Error Control on Mobile Station Sides in Collaborative Multiple-Input Multiple-Output Systems

Collaboration on mobile station (MS) sides considerably improves signal detection performance, especially for multiple-input multiple-output (MIMO) transmission systems. In this study, a novel detector collaboration system is proposed to reduce the traffic volume on inter-MS collaboration links. Multiple MSs in the immediate vicinity are used to collaboratively decode the MIMO signals received from a base station. Furthermore, we consider a distributed detection system, in which multiple detection MSs decode the MIMO signals independently. Multiple decision results are exploited to improve the error performance. Residual interference coefficients were used to finalize the decision results. The error ratio performance and the traffic volume over collaboration wireless links were compared with those of two combining schemes through computer simulations and field experiments. The results revealed that the proposed error control scheme on mobile station sides offers a better tradeoff between the error performance and the traffic volume on the collaboration wireless links.


I. INTRODUCTION
C OLLABORATION on a mobile station (MS) sides can considerably improve signal detection performance [1]- [4]. Especially, in multiple-input multiple-output (MIMO) transmission systems, the increased number of antennas on the MS side can be used to enhance the channel capacity [5] and detection performance [6], [7]. In collaborative MIMO detection systems, collaborative MS groups that consists of MSs in the immediate vicinity are formed to collaboratively decode the MIMO signals transmitted from a base station (BS).
We focus on physical-layer collaboration to improve transmission performance from the BS to the collaborative MS group. An MS in the collaborative MS group forwards the signal waveform received from the BS to an MS in charge of detection (detection MS). In this scenario, the number of receive antennas on the MS side is considerably higher than that of a single MS. Therefore, the channel capacity and detection performance [7], [8] can be enhanced.
Wireless links connecting MSs for collaboration are crucial for this collaborative detection system. Furthermore, the wireless links should be high speed and low latency to provide a physical-layer collaboration of MSs in the group. Thus, a higher-frequency band transmission technology should be preferred (e.g. 5G NR). Increasing the number of MSs in the collaborative MS group offers a superior detection performance [9]. However, more collaboration traffic is incurred in the collaborative wireless links because of the increased number of forwarded waveforms.
The authors in [10] focused on the broadcast of wireless media and proposed distributed detection schemes to improve detection performance with the same number of forwarded waveforms. In these schemes, a neighboring MS (second-detection MS) overhears the forwarded waveforms and then independently decodes the MIMO signals transmitted from the BS. If a unique set of signals is used in each detection MS, the decision results differ. Therefore, MIMO detection performance can be improved by appropriately utilizing the results of multiple detection MSs. Notably, overhearing does not require additional traffic. The traffic volume of the decision result exchange is generally lower than that of waveform forwarding.
In the distributed detection scheme [10], detection MSs independently decodes the MIMO signal streams from the BS. Each detection MS uses the waveforms forwarded by the helper MSs as well as its own received signal from the BS. Thus, distinct sets of MIMO received signals are used in each detection MS, delivering different decision results. This difference can be exploited to improve detection performance. In [10], every detected bit sequence (DBS) was gathered through collaboration links to determine the most reliable DBS for each stream. This scheme always imposes additional traffic on the collaboration wireless links to gather the decision results from other detection MSs.
We improve our prior approach [10] and propose an errorcontrol scheme with reduced collaboration traffic on the MS side. In the proposed scheme, multiple detection MSs are used to enhance detection performance, similar to the approach in [10], while keeping the collaboration traffic volume as small as possible by using on-demand DBS exchange based on reliability information [11]. For simplicity, we assume that one of the detection MSs is a target information sink. The proposed scheme operates as follows: First, a target MS checks the reliabilities of its own DBSs. Provided its own DBS of a stream is of low reliability, the target MS requests a DBS of the stream along with its reliability information from another detection MS. This process is repeated until the DBSs of all detection MSs are examined or the reliability satisfies the criterion. In this study, the error performance is investigated through extensive computer simulations and experimental evaluations.
The major contributions of this paper are as follows: 1) An on-demand reliability-based MS-side error-control scheme that utilizes multiple detection MSs is described.
2) The frame error ratio (FER) performance of the proposed scheme is compared with that of the majority combining (MC) scheme and log-likelihood ratio combining schemes.
3) The FER performance comparison is performed assuming correlated fading channels. 4) The performance advantage of the proposed scheme is demonstrated using the recorded signals of the measurement campaign. This study expanded the results of [11]. The points 2), 3), and 4) presents new results. The remainder of this paper is organized as follows. The system model of the collaborative MIMO systems is described in Section II. Section III introduces an iterative equalization and detection scheme in the frequency domain. The proposed reliability-based MS-side error-control scheme is described in Section IV. Section V presents the computer simulation results. The experimental setup and experimental results are discussed in Section VI. Finally, the conclusions are presented in Section VII.

II. SYSTEM MODEL
A system model of an MS-side error-control scheme in a distributed MIMO detection system is displayed in Fig. 1  In the collaborative MS group, the detection MSs receive the forwarded signals as well as the signal transmitted from the BS. Using these signals, each detection MS independently decoded the MIMO signal streams from the BS. The decision results of each detection MS may differ from those of the other detection MSs because each detection MS received signal for detection. For simplicity, we assumed that the M signal streams are transmitted to a single-detection MS (target MS). Thus, the target MS is an information sink, and d decision results are available in the collaborative MS group. To take advantage of the multiple decision results, the reliability of the decision results is employed as a result selection metric in [10]. We proposed an error-control method on the MS side to reduce the traffic volume over collaboration wireless links. In the proposed technique, the target MS requests results from another detection MS when the target MS finds that: the reliability of the current results is not satisfactory.

A. ITERATIVE MIMO DETECTION IN THE FREQUENCY DOMAIN
The frequency-domain (FD) iterative MIMO detection scheme is illustrated in Fig. 2. This detection scheme iteratively decodes single-carrier MIMO signals using FD soft cancellation followed by a minimum mean-squared error (MMSE) filter [12], [13]. In this detector, the L = h + 1 received signals available at the detection MSs, namely the own received signals and the h signals forwarded from the helper MSs, are used. The iterative detection scheme includes three processes: i) Interference (other streams) cancellation using soft replicas (after the first iteration), ii) MMSE-based MIMO signal separation and equalization, and iii) soft decoding with belief propagation (BP).
The received kth where the superscript (.) T denotes the transpose operation, H ∈ C L×M is a channel matrix in which the channel variations are negligible over the K-symbol period, and x(k) ∈ C M ×1 and n(k) ∈ C L×1 are the transmitted symbol vector and additive white Gaussian noise vector, respectively. The FD MIMO received signal vector y(f ) ∈ C L×1 is equalized in the MMSE filters w m (f ) ∈ C L×1 as follows: where superscript (.) H denotes the Hermitian transpose and h i (f ) ∈ C L×1 represents the ith column of the FD channel matrix H(f ). σ 2 is the noise variance, and I L is the L × L identity matrix. The MMSE filter output signalsx(k) ∈ C M ×1 in the time domain (TD) are fed into the BP decoder. In the BP decoder, log-likelihood ratios (LLRs) L(c m,k,i ) are calculated iteratively (inner iteration), where c m,k,i denotes the ith bit of the kth symbol in the mth signal stream.
Provided that quadrature phase-shift keying (QPSK) are generated in an FD soft replica generator as follows: The TD soft-decision symbolsx(k) are converted into FD are given by the following expression: The soft cancellation and MMSE MIMO signal separation and equalization can be expressed as follows: where and w m (f ) ∈ C L×1 is an MMSE filter with residual interference coefficients β m (0 ≤ β m ≤ 1) as presented below [12], [14]: Thus, β m is set to 0 by satisfying all the parity-check equations of the mth stream based on hard decisions on a posterior LLRs. The coefficient β m indicates the average residual symbol interference after cancellation [14]. The aforementioned processes, namely (4)-(8) and soft decoding, are repeated as the outer iteration.

B. EARLY STOPPING
Early stopping (ES) can reduce the computational complexity of iterative signal processing. In [15], it was revealed that the ES can improve the error performance in experimental performance evaluation. In this study, the residual interference coefficients given by (8) are exploited as a stopping metric. The outer iteration ended on satisfying the following inequality. M m=1 β m ≤ε.
The ε is an iteration control threshold. Therefore, ε can be adjusted to reduce the number of outer iterations, resulting in reduced computational complexity.

IV. ERROR-CONTROL SCHEME ON THE MS SIDE A. RESIDUAL INTERFERENCE COEFFICIENTS BASED SELECTION SCHEME
In the proposed MS-side error-control scheme, the decision results of multiple detection MSs were used to improve detection performance. The residual interference coefficient β m was used as reliability information. Because this coefficient is inherent in FD iterative equalization, no increase in computational complexity was observed. The most reliable DBS is determined as the final bit sequence based on β m . The error control on the MS side is performed on each stream independently.
The target MS checks its own residual interference coefficient, β m . If β m is larger than the threshold value β 0 , the target MS sends a request to other detection MSs. The request VOLUME 4, 2016 packet contains β m ∀m to avoid transferring a less reliable DBS. Specifically, the reliability metric of the mth stream in detection MSi is represented by β i,m . When the detection MSi receives the request packet, the detection MSi transfers its own DBS to the target MS if β i,m < β h+1,m holds, and MS(h + 1) is the target MS. The detailed process of this MSside error-control scheme is described in Algorithm 1. The error ratio performance with the collaboration traffic volume were investigated through computer simulations. The BS ecmployed four transmit antennas and transmitted M = 4 independent signal streams. The transmission packet is composed of a 39-symbol long orthogonal training sequence (TS) including a seven-symbol cyclic extension, four-symbol cyclic prefix (CP), and QPSK-modulated data sequence (DATA) of 192 symbols (low-density parity-check code, rate 1/2). The TSs are assigned to the signal streams in a deterministic but arbitrary manner.
In the collaborative group, we have six (h + d = 6) MSs, where several cases of h and d combinations are examined. The frame structure is displayed in Fig. 3. The M transmitted packets from the BS are received by the six MSs. The h helper MSs forwarded the received signals to the d detection MSs. The collaboration wireless links are supposed to be error free for simplicity because the transmission distance of the collaboration wireless links are assumed to be short. The threshold β 0 is assumed to be 0, while the channel matrices are estimated using the least square method. The numbers of outer and inner iterations were three and twelve, respectively.

B. SPATIAL CORRELATION
The effect of spatial correlation in the channel from the BS to the MSs on the error performance was studied. The transmit and receive correlation matrices T = E[H H H] and R = E[HH H ] in the Kronecker model were formed according to the exponential model of [16], where E[·] is the expectation operator. The channel matrix with spatial correlation can be obtained as follows: where G is a pseudo-random L × M matrix whose elements follow an independently and identically distributed (i.i.d.) complex Gaussian process with zero mean and unit variance. The R 1/2 and T 1/2 are positive-semidefine matrices. κ is the trace of R and T . The spatial correlation matrices are given by exponential correlation matrices, where [·] i,j denotes the element in the ith row and the jth column of the matrix, and the parameter ρ is a real number ranging from 0 to 1.

C. TWO COMBINING SCHEMES FOR PERFORMANCE COMPARISON
The performance of the error-control scheme on the MS side with residual interference coefficients was compared with those of two combining schemes, namely an MC scheme [17] and an LLR combining scheme [18]. In the MC scheme, the target MS receives DBSs from other detection MSs, followed by a bit-by-bit majority combination using three DBSs. In the LLR combining scheme, the target MS receives LLR values of all bits from other detection MSs, and then hard decisions are made on the sum of the LLR values.

D. TRAFFIC OVER COLLABORATION LINKS
The traffic volume over the collaboration wireless links is measured in units of DBS (192 bits). The number of transferred DBS (TDBS) is incremented by one when a detection MS transfers a DBS of a single stream to the target MS. The traffic volume of waveform forwarding is measured in TDBS by assuming that the I and Q components of the received signal are quantized in eight bits each. Thus, forwarding a single received packet incurs 16 TDBS. Furthermore, a simple two-bit quantization (the boundaries are −20, 0, 20) is assumed to transfer the LLR values of a packet. Therefore, transferring LLR values of a single stream corresponds to two TDBS.

E. COMPUTER SIMULATION RESULTS
The system that consists of d detection MSs and h helper MSs is denoted as dDethH. The normalized maximum Doppler frequency f D T s was 6.4 × 10 −5 throughout the computer simulations. Figs. 4 and 5 display the average FER performance of the proposed scheme in comparison with two combining schemes LLR and MC. The collaborative group included three detection MSs and three helper MSs (3Det3H, The average FER performance as a function of the average signal-to-noise ratio (SNR)γ over frequency-flat i.i.d. Rayleigh fading channels is displayed in Fig. 4. The average FER performance of a single-detection MS scheme (1Det3H) is also displayed in this figure for comparison purposes. MSside error control is not performed in 1Det3H because a single DBS is available for each stream. The average FER performance of the proposed RIC scheme was considerably improved compared with that of 1Det3H. This result revealed that the RIC scheme can select a superior DBS using the residual interference coefficients. The RIC scheme achieved a better average FER performance than the MC and LLR schemes.
The average FER performance over the frequency-   selective channel is displayed in Fig. 5. As a channel model, a symbol-spaced four-tap i.i.d. Rayleigh fading with a flat power-delay profile is considered. The average FER performance of all schemes considerably improved because of the frequency diversity effects from FD MMSE equalization. The RIC scheme achieves the best FER performance in all schemes. These results reveal that the proposed RIC scheme outperformed the combining schemes in both frequency-flat and frequency-selective fading channels.
The average FER performance of the MS-side errorcontrol schemes that included two detection MSs and four helper MSs (2Det4H) was studied. Fig. 6 illustrates the average FER performance over frequency-flat i.i.d. Rayleigh fading channels. Compared with Fig. 4, the average FER performances of 1Det4H and the LLR scheme were improved because the five received signals were used by FD MMSE equalization. The proposed RIC scheme outperformed 1Det4H and LLR schemes.
Identifying the performance degradation of a multipledetector system in a spatially correlated channel is a critical consideration. The average FER performance over spatially correlated frequency-flat Rayleigh fading channels is presented in Fig. 7). The average SNRγ is 13 dB. This figure reveals the average FER performance of the RIC scheme, two combining schemes, and 1Det in both the h = 3 and h = 4 cases. The performance of the MC scheme is presented for the h = 3 case. As expected, spatial correlation exhibited a negative effect on the average FER performance in both cases. The average FER performance of the RIC scheme was superior to that of 1Det in both cases, even over spatially correlated channels.
Various combinations of d and h are displayed in Figs. ?? and 9. In Figs. ?? and 9, frequency-flat channels withγ = 12 dB, and frequency-selective channels withγ = 8 dB, respectively, were assumed. The vertical axis represents the average FER, and the horizontal axis represents the average TDBS. As observed in both figures, the proposed RIC scheme achieved superior or comparable FER performance to the LLR scheme with the same combination of d and h. The average TDBS of the RIC scheme is always less than that of the LLR scheme. The RIC scheme was superior to the 1Det scheme in terms of the average FER performance of the RIC and 1Det schemes for the same h, whereas the TDBSs were almost the same. The average FER performance and average TDBS of the MC scheme were between those of the 1Det and LLR schemes. Both figures included the performance of the 1Det scheme with five helpers (1Det5H) as a benchmark. 1Det5H performs the best in terms of the average FER performance at the expense of the increased traffic volume.

A. EXPERIMENTAL SETUP
As displayed in Fig. 10, four packets are transmitted simultaneously from the BS to six MSs every 50 ms. The packet included a 15-symbol synchronization word for timing detection, an orthogonal TS, a 15-symbol control block  (CTRL), 4-symbol CP, and a 192-symbol QPSK-modulated data block. The TS and DATA were the same as those used in computer simulation. The data bits were successively drawn from a pseudo-random sequence generator. The symbol rate was 312.5 kilo symbols per second (ksps) because of the bandwidth limitation of the radio license. The frequency and timing synchronizations were managed by 10 MHz signals and 1-pulse-per-second signals of global-positioning-systembased oscillators. The number of outer iterations was controlled by the ES, in which the iteration control threshold ε was 0.01. The noise variance was adjusted to provide the best performance. Table 1 reveals the major parameters of the field measurements.
The carrier frequency and transmission power were 427.2 MHz and 1 W per antenna, respectively. As displayed in Fig. 11, four BS antennas were located 25.5 m above the ground and placed in a 3.8 m × 2.5 m rectangle located on the rooftop of the building on the campus of Kyoto University. The BS antennas were 5.8 dBi omnidirectional in the horizontal plane. Six MS receive antennas were installed on the   Fig. 12. The receiving antennas were a λ/4 omnidirectional monopole antennas.
To record the received signals, the vehicle moved twice (i.e. trial 1 and 2) along the Imadegawa-dori and Shirakawadori streets in Kyoto city, as displayed in Fig. 13.

B. EXPERIMENTAL RESULTS
Fig. 14 illustrates the FER performance averaged over the trials 1 and 2. The horizontal axis is the average TDBS. The number of helper MSs ranged from two to five because six MSs were considered in this measurement. The helper MSs and the detection MSs were selected in the numerical order; for example, MS1 and MS2 are helpers for the two-helper case, and MS1 through MS5 are helpers for the five-helper case. The detection MSs are the rest of the MSs.
As displayed in this figure, the RIC scheme achieved almost the best FER performance among all schemes with the same number of helper MSs h. Furthermore, comparing the RIC scheme and the 1Det scheme with the same number of h revealed that the average TDBS of the RIC scheme was marginally larger than that of the 1Det scheme. This increase in the average TDBS becomes negligible in the low FER region. In contrast to the previous results of the computer simulation, the 1Det5H scheme performance was almost the same as the RIC and LLR schemes of 2Det4H. The cause of this phenomenon requires further investigation.

VII. CONCLUSION
An MS-side error-control scheme that incorporates reliability metrics on a per-stream basis was proposed in this study. To demonstrate the effectiveness of the proposed scheme, the FER performance determined by computer simulations and field experiments were compared with those of two combining schemes. The proposed scheme can effectively improve FER performance by using residual interference coefficients to select better bit sequences. The proposed scheme that considers spatial correlation in fading channels exhibited a similar relationship between FER performance and spatial correlation. Furthermore, the proposed scheme suppressed the collaboration traffic volume by using multiple detection MSs, and the differences in the DBSs of multiple detection MSs are exploited with residual interference coefficients.