Efficient embedded signaling scheme for nodes identification using block coding with blind phase estimation in relay systems Mariem Ayedi
Noura Sellami
Mohamed Siala
MEDIATRON laboratory, SUP’COM Carthage University, Tunisia Email:
[email protected]
LETI laboratory, ENIS Sfax University, Tunisia Email:
[email protected]
MEDIATRON laboratory, SUP’COM Carthage University, Tunisia Email:
[email protected]
Abstract—In this paper, we propose a nodes identification scheme based on embedded signaling for relay systems where a data sequence transmitted by a source node is forwarded by a selected relay node before reaching the destination node. In the proposed identification scheme, source and relay nodes incorporate precoding sequences, based on codewords generated from block codes, into the data sequence. A soft decoding at the destination node allows it to efficiently recover in one step the identities of transmitting source and relay nodes of received packets. The proposed scheme is an alternative to classical explicit identification scheme based on exchanging signaling information before the data exchange and including identities in the data sequences. We also propose a blind estimation technique allowing the destination to estimate the phase of the channel. We consider the Opportunistic Relay Selection (ORS) and the Partial Relay Selection (PRS) to select relay nodes. Numerical results confirm the performance of the proposed identification scheme. Index Terms—relay systems, embedded signaling, precoding sequences, block codes, relay selection, blind estimation.
I. I NTRODUCTION In relay wireless systems, relay nodes are used to help the transmission between source and destination nodes which cannot communicate directly. Relay communication is then a promising technique in wireless systems since it achieves high capacity and throughput and extends coverage [1]. The increase of networks density and the diversification of wireless applications generate an important explicit signaling load, maximizing the energy consumption, the radio ressource saturation and the transmission delay [2, 3]. Special attention should be given to signaling issue optimization in new technologies like Long Term Evolution Advanced (LTE-A). In [7–9], authors have evaluated the signaling cost in LTE-A relay networks in terms of handover and flow control signaling overhead. Embedding signaling information into the data sequence before transmission is actually an interesting technique which can efficiently substitute explicit signaling information exchange. Some researchers have proposed embedded signaling solutions for the channel estimation context [4] and for the Peak to Average Power Ratio (PAPR) reduction in Orthogonal Frequency-Division Multiplexing (OFDM) systems [5, 6]. In [10, 11], we addressed the problem of nodes identification and
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we proposed a blind identification signaling scheme based on embedding specific sequences called precoding sequences into the data sequence at each source and relay node in a multisource multi-relay wireless system. In [10], we propose to use Maximum Length Sequences (MLS) as precoding sequences and to use the Fast Walsh Hadamard Transform (FWHT) in order to reduce the computational complexity. The same precoded alphabet is used by source and relay nodes and the destination node decodes the received signals to recover the identities of the relay and of the source nodes engaged in the communication. In [11], we proposed to take advantages from classical coding to design the precoding sequences. Hence, precoding sequences are formulated by using codewords of block codes. Two block codes are used to identify source and relay nodes respectively and different precoded alphabets are used by source and relay nodes. The destination node performs hierarchical decoding of the received signals to first recover the identity of the relay and second that of the source engaged in the communication. In [10, 11], we have considered that the phase of the channel is perfectly known by the destination. In this paper, we propose to use precoding sequences based on codewords of block codes as in [11]. To improve the identification error rate performance compared to the hierarchical identification scheme proposed in [11], we propose here to use one block code to reliably identify source and relay nodes in only one step. Indeed, the same precoded alphabet is used by source and relay nodes and the destination node decodes the received signals to recover at the same time the source and relay nodes identities. We also propose a blind phase estimation allowing the destination to estimate the phase of the channel without the need of any explicit information exchange. The present paper is organized as follows. In Section II, we describe the relay wireless system model. In Section III, we present the proposed nodes identification scheme. In Section IV, we present the blind phase estimation technique. In Section V, we present simulation results. In Section VI, we give conclusions.
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II. R ELAY WIRELESS SYSTEM MODEL We consider a relay wireless network consisting of NS source nodes communicating through the help of half-duplex NR relay nodes with one common destination node D, as shown in figure 1. Hence, each wireless link l is a twohop wireless link composed of one source node, one relay node and the destination node (Su , Rv , D), u ∈ [1, NS ], v ∈ [1, NR ]. We assume Rayleigh block fading channels. Hence, the channel, denoted by hXY , relating each transmitting node X ∈ {Su , Rv }, u ∈ [1, NS ], v ∈ [1, NR ] and each receiving node Y ∈ {Rv , D}, v ∈ [1, NR ], is constant on a block of length JN symbols, where {J, N } ∈ N∗ and varies independently from one block to author. We consider the path loss model given by −α dXY , (1) E(|hXY |2 ) = d0 where E(.) denotes the expectation, d0 is a reference distance, dXY is the distance between X and Y and α is the path loss exponent. We consider that nodes X ∈ {Su , Rv }, u ∈ [1, NS ], v ∈ [1, NR ] transmit blocks of length JN . Each block is composed of J concatenated sub-blocks yjX , j ∈ [1, J] of length N . At the source node Su , u ∈ [1, NS ], and for the jth subblock, a data sequence of qN information carrying bits bjSu = (bjSu 1 , ..., bjSu qN ) is mapped into a sequence of M-ary Phase
Shift Keying (M-PSK) symbols xjSu = (xjSu 1 , ..., xjSu N ) using q a modulation alphabet Ω = exp( i2kπ 2q ), k ∈ [0, 2 − 1] of size 2q symbols, whith i is the complex imaginary unit and q ≥ 1 is the number of bits per symbol. Then, thee symbols of the modulated obtained sequence xjSu are multiplied by complex coefficients of a precoding sequence pSu = (pSu 1 , ..., pSu N ) to obtain the precoded sequence yjSu = (xjSu 1 pSu 1 , ..., xjSu N pSu N ) of the source node Su . We notice that the same precoding sequence is used for all subblocks. The communication process involves two steps. In the first step, a source node Su , u ∈ [1, NS ] transmits its precoded block ySu = (y1Su , ..., yJSu ) to the relay nodes. We present here the treatment relative to one sub-block yjSu and we notice that the treatment is the same for all sub-blocks. Then, the subblock received at each relay node Rv , v ∈ [1, NR ] is given by p (2) zjSu Rv = ESu hSu Rv yjSu + wjSu Rv , where ESu is the transmitted energy per symbol by the source Su , hSu Rv is the Rayleigh channel gain between Su and Rv and wjSu Rv is a zero-mean complex additive white gaussian 2 = N0 . noise vector with variance σw In the second step, only one selected relay will retransmit the received block to the destination node. We consider two distributed relay selection schemes which are the ORS and the PRS. For the ORS scheme [12], the relay node having the highest instantaneous equivalent Signal to Noise Ratio (SNR),
Fig. 1: Relay wireless system model.
ΓSu Rv D , of the links (Su , Rv , D), u ∈ [1, NS ], v ∈ [1, NR ] is selected. The SNR of the link (Su , Rv , D) is given by Γ S u Rv D =
Γ S u R v Γ Rv D , 1 + Γ S u Rv + Γ Rv D
(3)
where ΓXY =
EX |hXY |2 , N0
(4)
with EX is the transmitted energy per symbol by the transmitting node X. Since, the ORS scheme selects the relay node basing on the quality of the totality of the link, this scheme achieves good performance but it requires channel state information knowledge from the destination node. To reduce the acquisition of channel state information, the PRS scheme is proposed by [13]. For this scheme, the relay which has the highest instantaneous SNR, ΓSu Rv , of only the first hop, source-relay, will be selected. The SNR of the hop (Su , Rv ) is given by Γ S u Rv =
ESu |hSu Rv |2 . N0
(5)
At the selected relay node Rv , the received sequences are multiplied by complex coefficients of a precoding sequence pRv = (pRv 1 ...pRv N ) to obtain the precoded sub-block yjRv = (zSj u Rv 1 pRv 1 ...zSj u Rv N pRv N ). Hence, the relay node Rv amplifies and forwards the obtained precoded sequence to the destination node D. The received signal at D corresponding to one sub-block yjRv is zjRv D = βhRv D yjRv + wjRv D , where β is an amplification factor given by s ERv β= , ESu |hSu Rv |2 + N0
(6)
(7)
ERv is the transmitted energy per symbol by the relay node Rv , hRv D is the Rayleigh channel gain between Rv and D and wjRv D is a zero-mean complex additive white gaussian 2 = N0 . noise vector with variance σw In the next section, we detail the structure of precoding sequences and the destination node treatment in our proposed identification signaling scheme.
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III. P ROPOSED NODES IDENTIFICATION SCHEME In [11], the proposed identification scheme allows the destination to recover hierarchically (in two steps) the relay node and the source node by using two linear block codes. In this paper, we consider only one linear block code, denoted by C(N, K), with K = KS + KR where KS = ⌈log2 (NS )⌉ and KR = ⌈log2 (NR )⌉, with ⌈.⌉ denoting the ceiling operator. We denote by G the (K × N ) generating matrix of the code. We associate to each source node Su an identification information sequence dSu given by dSu = (dSu 1 , ..., dSu KS , 0, ..., 0), | {z }
(8)
dRv = (0, ..., 0, dRv 1 , ..., dRv KR ), | {z }
(9)
cX = dX G.
(10)
KR
where (dSu 1 , ..., dSu KS ) is the binary representation of an integer belonging to [0, 2KS − 1]. Furthermore, we associate to each relay node Rv an identification information sequence dRv given by
Then, the destination D performs a soft decoding process by determining the correlation vector Λ given by ! Λ = B(C)ℜ (ˇzRv D )T (15)
where B(X) is the matrix composed of bipolar versions of entries of the matrix X ,i.e, B(X) = −(2X − 1) and ℜ(.) denotes the real part. Hence, D finds an estimate of l, the index of the link (Su , Rv , D), given by ˆ l = arg
The modulo 2 binary addition of a pair of a source codeword cSu , u ∈ [1..NS ] and a relay codeword cRv , v ∈ [1..NR ] represents the identification sequence cSu Rv of the lth link (Su , Rv , D), where l ∈ [1..NS NR ], given by (11)
where ⊕ is the modulo 2 binary addition. We define C as the (NS NR × N ) matrix regrouping all links codewords given by C = ((cS1 R1 )T , . . . , (cSNS RNR )T )T , where (.)T denotes the transposition. The precoding sequence pX of each node X ∈ {Su , Rv } is then defined as iπcX pX = exp( q ). (12) 2 First, the destination node D raises the received sequence zRv D = (z1Rv D , ..., zJRv D ) component-wise to the power 2q to obtain the sequence denoted by zqRv D . Then, D calculates the average sub-block-wise zq,avg Rv D , carried over the J sub-blocks. The obtained sequence is given by q
(13)
where B(x) denotes the bipolar version of a binary sequence x, i.e, B(x) = −(2x− 1), hp eqv is the equivalent received channel gain given by heqv = (β ESu hRv D hSu Rv ) and wq,avg Rv D is the vector obtained after averaging the J equivalent noise vectors raised to the power 2q . In thisq section, we assume that D knows the phase ϕSu Rv of heqv 2 . Then, it computes ˇzRv D = exp(−iϕSu Rv )zq,avg Rv D .
(16)
IV. B LIND PHASE ESTIMATION TECHNIQUE
where (dRv 1 , ..., dRv KR ) is the binary representation of an integer belonging to [0, 2KR − 1]. We define the codewords cX of nodes X ∈ {Su , Rv } as
q,avg 2 zq,avg Rv D = heqv B(cSu Rv ) + wRv D ,
{Λl } ,
where Λl , ∈ [1, NS NR ] are the elements of the vector Λ. Therefore, the proposed scheme succeeds in allowing the destination node D to reliably identify the indexes of the source and the relay nodes transmitters of received packets in one step without using any additional signaling information exchange. In the following section, we consider a more realistic case q where the phase ϕSu Rv of heqv 2 is not known at D.
KS
cSu Rv = (cSu ⊕ cRv ),
max
l∈[1,NS NR ]
(14)
We propose in the following a blind phase estimation method allowing the destination to estimate the phase ϕSu Rv . We propose to search via numerical computations the phase ϕˆuv ∈ [0, π] which maximizes N X
q,avg [ℜ ((zuv )n exp(−iϕˆuv ))]
2
n=1 q,avg where (zuv )n , n ∈ [1, N ] are elements of zq,avg . uv Since elements of B(cSu Rv ) are bipolar, the estimate of ϕuv is obtained with an ambiguity of π. The obtained phase ϕˆuv is then an estimate of ϕuv or of ϕuv + π. Using these two phases in the correlation computation, we obtain two opposite sequences. Here, we distinguish two cases : • If (1, ..., 1) is not a codeword, there are no opposite codewords in C. The destination D selects the codeword obtained by using ϕˆuv or ϕˆuv + π which leads to the highest correlation in the soft decoding calculation. In this case, we have K = KS + KR . • if (1, ..., 1) is a codeword, then each codeword of C has its opposite in C. We assume, without loss of generality, that the last row of G is (1, ..., 1). We propose in this case not to consider the last bit in the relay identification sequence dRv . This bit is set to 0 or 1 and is then used by D to get rid of the π ambiguity. In this case, we have, K = KS + KR + 1.
V. N UMERICAL RESULTS AND DISCUSSIONS In this section, we present simulation results illustrating the performance of the proposed embedded nodes identification scheme. We consider that source and relay nodes transmit packets with the same energy which is equal to Es . We consider that relay nodes are closer to the destination node D than sources nodes. Then, dSu Rv = 1 and dRv D = 0.5, for u ∈ [1, NS ], v ∈ [1, NR ]. The path loss exponent α is set to 4. Figures 2, 3, 4 and 5 illustrate the identification error rate
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performance of links (Su , Rv , D), u ∈ [1, NS ], v ∈ [1, NR ], versus Eb /N0 , where Eb being the bit information energy equal to Es /q. Figure 2 illustrates the identification error rate performance of the proposed scheme for Binary Phase Shift Keying (BPSK) modulation scheme, i.e, q = 1 and Quadrature Phase Shift Keying (QPSK) modulation scheme, i.e, q = 2. The PRS scheme is used to select the relay nodes. The phase ϕuv is perfectly known by D. The wireless system consists of two-hop links relating NS = 16 source nodes and NR = 8 relay nodes to the destination node D. For the identification scheme, we use the BCH code C(63, 7). Hence, N = 63 and K = KS + KR = 7 where KS = log2 (NS ) = 4 and KR = log2 (NR ) = 3. The number of sub-blocks J is in {2, 5, 20} for BPSK modulation and J = 20 for QPSK modulation. Clearly, the identification error rate performance improves when the number of sub-blocks J increases since the noise effect on the identification scheme error rate is minimized as a result of the averaging on the J received sub-blocks at the destination. We also remark that performance degrades when the modulation QPSK is used due to the rise of the received noise to the power 4 compared to that for BPSK modulation. Hence, when using the QPSK modulation, the number of sub-blocks J should be increased to obtain comparable identification reliability with BPSK modulation. The figure also illustrates the identification error rate performance obtained when the classical explicit coded signaling scheme is used. For the explicit coded signaling scheme, 7 identifying bits, which contain the source and relay nodes identities, are coded and added to the data sequence of length JN . The destination node decodes and detects received packets to recover the nodes identities. We use cyclic codes C(12, 4) and C(9, 3) to encode respectively the source and the relay nodes identifying bits. For the the explicit scheme, the increase of J has no effect on the error identification rate performance. When the BPSK modulation is used, the identification error rate performance of our proposed identification scheme is better than that of the explicit coded signaling scheme. When the QPSK modulation is used, our proposed identification scheme has slightly worse performance than the explicit signaling scheme for small values of J and has a better performance than the explicit coded signaling scheme for high values of J in terms of identification error rate. Obviously, our proposed identification scheme offers also better performance in terms of throughput and energy efficiency since it does not add additional identifying bits to the data sequence. Figure 3 illustrates the identification error rate performance of our proposed identification scheme when relay nodes are selected using the ORS scheme. The figure compares the performance of the proposed identification scheme for different codes and for different numbers of sub-blocks J. The phase ϕuv is perfectly known by D. The QPSK is used (q = 2). We consider a wireless system consisting of NS = 16 sources and NR = 4 relays for J ∈ {10, 20, 50} (pink curves). For the identification scheme, we use the BCH code C(31, 6). Hence, N = 31 and K = KS + KR = 6 where KS = log2 (NS ) = 4
and KR = log2 (NR ) = 2. We also consider a wireless system consisting of NS = 16 sources and NR = 8 relays for J ∈ {2, 5, 10} (blue curves). For the identification scheme, we use the BCH code C(63, 7). Clearly, using a more performant code, for the same value of J, (J = 10), enhances the nodes identification performance. We remark that identification link performance enhances significantly when the ORS scheme is used to select relay nodes compared to the results obtained in figure 2 for the PRS scheme since the ORS scheme selects the best relay based on the quality of the totality of the link. Figure 4 shows the identification error rate performance of the proposed identification scheme compared to the hierarchical identification scheme proposed in [11] for different numbers of sub-blocks J. For both schemes, the PRS scheme is used to select the relay nodes. The phase ϕuv is perfectly known by D. We consider a wireless system consisting of NS = 8 sources and NR = 8 relays. For the proposed identification scheme (blue curves), we use the BCH code C(31, 6). Hence, N = 31 and K = KS + KR = 6 where KS = log2 (NS ) = 3 and KR = log2 (NR ) = 3. The BPSK is used (q = 1). For the hierarchical identification scheme (pink curves), we use the cyclic code C(15, 3) twice to identify the source and the relay nodes respectively. Then, N = 15, KS = log2 (NS ) = 3 and KR = log2 (NR ) = 3. For the hierarchical identification scheme, source and relay nodes use different precoded alphabets. Thus, at source nodes, the BPSK is used to modulate data sequences, i.e, q = 1 and at relay nodes, the precoded alphabet q˜ is set to 2. The destination identifies, in the first step, the relay node by raising the received sequence to the power 2q˜ = 4 and identifies, in the second step, the source node by raising the received sequence to the power 2q = 2. To have comparable level of complexity, codes used in the proposed identification scheme and the hierarchical identification scheme have roughly the same rate. Also, we use J ∈ {10, 50} for the proposed identification scheme and J ∈ {20, 100} for the hierarchical identification scheme to have the same length of block JN . Clearly, the proposed identification scheme, achieves better performance than the hierarchical scheme due to the rise of the received noise to the power 4 at the relay node identification step for the hierarchical scheme. The performance is obtained with a cost of additional complexity in the correlation computation process since the number of correlation is equal to (NS NR ) for the proposed scheme compared to (NS + NR ) for the hierarchical scheme. Figure 5 illustrates the identification error rate performance of the proposed identification scheme in the case where the phase ϕuv is perfectly known by the destination D (solid curves) and in the case where the phase ϕuv is estimated by D using the blind phase estimation proposed in the section IV (dotted curves). We consider a wireless system consisting of NS = 16 sources and NR = 4 relays for J ∈ {2, 5, 20}. For the identification scheme, we use the BCH code C(63, 7). The BCH code generates opposite codewords, so the last bit in the identification sequence is not considered. Hence, K = KS + KR + 1 = 7 where KS = log2 (NS ) = 4 and
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Fig. 2: Link identification error rate performance of the proposed identification scheme using the PRS scheme, BPSK modulation (q = 1) and QPSK modulation (q = 2) for different numbers of sub-blocks compared to the explicit coded signaling scheme.
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Fig. 4: Identification error rate performance of the proposed identification scheme using the PRS scheme and BPSK modulation (q = 1) for different numbers of sub-blocks compared to the hierarchical identification scheme.
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Fig. 3: Link identification error rate performance of the proposed identification scheme using the ORS scheme and QPSK modulation (q = 2) for different numbers of sub-blocks and different codes.
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KR = log2 (NR ) = 2. The PRS scheme is used to select the relay nodes. The BPSK modulation is used. We remark that obtained performance when the phase estimation is used is close to that obtained when the phase is known by the destination. The precision is improved when J increases.
0
Fig. 5: Identification error rate performance of the case where the phase ϕuv is perfectly known by D (solid curves) and the case where the phase ϕuv is estimated (dashed curves) using the PRS scheme and BPSK modulation (q = 1) for different numbers of sub-blocks.
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VI. C ONCLUSION In this paper, we proposed a powerful blind embedded identification signaling scheme for multi-source multi-relay wireless systems. Source and relay nodes use precoded sequences with the same precoding alphabet and the destination node performs a soft decoding of received signals to identify in one step the source and the relay identities without exchanging explicit signaling information nor adding signaling bits. A blind phase estimation was also proposed. Simulation results illustrated the good performance of our proposed identification scheme compared to that of the explicit coded signaling scheme and compared to that of the hierarchical identification scheme. The accuracy of the blind phase estimation is also confirmed. R EFERENCES
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