# Partial PIC-MRC Receiver Design for Single Carrier Block Transmission System over Multipath Fading Channels

Authors: Juinn-Horng Deng; Sheng-Yang Huang
Journal: International Journal of Antennas and Propagation
 (2012)

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## Abstract

Single carrier block transmission (SCBT) system has become one of the most popular modulation systems due to its low peak-to-average power ratio (PAPR), and it is gradually considered to be used for uplink wireless communication systems. In this paper, a low complexity partial parallel interference cancellation (PIC) with maximum ratio combining (MRC) technology is proposed to use for receiver to combat the intersymbol interference (ISI) problem over multipath fading channel. With the aid of MRC scheme, the proposed partial PIC technique can effectively perform the interference cancellation and acquire the benefit of time diversity gain. Finally, the proposed system can be extended to use for multiple antenna systems to provide excellent performance. Simulation results reveal that the proposed low complexity partial PIC-MRC SIMO system can provide robust performance and outperform the conventional PIC and the iterative frequency domain decision feedback equalizer (FD-DFE) systems over multipath fading channel environment.


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## Body

## 1. Introduction

Over past decade, orthogonal frequency-division multiplexing (OFDM) system has become one of the most popular systems in wireless communication. This technique is seen today as a strong candidate for future generations of cellular mobile networks, but it involves the problem of high peak-to-average power ratio (PAPR), it will cause power amplifier working in the nonlinear area. Thus, it needs to back off output power which will reduce the efficiency of power amplifier. For single carrier block transmission (SCBT) system, it is the one of the popular themes in recent years [1–6]. It can provide low PAPR performance, so we try to study the interference cancellation technique to provide the excellent bit error rate (BER) performance and reduce the computation complexity at receiver.References [2, 3] with the iterative frequency domain decision feedback equalizer (FD-DFE) are proposed for SCBT system. It is noted that the decision and iteration of the FD-DFE scheme are processed on frequency domain. And after more iteration, the performance of BER is improved obviously. Moreover, the BER performance of these systems is performed obviously only when the iterations number is enough high. However, large number of iterations will induce high complexity at the receiver. Parallel interference cancellation (PIC) scheme in [7–10] can overcome the intersymbol interference (ISI) problem effectively and improve the BER performance obviously. However, the BER performance is worse than FD-DFE in [3] even use more iteration loops.Therefore, in order to alleviate the above problem, the partial PIC with maximum ratio combing (MRC) technique is proposed in this paper. That is, with the aid of MRC scheme [11], the proposed partial PIC technique can effectively perform the interference cancellation and acquire the benefit of time diversity gain. In fact, with more taps for weighting combination, it will lead to higher time diversity gain. Furthermore, it indicates that the proposed technique can achieve better BER due to the diversity gain. This can mainly be attributed to the ability of this scheme to effectively deal with interference effects and achieve inherent time diversity with MRC. And it also can extend to multiple antenna system and obtain further performance. Moreover, the antenna selection technique (AST) [12–15] is used to reduce the cost and power associated with the single input multiple output (SIMO) system. Simulation results reveal that the proposed low complexity partial PIC-MRC system can provide lower receiver complexity and robust performance than the conventional PIC and the iterative FD-DFE systems over multipath fading channel environment.The remainder of this paper is organized as follows: Section2 introduces the system model and the FD-DFE for the SCBT systems. In Section 3, PIC algorithm is used to cancel the block interference, and iterative partial PIC-MRC scheme is proposed to enhance BER performance further. In Section 4, the proposed system is extended to the multiple antenna system. Results of performance tests of the proposed system are then given in Section 5, and Section 6 concludes the study.


## 2. System Model

### 2.1. Frequency Domain Equalization System

Figure1 shows a basic configuration of the SCBT system. First the nth information signal block of size N×1 can be defined as x(n)=[x0(n),…,xN-1(n)]T, where the superscript  (·)T  stands for the transpose. The transmitted signal block of size  (N+K)×1  is generated from  x(n) by adding the cyclic prefix (CP) of K symbols length as the guard interval (GI). Tcp donates the CP insertion matrix of size  (N+K)×N  defined as
(1)Tcp=[OK×(N-K)IKIN](N+K)×N.OK×(N-K)  is a zero matrix of size K×(N-K), and IN is an identity matrix of size N×N. The received signal block   y^(n)  is written as
(2)y^(n)=HTcpx(n)+n′(n)=h⊗cx^(n)+n′(n),
where  n′(n) is a channel noise vector of size  (N+K)×1.⊗c  represents as circular convolution and h={h0,…,hG-1} denotes the channel impulse response which can arrange the Toeplitz channel matrices  H  of size (N+K)×(N+K), and G is the length of multipath. After discarding the CP portion of the received signal block, the received signal block  y(n)  of size N×1 can be written as
(3)y(n)=RcpHTcpx(n)+n(n),
where  Rcp  denotes the CP discarding matrix of size N×(N+K) defined as
(4)Rcp=[ON×KIN]N×(N+K)
and  n(n)=Rcpn′(n). Next, after CP insertion and discarding CP portion, the channel matrix  H will be changed into a circulant matrix  Hc of size  N×N, which can be written as
(5)Hc=RcpHTcp=FHΛF,
where Λ is the frequency-domain channel response, and F is defined as a discrete Fourier transform (DFT) matrix. After DFT, frequency domain equalizer W      and IDFT ara processing, the equalized signal can be written as
(6)x^(n)=FHWΛFx(n)+FHWFn(n),
where (·)H  stands for the conjugate transpose. The equalizer consists of zero-forcing (ZF) and minimum mean square error (MMSE) equalizers, where ZF is defined as WZF=Λ-1 and MMSE is defined as  WMMSE=(ΛHΛ+σn2/σx2IN)-1ΛH,  and σn2 and σx2 are the variance of noise and signal. The equalized signal can be rewritten as
(7)x^(n)=FHWMMSEFHcx(n)+FHWMMSEFn(n)=H-x(n)+FHWMMSEFn(n),
where H-=FHWMMSEFHc,  and H- is a new channel matrix of size N×N. In Figure 3, the energy of H- is concentrated on the diagonal, but there still have residue ISI, which will degrade the system performance. So interference cancellation systems are proposed to cancel the ISI and achieve better performance.Figure 1
Block diagram of SCBT system.


### 2.2. Frequency-Domain Decision Feedback Equalizer

#### 2.2.1. Iterative MMSE Decision Feedback Equalizer

Figure2 shows a bock diagram of FD-DFE system, suppose that the received block is fed to the DFT operator, whose output block is denoted as (Y0,Y1,…,YN-1). The equalizer multiplies this signal block with its feedforward coefficients (F0,F1,…,FN-1), and the resulting signal block enters an inverse DFT, which yields the output block (x^0,x^1,…,x^N-1) on which the threshold detector bases its first decisions for the transmitted signal block.Figure 2
Block diagram of iterative FD-DFE.Figure 3
The characteristics of time domain channel matrixH-.Once the receiver makes a first set of decisions, the decision block is fed to a feedback filter with coefficients (B0,B1,…,BN-1), and an iterative DFE is implemented. At the lth      iteration, the feedforward and feedback filter block supplies
(8)Rn(l)=Fn(l)Yn+Bn(l)Dn(l-1),n=0,1,…,N-1,
where the Fn(l) and Bn(l) coefficient sets are, respectively, the feedforward and feedback filter coefficients at the lth  iteration, and the Dn(l-1) is the frequency-domain decisions at the previous iteration. The initial MMSE equalizer is given as
(9)Fn(0)=Λn*σn2/σx2+(|Λn|)2,n=0,1,…,N-1,
where   Λn  is frequency-domain channel response, and initial feedback filter coefficient is given as
(10)Bn(0)=0.
The first equalizer decisions are obtained using  α0=1,  and the definition of  αk  is given in [4]
(11)αl=1-lL10,
where L  is the number of iterations. At the  lth  iteration, the feedforward and the feedback filter coefficients are, respectively, given by
(12)Fn(l)=Λn*σn2/σx2+(1-αl-12)|Λn|2,Bn(l)=αl-1[ΛnFn(l)-1N∑n=1NΛnFn(l)].


#### 2.2.2. Iterative MF-Based Decision Feedback Equalizer

In the iterative DFE proposed in [5], the feedforward filter in that DFE shifts linearly from a linear MMSE filter at the first  (L-1)  iterations to the matched filter (MF) at the last iteration. At the lth iteration, the feedforward and the feedback filter coefficients are, respectively, given by
(13)Fn(l)=αlΛn*σn2/σx2+|Λn|2+(1-αl)Λn*,Bn(l)=1-Fn(l)Λn.
The first equalizer decisions are obtained using α0=1 that is, the equalizer is clearly a linear MMSE equalizer. Then, the  αl  parameter decreases linearly as
(14)αl=1-lL.
At the last iteration, αl=0,  and the feedforward filter becomes an MF.


## 2.1. Frequency Domain Equalization System

Figure1 shows a basic configuration of the SCBT system. First the nth information signal block of size N×1 can be defined as x(n)=[x0(n),…,xN-1(n)]T, where the superscript  (·)T  stands for the transpose. The transmitted signal block of size  (N+K)×1  is generated from  x(n) by adding the cyclic prefix (CP) of K symbols length as the guard interval (GI). Tcp donates the CP insertion matrix of size  (N+K)×N  defined as
(1)Tcp=[OK×(N-K)IKIN](N+K)×N.OK×(N-K)  is a zero matrix of size K×(N-K), and IN is an identity matrix of size N×N. The received signal block   y^(n)  is written as
(2)y^(n)=HTcpx(n)+n′(n)=h⊗cx^(n)+n′(n),
where  n′(n) is a channel noise vector of size  (N+K)×1.⊗c  represents as circular convolution and h={h0,…,hG-1} denotes the channel impulse response which can arrange the Toeplitz channel matrices  H  of size (N+K)×(N+K), and G is the length of multipath. After discarding the CP portion of the received signal block, the received signal block  y(n)  of size N×1 can be written as
(3)y(n)=RcpHTcpx(n)+n(n),
where  Rcp  denotes the CP discarding matrix of size N×(N+K) defined as
(4)Rcp=[ON×KIN]N×(N+K)
and  n(n)=Rcpn′(n). Next, after CP insertion and discarding CP portion, the channel matrix  H will be changed into a circulant matrix  Hc of size  N×N, which can be written as
(5)Hc=RcpHTcp=FHΛF,
where Λ is the frequency-domain channel response, and F is defined as a discrete Fourier transform (DFT) matrix. After DFT, frequency domain equalizer W      and IDFT ara processing, the equalized signal can be written as
(6)x^(n)=FHWΛFx(n)+FHWFn(n),
where (·)H  stands for the conjugate transpose. The equalizer consists of zero-forcing (ZF) and minimum mean square error (MMSE) equalizers, where ZF is defined as WZF=Λ-1 and MMSE is defined as  WMMSE=(ΛHΛ+σn2/σx2IN)-1ΛH,  and σn2 and σx2 are the variance of noise and signal. The equalized signal can be rewritten as
(7)x^(n)=FHWMMSEFHcx(n)+FHWMMSEFn(n)=H-x(n)+FHWMMSEFn(n),
where H-=FHWMMSEFHc,  and H- is a new channel matrix of size N×N. In Figure 3, the energy of H- is concentrated on the diagonal, but there still have residue ISI, which will degrade the system performance. So interference cancellation systems are proposed to cancel the ISI and achieve better performance.Figure 1
Block diagram of SCBT system.


## 2.2. Frequency-Domain Decision Feedback Equalizer

### 2.2.1. Iterative MMSE Decision Feedback Equalizer

Figure2 shows a bock diagram of FD-DFE system, suppose that the received block is fed to the DFT operator, whose output block is denoted as (Y0,Y1,…,YN-1). The equalizer multiplies this signal block with its feedforward coefficients (F0,F1,…,FN-1), and the resulting signal block enters an inverse DFT, which yields the output block (x^0,x^1,…,x^N-1) on which the threshold detector bases its first decisions for the transmitted signal block.Figure 2
Block diagram of iterative FD-DFE.Figure 3
The characteristics of time domain channel matrixH-.Once the receiver makes a first set of decisions, the decision block is fed to a feedback filter with coefficients (B0,B1,…,BN-1), and an iterative DFE is implemented. At the lth      iteration, the feedforward and feedback filter block supplies
(8)Rn(l)=Fn(l)Yn+Bn(l)Dn(l-1),n=0,1,…,N-1,
where the Fn(l) and Bn(l) coefficient sets are, respectively, the feedforward and feedback filter coefficients at the lth  iteration, and the Dn(l-1) is the frequency-domain decisions at the previous iteration. The initial MMSE equalizer is given as
(9)Fn(0)=Λn*σn2/σx2+(|Λn|)2,n=0,1,…,N-1,
where   Λn  is frequency-domain channel response, and initial feedback filter coefficient is given as
(10)Bn(0)=0.
The first equalizer decisions are obtained using  α0=1,  and the definition of  αk  is given in [4]
(11)αl=1-lL10,
where L  is the number of iterations. At the  lth  iteration, the feedforward and the feedback filter coefficients are, respectively, given by
(12)Fn(l)=Λn*σn2/σx2+(1-αl-12)|Λn|2,Bn(l)=αl-1[ΛnFn(l)-1N∑n=1NΛnFn(l)].


### 2.2.2. Iterative MF-Based Decision Feedback Equalizer

In the iterative DFE proposed in [5], the feedforward filter in that DFE shifts linearly from a linear MMSE filter at the first  (L-1)  iterations to the matched filter (MF) at the last iteration. At the lth iteration, the feedforward and the feedback filter coefficients are, respectively, given by
(13)Fn(l)=αlΛn*σn2/σx2+|Λn|2+(1-αl)Λn*,Bn(l)=1-Fn(l)Λn.
The first equalizer decisions are obtained using α0=1 that is, the equalizer is clearly a linear MMSE equalizer. Then, the  αl  parameter decreases linearly as
(14)αl=1-lL.
At the last iteration, αl=0,  and the feedforward filter becomes an MF.


## 2.2.1. Iterative MMSE Decision Feedback Equalizer

Figure2 shows a bock diagram of FD-DFE system, suppose that the received block is fed to the DFT operator, whose output block is denoted as (Y0,Y1,…,YN-1). The equalizer multiplies this signal block with its feedforward coefficients (F0,F1,…,FN-1), and the resulting signal block enters an inverse DFT, which yields the output block (x^0,x^1,…,x^N-1) on which the threshold detector bases its first decisions for the transmitted signal block.Figure 2
Block diagram of iterative FD-DFE.Figure 3
The characteristics of time domain channel matrixH-.Once the receiver makes a first set of decisions, the decision block is fed to a feedback filter with coefficients (B0,B1,…,BN-1), and an iterative DFE is implemented. At the lth      iteration, the feedforward and feedback filter block supplies
(8)Rn(l)=Fn(l)Yn+Bn(l)Dn(l-1),n=0,1,…,N-1,
where the Fn(l) and Bn(l) coefficient sets are, respectively, the feedforward and feedback filter coefficients at the lth  iteration, and the Dn(l-1) is the frequency-domain decisions at the previous iteration. The initial MMSE equalizer is given as
(9)Fn(0)=Λn*σn2/σx2+(|Λn|)2,n=0,1,…,N-1,
where   Λn  is frequency-domain channel response, and initial feedback filter coefficient is given as
(10)Bn(0)=0.
The first equalizer decisions are obtained using  α0=1,  and the definition of  αk  is given in [4]
(11)αl=1-lL10,
where L  is the number of iterations. At the  lth  iteration, the feedforward and the feedback filter coefficients are, respectively, given by
(12)Fn(l)=Λn*σn2/σx2+(1-αl-12)|Λn|2,Bn(l)=αl-1[ΛnFn(l)-1N∑n=1NΛnFn(l)].


## 2.2.2. Iterative MF-Based Decision Feedback Equalizer

In the iterative DFE proposed in [5], the feedforward filter in that DFE shifts linearly from a linear MMSE filter at the first  (L-1)  iterations to the matched filter (MF) at the last iteration. At the lth iteration, the feedforward and the feedback filter coefficients are, respectively, given by
(13)Fn(l)=αlΛn*σn2/σx2+|Λn|2+(1-αl)Λn*,Bn(l)=1-Fn(l)Λn.
The first equalizer decisions are obtained using α0=1 that is, the equalizer is clearly a linear MMSE equalizer. Then, the  αl  parameter decreases linearly as
(14)αl=1-lL.
At the last iteration, αl=0,  and the feedforward filter becomes an MF.


## 3. Parallel Interference Cancellation

The residue ISI will degrade the system performance. Thus, in this section, the PIC is used to cancel the ICI problems in SCBT system.


### 3.1. Conventional Parallel Interference Cancellation

Figure4 is the schematic diagram of interference, the colored boxes are interference in the received symbols.  H-i,d is expressed as the  dth  symbol data to the ith interference symbol. When i is different from d, that is,  i≠d,H-i,dx(n) is the ISI which will degrade the system performance. Figure 5 is the block diagram of PIC in SCBT system. x~n is the equalized signal x^n in (7) after canceling the ISI, which can be given as
(15)x~n=(x^n-(h-n-hn)(d~-d~n))H-n,n-1,
where  h-n  is the  (n+1)th  row vector of  H-, and hn is defined as hn=[01×nH-n,n01×(N-n-1)],d~  is the modulated signal of QPSK after the decision
(16)d~=[d~0d~1⋯d~N-1]T
and  d~n is defined as
(17)d~n=[01×nd~n01×(N-n-1)]T.
After canceling the ISI terms, the interference cancelled signal x~ can be detected by the decision operation.Figure 4
Schematic diagram of intersymbol interference.Figure 5
Block diagram of PIC in SCBT system.


### 3.2. Partial PIC with Maximum Ratio Combining

PIC algorithm can overcome the ISI problem effectively and improve the BER performance obviously. However, as shown in (15) for only one-tap equalizer, it will result in the loss of energy for the symbol detection. Besides, in order to enhance the receiver performance in Section 3.1, the number of iterations needs to be increased. It will induce more computation complexity. Therefore, in order to alleviate the above problem, the partial PIC with maximum ratio combing technique is proposed in this paper. That is, with the aid of MRC scheme, the proposed partial PIC technique can effectively perform the interference cancellation and acquire the benefit of time diversity gain. In fact, with more taps for weighting combination, it will lead to higher time diversity gain. Furthermore, it indicates that the proposed technique can achieve better BER due to the diversity gain. This can mainly be attributed to the ability of this scheme to effectively deal with interference effects and achieve inherent time diversity with MRC.The block diagram is shown in Figure6 and the illustration of partial PIC is shown in Figure 7. Its structure is similar to PIC. The main difference is that PIC-MRC doing partial PIC first and then combines the partial energy from other received symbols by MRC algorithm. Finally, using the MRC equalizer can obtain the detected signal. To simplify the exposition, we consider a simple case. First, from (7) and (15), the partial parallel interference is reconstructed by G0(H--H-0)(d~-d~0), where G0 is the partial selection matrix of parallel interference with window size M selection, that is, G0=[[IM/2×M/20M/2×M/2]T0M×(N-M)[0M/2×M/2IM/2×M/2]T] with the identity matrix IM/2×M/2, the zero matrices 0M×(N-M) and 0M/2×M/2. Next, the received partial signal G0x^ can be subtracted by the partial parallel interference. The residual signal can be expressed by
(18)p^0=G0x^-G0(H--H-0)(d~-d~0),
where  H-0=[h~00N×(N-1)], d~  and  d~0  are the modulated signal after decision in (16)-(17), and h~0 is the first column vector of H-. After MRC operation, the detected signal can be obtained by the MRC equalization
(19)x~0=h~0HG0(x^-(H--H-0)(d~-d~0))‖G0h~0‖2.
Similarly to the procedures of (18) and (19), the nth partial PIC-MRC signal can be obtained by
(20)x~n=h~nHGn(x^-(H--H-n)(d~-d~n))‖Gnh~n‖2,
where H-n=[0N×nh~n0N×(N-n-1)],  h~n is the (n+1)th  column vector of H-, and the partial selection matrix  Gn  is(21)Gn={[[I(M/2+n)×(M/2+n)0(M/2-n)×(M/2+n)]T0M×(N-M)[0(M/2+n)×(M/2-n)I(M/2-n)×(M/2-n)]T],ifn<M2[0M×(n-M/2)IM×M0M×(N-M/2-n)],ifn≥M2,n≤N-M2[[I(M/2+n-N)×(M/2+n-N)0(M/2-n+N)×(M/2+n-N)]T0M×(N-M)[0(M/2+n-N)×(M/2-n+N)I(M/2-n-N)×(M/2-n+N)]T]ifn>N-M2.Figure 6
Block diagram of iterative partial PIC-MRC in SCBT system.Figure 7
The illustration of partial selection matrix for partial PIC-MRC.It is noteworthy that the equalizers in (19) and (20) are still one-tap equalizer with low complexity, which do not induce noise enhancement problem due to ∥Gnh~n∥2 with the robust summarized channel responses. The partial PIC-MRC algorithm not only can acquire time diversity gain, but also reduce the computation complexity than the conventional PIC scheme in Section 3.1 because it needs more iteration loops to enhance performance at receiver side.


## 3.1. Conventional Parallel Interference Cancellation

Figure4 is the schematic diagram of interference, the colored boxes are interference in the received symbols.  H-i,d is expressed as the  dth  symbol data to the ith interference symbol. When i is different from d, that is,  i≠d,H-i,dx(n) is the ISI which will degrade the system performance. Figure 5 is the block diagram of PIC in SCBT system. x~n is the equalized signal x^n in (7) after canceling the ISI, which can be given as
(15)x~n=(x^n-(h-n-hn)(d~-d~n))H-n,n-1,
where  h-n  is the  (n+1)th  row vector of  H-, and hn is defined as hn=[01×nH-n,n01×(N-n-1)],d~  is the modulated signal of QPSK after the decision
(16)d~=[d~0d~1⋯d~N-1]T
and  d~n is defined as
(17)d~n=[01×nd~n01×(N-n-1)]T.
After canceling the ISI terms, the interference cancelled signal x~ can be detected by the decision operation.Figure 4
Schematic diagram of intersymbol interference.Figure 5
Block diagram of PIC in SCBT system.


## 3.2. Partial PIC with Maximum Ratio Combining

PIC algorithm can overcome the ISI problem effectively and improve the BER performance obviously. However, as shown in (15) for only one-tap equalizer, it will result in the loss of energy for the symbol detection. Besides, in order to enhance the receiver performance in Section 3.1, the number of iterations needs to be increased. It will induce more computation complexity. Therefore, in order to alleviate the above problem, the partial PIC with maximum ratio combing technique is proposed in this paper. That is, with the aid of MRC scheme, the proposed partial PIC technique can effectively perform the interference cancellation and acquire the benefit of time diversity gain. In fact, with more taps for weighting combination, it will lead to higher time diversity gain. Furthermore, it indicates that the proposed technique can achieve better BER due to the diversity gain. This can mainly be attributed to the ability of this scheme to effectively deal with interference effects and achieve inherent time diversity with MRC.The block diagram is shown in Figure6 and the illustration of partial PIC is shown in Figure 7. Its structure is similar to PIC. The main difference is that PIC-MRC doing partial PIC first and then combines the partial energy from other received symbols by MRC algorithm. Finally, using the MRC equalizer can obtain the detected signal. To simplify the exposition, we consider a simple case. First, from (7) and (15), the partial parallel interference is reconstructed by G0(H--H-0)(d~-d~0), where G0 is the partial selection matrix of parallel interference with window size M selection, that is, G0=[[IM/2×M/20M/2×M/2]T0M×(N-M)[0M/2×M/2IM/2×M/2]T] with the identity matrix IM/2×M/2, the zero matrices 0M×(N-M) and 0M/2×M/2. Next, the received partial signal G0x^ can be subtracted by the partial parallel interference. The residual signal can be expressed by
(18)p^0=G0x^-G0(H--H-0)(d~-d~0),
where  H-0=[h~00N×(N-1)], d~  and  d~0  are the modulated signal after decision in (16)-(17), and h~0 is the first column vector of H-. After MRC operation, the detected signal can be obtained by the MRC equalization
(19)x~0=h~0HG0(x^-(H--H-0)(d~-d~0))‖G0h~0‖2.
Similarly to the procedures of (18) and (19), the nth partial PIC-MRC signal can be obtained by
(20)x~n=h~nHGn(x^-(H--H-n)(d~-d~n))‖Gnh~n‖2,
where H-n=[0N×nh~n0N×(N-n-1)],  h~n is the (n+1)th  column vector of H-, and the partial selection matrix  Gn  is(21)Gn={[[I(M/2+n)×(M/2+n)0(M/2-n)×(M/2+n)]T0M×(N-M)[0(M/2+n)×(M/2-n)I(M/2-n)×(M/2-n)]T],ifn<M2[0M×(n-M/2)IM×M0M×(N-M/2-n)],ifn≥M2,n≤N-M2[[I(M/2+n-N)×(M/2+n-N)0(M/2-n+N)×(M/2+n-N)]T0M×(N-M)[0(M/2+n-N)×(M/2-n+N)I(M/2-n-N)×(M/2-n+N)]T]ifn>N-M2.Figure 6
Block diagram of iterative partial PIC-MRC in SCBT system.Figure 7
The illustration of partial selection matrix for partial PIC-MRC.It is noteworthy that the equalizers in (19) and (20) are still one-tap equalizer with low complexity, which do not induce noise enhancement problem due to ∥Gnh~n∥2 with the robust summarized channel responses. The partial PIC-MRC algorithm not only can acquire time diversity gain, but also reduce the computation complexity than the conventional PIC scheme in Section 3.1 because it needs more iteration loops to enhance performance at receiver side.


## 4. Partial PIC-MRC SIMO System

In this section, the proposed partial PIC-MRC system is extended into multiple antenna systems.


### 4.1. Partial PIC-MRC SIMO System

The advantage of SIMO systems is that better BER performance can be achieved without using any additional transmit power and bandwidth. The SIMO system with one transmit andNR receive antennas is shown in Figure 8. At each receive antenna, the same procedures of equalizer are processed, for example, frequency domain equalization and partial PIC-MRC operation with iteration number  L. Finally, the decision scheme is used to detect the combination signal from the NR equalizers.Figure 8
Block diagram of the partial PIC-MRC SIMO SCBT system.


### 4.2. Antenna Selection Technique

Although the SIMO system in Section4.1 can provide better BER performance than the conventional single input single output (SISO) antenna system, the main drawback of the SIMO system is the requirement of the additional high-cost radio frequency (RF) modules. RF module includes low noise amplifier, mixer, band pass filter, low pass filter, and analog-to-digital converter. For multiple RF modules in SIMO system, the higher cost and power consumption are needed. In order to reduce the cost and power associated with the SIMO system, the antenna selection technique is used in the proposed SIMO system, that is, the number of the receive antenna being larger than the RF modules. Figure 9 is the block diagram of antenna selection technique (AST) in which only Q RF modules are used to support  NR  receive antennas.Figure 9
The structure of antenna selection withQ RF modules and NR receive antennas.To do the AST algorithm, we first use the channel capacity algorithm, that is,(22)Ci=log2det⁡(IN+σx2σn2HciHciH),i=1,…,NR,
where Hci is the channel matrix of the selected ith receive antenna. Next, based on the different combination of channel matrix, the AST algorithm finally chooses the Q receive antennas, which can provide the maximum channel capacity Ci to use for the proposed SIMO system.


## 4.1. Partial PIC-MRC SIMO System

The advantage of SIMO systems is that better BER performance can be achieved without using any additional transmit power and bandwidth. The SIMO system with one transmit andNR receive antennas is shown in Figure 8. At each receive antenna, the same procedures of equalizer are processed, for example, frequency domain equalization and partial PIC-MRC operation with iteration number  L. Finally, the decision scheme is used to detect the combination signal from the NR equalizers.Figure 8
Block diagram of the partial PIC-MRC SIMO SCBT system.


## 4.2. Antenna Selection Technique

Although the SIMO system in Section4.1 can provide better BER performance than the conventional single input single output (SISO) antenna system, the main drawback of the SIMO system is the requirement of the additional high-cost radio frequency (RF) modules. RF module includes low noise amplifier, mixer, band pass filter, low pass filter, and analog-to-digital converter. For multiple RF modules in SIMO system, the higher cost and power consumption are needed. In order to reduce the cost and power associated with the SIMO system, the antenna selection technique is used in the proposed SIMO system, that is, the number of the receive antenna being larger than the RF modules. Figure 9 is the block diagram of antenna selection technique (AST) in which only Q RF modules are used to support  NR  receive antennas.Figure 9
The structure of antenna selection withQ RF modules and NR receive antennas.To do the AST algorithm, we first use the channel capacity algorithm, that is,(22)Ci=log2det⁡(IN+σx2σn2HciHciH),i=1,…,NR,
where Hci is the channel matrix of the selected ith receive antenna. Next, based on the different combination of channel matrix, the AST algorithm finally chooses the Q receive antennas, which can provide the maximum channel capacity Ci to use for the proposed SIMO system.


## 5. Simulation Results

In this section, simulation results are conducted to demonstrate the performance of the proposed partial PIC-MRC system, and Table1 is the system parameter settings. Perfect channel state information is assumed for simulation.Table 1
System simulated parameters.
Parameter
Specification
Modulation type
QPSK
FFT length (N)
64
Multipath number
6
Channel model
Equal gain rayleigh fading channel
CP length
16Figure10 shows the BER performance of iterative MMSE decision feedback equalizer and iterative MF-based decision feedback equalizer. The number of iteration is 2, 4, and 6 times. As shown in Figure 10, the system performance is better as the number of iteration increases. Besides, for the iteration number being 2, the performance of the iterative MMSE FDE can approach to the MMSE equalizer. At the iteration number being 4 and 6, the performance of the iterative MMSE FDE increases about 1 dB and 1.5 dB than MMSE equalizer at BER=4×10-5, respectively. When the number of iteration is 6, the performance of iterative MMSE DFE is better than the iterative MF-based DFE receiver about 1.4 dB at  BER=2×10-5.Figure 10
BER performance of iterative MMSE/MF-based DFE.For partial PIC-MRC in SCBT system, the window sizeM  in (18)–(20) can be selected by the simulation result which is shown in Figure 11. It is obviously that when M is larger than 16 under different  Eb/N0, the performance will achieve to the bound of full PIC-MRC system. Therefore, on the basis of the result, the size of the window  M=16  will be utilized for the following simulations.Figure 11
BER performance partial PIC-MRC under different window sizeM in SCBT system.Figure12 shows the BER performance of PIC and partial PIC-MRC in SCBT system. The dotted lines are the best performance bound of PIC and partial PIC-MRC, respectively. Note that the bound performance is evaluated for the assumption of the perfect signal detection used for PIC cancellation. Next, we can see that the performance of the proposed partial PIC-MRC scheme is better than the conventional PIC scheme about 1 dB at BER=10-5,  but the performance is lower than iterative MMSE DFE  (L=6)  about 0.6 dB.Figure 12
BER performance of PIC, partial PIC-MRC, and MMSE-DFE in SCBT system.Next, the BER performance is evaluated for the iterative partial PIC-MRC and MMSE DFE systems. As shown in Figure13, after more iteration, the performance of the proposed partial PIC-MRC system has increased obviously. After 2 iterations, the performance has been better than the iterative MMSE DFE system 0.6 dB at  BER=4×10-6, and then the performance increases again about 0.2 dB after 3 iterations. From above simulation results, the proposed iterative partial PIC-MRC scheme in SCBT system can actually acquire better BER performance and provide low complexity computation. For the computation complexity in Figure 13, the number of complex multiplication of the iterative MMSE DFE (L=6)  is computed about O(3LNlog2N+7NL) due to the iterative DFE-MMSE weight operation. Next, for the proposed partial PIC-MRC scheme in (19)-(20), it involves the advantage of  d~  with the fixed values (i.e., QPSK symbol: ±1±j). Therefore, it does not need complex multiplication for the parallel interference reconstruction. Furthermore, the number of complex multiplication of the proposed partial PIC-MRC (L=3) can be computed about O(2Nlog2N+2N+2ML). For example, considering the iterative MMSE DFE system in Figure 13 with  L=6  and  N=64, the number of complex multiplication is about 9600. And considering the proposed partial PIC-MRC system in Figure 13 with L=3, M=16, and N=64, the number of complex multiplication is about 992. It is obvious that the proposed scheme with the lower window size M and iteration size L can provide the advantage of the lower computation complexity.Figure 13
BER performance of iterative partial PIC-MRC and MMSE-DFE in SCBT system.Finally, the proposed system is extended to multiple antenna system. Figure14 shows the BER performance of the proposed partial PIC-MRC SIMO systems with the receive antenna number from 2 to 4. With more receive antennas, the BER performance is shown better obviously. And Figure 15 is the BER performance of the proposed AST technique in the partial PIC-MRC SIMO system. Assume the RF modules Q is one and total receive antenna number is from 2 to 4. If antenna number equals to 2, the performance increases about 3 dB at BER=10-5  than SISO system. When the receive antenna number equals to 4, the performance almost achieves the SIMO system with one tranmit antenna and two receive antennas at Eb/N0=14dB. Note that the proposed AST system with low cost and power benefit is due to the RF module Q=1  and the receive antenna number NR=4, where RF module of the proposed scheme is smaller than the RF modules Q=2  of the SIMO system. It is noteworthy that the proposed SIMO PIC-MRC system with AST algorithm under Q=1 and NR=4 scenario is the SISO system with single RF and multiple antennas for selection. Therefore, in this scenario, the proposed AST SIMO system is still a SISO system with multiple antenna extension. Next, as shown in Figure 15, the proposed AST SIMO system can approach to the BER performance of the SIMO system with  Q=2  (two RFs). Therefore, the proposed AST SIMO system involves the advantage of the flexible structure of multiple antennas and RFs selection.Figure 14
BER performance of partial PIC-MRC SIMO systems.Figure 15
BER performance of partial PIC-MRC with antenna selection technique.


## 6. Conclusions

The partial PIC-MRC system is proposed for SCBT system, which is in order to achieve better BER performance and low complexity at the receiver side. With the aid of MRC scheme, the proposed partial PIC technique can effectively perform the interference cancellation and acquire the benefit of time diversity gain, which can achieve better BER performance. And it also can extend to multiple antenna structure with better BER performance. AST will introduce the select diversity and reduce the cost and power consumption of the SIMO system. Simulation results confirm that the proposed partial PIC-MRC SIMO system with the AST scheme can provide robust performance over multipath fading channel environment.



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*Source: 910824-2012-09-08.xml*