The Performance Comparison between V-BLAST and the Proposed

Chapter 3 Iterative Multi-Layered Detection Methods for MIMO MC-CDMA

3.4 Performance Results

3.4.3 The Performance Comparison between V-BLAST and the Proposed

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

1^st 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 b_t =[b ,b ]⁰_t ¹_t are encoded to three bits C_t=[C ,C ,C ]⁰_t ¹_t ²_t , 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 V_t=[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. ⁱ_t

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 + n_t × _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

The extrinsic information term output by the demapper is

After the first decoding, the extrinsic information of coded bits Λ_ex(C )ⁱ_t is delivered by the decoder to the interleaver and becomes Λ_a(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 Λ_ex(b )ⁱ_t , 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 (≠V_tⁱ) 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 Λ_ex(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, Λ_a(C )ⁱ_t 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, γ_t( , ')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, α_t and β_t, intead of the probability to express the forward and backward recursions, where =ln( ) α_t α_t 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 α_t(s )_t and β_t(s )_t .

Define ϒ and ⁰_i ϒ are the set of state transitions ( ', )¹_i 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 ⁱ_t is given by

Λ is obtained from the a-prior information of the other coded bits by the trellis structure of the code, and Λ_a(C )ⁱ_k is supplied by the deinterleaver output. The extrinsic

information Λ_ex(C )ⁱ_k 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.

₁ ² _a ^i'_t+1 ^i'

Similarly, define Γ and ⁰_i Γ are the set of state transitions ( ', )¹_i s s such that the ith data bit

4.2 Transmit End of the MIMO

MC-CDMA System with BICM

The block diagram of the transmit end is showed in Fig. 4.4. The coding scheme which concatenates the convolutional encoder, interleaver and mapper is used to preprocess the data bits b before spatial multiplexing. The interleaver is a parallel connection of three ⁱ_t independent bit interleavers, and the length of each bit interleaver is equal to the number of symbols in a transmitted block, a multiple of L K× . After Gray labeling mapping, the 8-PSK symbols are spatially multiplexed to L symbol streams which are delivered to L transmitters.

Fig. 4.4: The transmitter block diagram of the MIMO MC-CDMA system

Fig. 4.5: The scheme diagram of the lth MC-CDMA transmitter

The scheme diagram of the lth MC-CDMA transmitter is showed in Fig. 4.5. The only difference of the systems between Fig. 4.5 and Fig. 2.2 is that the input here is the 8-PSK symbol streams and the QPSK modulator is taken away, thus we can express transmit signals here as in Section 2.1. The symbol streams are processed by multiplexing to K symbol stream and spread by individual spread codes. After summing, serial-to-parallel and scrambling, the signal can be expressed as

After being modulated to the OFDM symbosls and inserting GI, all signals at L transmitters are transmitted simultaneously.

4.3 Parallel Iterative Multi-Layered Detection Method

4.3.1 Receive Signal

The signals transmitted by all L transmitters propagate through the multipath channel and are received by M receivers. As described in Section 2.2, the baseband signals at jth receiver which are obtained by the OFDM demodulator in Fig. 2.3 can be expressed as

4.3.2 Overview on the Parallel Iterative Multi-layered

Detection Method

The parallel multi-layered detection method exploits the soft information instead of hard decision results to implement adaptive MMSE equalization, MPIC and LAIC, thus the information of layered detection and decoding can be passed to each other and exchanged between layers adequately. For the reason of saving process time, we adopt parallel interference cancellation architecture in our proposed method.

The scheme diagram for the first iteration is shown in Fig.4.6. After OFDM demodulation, the baseband signal at jth receiver, r , passes through MMSE equalizer to suppress ^j layered-antenna interference and noise. After being despread, scrambled and summed up for all L receivers to combine receiver diversity, the signal is delivered to the BICM decoder block.

In the decoder block, the signal is demapped to the information of three coded bits firstly,

Fig.4.6: The first iteration of the multilayered detection method.

and the bit deinterleavers are used to return the information to the encoding order. After iteratively decoding and demapping, the a-posteriori information of coded bits will be obtained from the output of the decoder and be exploited to generate the soft symbol.

For the following iteration, the soft symbols of the previous iterations are utilized to reconstruct and cancel LAI. The soft symbol can also be exploited to adjust the factors of adaptive MMSE equalizer and calculate the statistics of signals to help demap. The block diagram is illustrated in Fig. 4.7.

Through several iterations, the soft symbols become more and more reliable, we can replace the MMSE equalizer by the MPIC scheme shown Fig. 3.3. After LAIC, MPIC exploits soft symbols to reconstruct and delete MPI, and matches each path individually to suppress intercode interference (ICI) and combine multipath diversity. The block diagram of the iteration with MPIC is shown in Fig. 4.8. The details of adaptive MMSE equalizer, MPIC, symbol demapper and soft symbol block are described as follows:

A. Adaptive MMSE equalizer

For the first iteration, because the soft information of the transmit symbols is not available, we use the factor derived in Eq.(3.1) to equalize r . Thus the signal before demapping in ^j Fig.4.6 can be expressed as

Fig. 4.7: The second iteration of the multilayered detection method.

Fig. 4.8: The MPIC iteration of the multilayered detection method.

( )

Layered Antenna Interference Enhanced Noise

M L K M N

Assuming transmitted symbols are independent to each other, z can be model as a _u^Q complex Gaussian distribution from the central limit theorem. It consists of four components:

the desired signal (DS), the inter-code interference (ICI), the layered antenna interference (LAI) and the enhanced noise (EN).The mean of the distribution comes from the DS term, and the variance comes from the other terms. Here we use h_eq to represent the equivalent channel gain for the desired signal. The means of the real part Re{ }z_u^Q and the imaginary

, ,

induced by the frequency selective channel effect, thus the variance of ICI is

, 2

= −

∑

, the equivalent channel gain of the ith subcarrier which deletes the common part for all N subcarriers, E denotes the power of 8-PSK symbol. _av

The variance of LAI and EN are, respectively, calculated as

, , 2

Afterward the mean and variance of z are applied in the demapper block. _u^Q

For the second and following iteration, the soft symbols ˆd^l are supplied, and LAIC can be applied. At the left of Fig. 4.7, the receive signal which has deleted LAI can be presented as

, , term is produced by LAI reconstruction block in the top of Fig. 4.7. Then the adaptive equalizer parameter σ² in Eq.(4.22) is adjusted to

where [ ]E • is the average operator for the transmitted symbol. Because the soft symbol d^ˆ_k^l is the mean of the transmitted symbol d and the mean of the 8-PSK symbol power is 1, it _k^l can be rewritten as

2 2 , 2 2 2

where the only difference with Eq.(4.21) is the residual LAI term which is induced by the

Then the mean and variance of ˆz are computed and delivered to the demapper block. _u^Q

B. MPIC

The MPIC scheme is applied in the condition that the soft symbol is accurate enough to cancel the multipath interference. As the LAI reduces gradually, the soft information becomes more and more reliable and the accuracy of soft symbol is improved, and we start to apply

( )

MPIC scheme which is illustrated in Fig. 3.3. The iteration of multi-layered detection method with MPIC is shown in Fig. 4.8.

In the same way mentioned in Section 3.2, the MPI-cancelled signal for the qth path can be derived as

Desired Signal Residual Multipath Interference

( ˆ )

where the diagonal matrix of multipath channel gain ^, ^,

a complex amplitude multiplied by a phase which shifts with the subcarrier frequency. When

, j Q

rq is matched by the complex conjugate of H_q^j,Q, chips on all subcarriers will suffer the same equivalent channel gain |a_p^{j Q}^, |² , and the ICI that induced by the loss of code orthogonality will be suppressed. After maximum ratio combining for all paths, the signal is despread and descrambled. The signal after combining for all receivers can be expressed as

( )

Desired Signal Residual Multipath Interference

( ) ( )

where the residual multipath interference (RMPI) term which induced by incorrect soft symbols replace the ICI term in Eq.(4.32). We can obtain the means of z _u^Q

The variance of RMPI, RLAI and EN are, respectively,

These parameters are exploited to help demap.

C. Demapper and soft symbol

The damapper block which translates symbol to bit information is applied after all receive signals are combined. The statistic parameters of the demapping signal, mean and variance, are sent to the demapper block and substituted into Eq.(4.10). We can compute the extrinsic LLR of the ithbit of the symbol for the lth layer as

where i= ∼0 2, w is the symbol included in Ω or ₀ⁱ Ω , ₁ⁱ h and _eq σ_z² change with different processes ( MMSE or MPIC ). Notice that the a-priori information Λ^l_a(V )_t^i' is equal to zero for the first demapping.

After demapping for all layers, Λ^l_ex(V )_tⁱ is dinterleaved to return to the coding order, and the soft-in soft-out decoder described in Section 4.1.2.B is used to output the extrinsic information of coded bit Λ_ex(C )ⁱ_t . Λ_ex(C )ⁱ_t is interleaved and taken as Λ^l_a(V )_tⁱ of the demapper. After several iteration of demapping and decoding, the final a-posteriori LLR

(C )t

Λ is passed to the soft symbol block.

2 z

=Var[ { }] Var[ { }]= (Var[RMPI]+Var[RLAI]+Var[EN])1 2

The soft symbol is the expectation of the transmitted symbol. The probability of the transmitted symbol is computed from the a-posteriori information of coded bits Λ(C )ⁱ_t by

{ }

and we can obtain the soft symbol by

3 i i soft symbols are passed to the next iteration for LAIC or MPIC.

4.4 Simulation Results

We will show the simulation results of the parallel iterative multi-layered detection method with BICM presented in this chapter. The simulation parameters are listed in Table 4.1. The assumptions on channel model and estimation are the same as the description in Section 3.4.

The number of transmitters / receivers 3 / 4

Number of subcarriers (N) 256

Length of Walsh codes (N) 256

Number of 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 or 6

Modulation 8-PSK

Code rate 2/3

Number of decoding iteration 4

Signal labeling Gray

Table 4.1:Simulation parameters

4.4.1 The Performance Results of the Parallel Iterative

Multi-layered Detection Method

a. In a two-path fading channel:

The BER performance of the iterative multi-layered detection method for bit-interleaved coded modulation in 2-path fading channel is shown in Fig. 4.9. The bandwidth efficiency of this system is 6 bits/Hz. We apply MMSE equalization at first, and use it and MPIC by turns from the second iteration to the fifth iteration. When layered-antenna interference becomes little and MMSE equalizer can’t improve performance any more, only the MPIC iteration is applied for the following iterations. Because Gray labeling is applied, the improvement by iterative demapping is not very obvious. The performance slope between 1dB and 3dB becomes sharper than at lower SNR and the performance is very close to that of perfect LAIC and MPIC. Thus, at high SNR, not only the diversity is obtained, but also the reliability of reconstructed soft symbol is good enough to cancel interference clearly. At Eb/N0= 2 ~ 3 dB, we can find that the performance improvement for each iteration is better than that in the system without BICM shown in Fig. 3.5 and the coding gain of 2 dB is supplied. In the same SNR region, the performance of the final iteration is very close to that of perfect LAIC and MPIC that shows the accuracy of the interference cancellation is improved by using BICM.

But it has worse performance at lower SNR.

The FER performance of the iterative multi-layered detection method for bit-interleaved coded modulation in 2-path fading channel is shown in Fig. 4.10. In the high SNR region, we can observe FER is low. Error bits concentrate in some frames which suffer worse channel effect, and no errors occur to other frames. If the soft information of most bits in a frame is

在文檔中應用於多輸入/輸出多載波分碼多重進接系統的遞迴式多層級偵測方法之研究 (頁 38-0)