logarithm of the probability, αt and βt, intead of the probability to express the forward and backward recursions, where =ln( ) αt αt and
ln( )
where Λ (C )i comes from the deinterleaver output. Substitute it into Eq.(4.12) and
Eq.(4.13), we have
and the denominator in Eq.(4.14) is normalized for all αt(s )t and βt(s )t .
Define ϒ and 0i ϒ are the set of state transitions ( ', )1i s s such that the ith coded bit is, respectively, 0 and 1. The a-posteriori LLR of the coded bit C at the output of the decoder it is given by
Λ is obtained from the a-prior information of the other coded bits by the trellis structure of the code, and Λa(C )ik is supplied by the deinterleaver output. The extrinsic
information Λex(C )ik is what the decoder sends to help demap for the following iterations.
We can also compute the a-posteriori LLR of the data bits for the final decoding results.
We can also compute the a-posteriori LLR of the data bits for the final decoding results.