Phase Shift Adjustable Pilots for Channel Acquisition in Vehicle-to-Vehicle Underlay Wideband Massive MIMO

Decrease of the pilot overhead is an important issue in vehicle-to-vehicle (V2V) underlay wideband massive multiple-input multiple-output (mMIMO) communication. To reduce the pilot overhead for channel acquisition, we propose phase shift adjustable pilots (PSAPs) for V2V underlay wideband mMIMO systems employing orthogonal frequency division multiplexing (OFDM). Motivated by the sparse property of the angle-delay (AD) domain channels in mMIMO, we first investigate channel acquisition for V2V underlay mMIMO-OFDM with PSAPs, and derive the optimal conditions to achieve the sum mean square error (sMSE) minimums of channel estimation and channel prediction, respectively. The optimal conditions indicate that the minimum sMSE can be achieved when the AD domain channel power spectra of cellular users (CUs) and transmitters in V2V communication pairs are non-overlapping after appropriate allocation of the available pilot phase shifts. Then an AD domain channel power spectrum based pilot allocation (ADCPS-PA)algorithm is developed according to the optimal conditions. Simulation results indicate that the achievable spectral efficiency for both cellular and V2V links can be significantly improved with PSAPs compared with that obtained by the conventional phase shift orthogonal pilot approach.


I. INTRODUCTION
With the arrival of 5G wireless communication, vehicleto-vehicle (V2V) communication has gained significant research interest for its potential in intelligent automotive and transportation industries. Compared to the vehicular communication introduced by 802.11p, the cellular based vehicleto-everything proposed by 3GPP can achieve lower latency, higher data rates, and longer transmission ranges [1]. In cellular based V2V communication, spectrum can be shared by means of the overlay or underlay schemes among cellular and V2V users [2]. In the overlay scheme, separate frequency bands are allocated to V2V and cellular transmission, which protects cellular users (CUs) but may decrease the spectral efficiency in some cases. Whereas in the underlay The associate editor coordinating the review of this manuscript and approving it for publication was Christoph Studer . scheme, all the users in cellular and V2V links can use the same spectrum resources in the mean while, which improves the spectrum utilization. Because of the growing demand for high data rates, massive multiple-input multiple-output (mMIMO), which can provide high efficiency in spectral and energy utilization, is envisioned as an attractive technology for future V2V communication [3]. Particularly, it has been suggested that V2V underlay mMIMO transmission is one of the promising technologies for future 5G communication networks [4], [5].
Orthogonal frequency division multiplexing (OFDM) is suited for wideband mMIMO communication, and channel acquisition plays an important role in mMIMO-OFDM systems. In the conventional orthogonal pilot approach to acquire channel state information (CSI), the channel response is estimated in the delay domain and the phase shifts of pilots for different transmit antennas need to satisfy the VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ orthogonality condition [6]. However, such phase shift orthogonal pilots (PSOPs) do not take the pilot overhead issue into consideration. Note that due to high mobility and fast V2V channel fading, channel acquisition might need to be performed more frequently in V2V underlay mMIMO-OFDM transmission, which leads to more pilot overhead and reduced system performance. Thus, the pilot overhead is considered as one of the bottlenecks in practical V2V underlay mMIMO-OFDM systems.
To decrease the pilot overhead, non-orthogonal pilots have obtained much research interest in recent years. [7]- [9] investigate non-orthogonal pilot approaches in the simple cellular user scenarios, based on the channel sparsity in the angle domain. [10] proposes a strategy where orthogonal pilots are assigned to cellular users while V2V links reuse another set of pilots. Further more, [11] and [12] expand pilot reuse to all the cellular and V2V users over the frequency-flat channels.
In this work, phase shift adjustable pilots (PSAPs) are proposed for V2V underlay mMIMO-OFDM transmission. Unlike conventional PSOPs, the phase shifts of different pilots in our proposed approach are adjustable and can be less than the maximum channel delay. Thus, more available pilots can be utilized to serve the increasing users, and significant reduction for the pilot overhead can be achieved. Based on the angle-delay (AD) domain channel sparsity [8], we first investigate channel acquisition for V2V underlay mMIMO-OFDM with PSAPs, and derive the optimal conditions under which the sum mean square error (sMSE) for channel estimation (CE) and channel prediction (CP) can be minimized, respectively. The optimal conditions indicate that the minimum sMSE can be achieved when the AD domain channel power spectra (CPS) of different CUs and transmitters in V2V communication pairs become non-overlapping with proper pilot phase shift allocation. Then an AD domain CPS based pilot allocation (ADCPS-PA) algorithm is developed based on the optimal conditions. Simulations show that the proposed PSAP approach can dramatically improve the spectral efficiency performance for both CUs and V2V links, compared with the conventional PSOP approach.
Notations and acronyms used throughout this paper and their explanations are detailed in Table 1 and Table 2, respectively.
respectively. Assume that the temporal correlations and joint spacefrequency (SF) domain correlations for the channels can be separated, and channels with different incidence angles, delays, and Doppler frequencies are uncorrelated, then we can obtain the following channel statistical property [8] E vec G xb where H xb k, ∈ C M ×N g and H xv k,d, ∈ C N d ×N g are the corresponding AD domain channel response matrices (ADCRMs) at the th OFDM symbol. Then when M , N d → ∞, we have the following statistical property [8] E H xb for x ∈ {c, v}. Similarly, the corresponding extended ADCPMs are defined as respectively.

III. CHANNEL ESTIMATION WITH PSAPs
We propose PSAPs for V2V underlay mMIMO-OFDM and investigate the CE performance with PSAPs in this section. Assume that pilot signals are simultaneously sent from all the CUs and VTxs over the th OFDM symbol, then the received signals at the BS and the dth VRx in the SF domain can be represented by where 203796 VOLUME 8, 2020 are the additive white Gaussian noise (AWGN) matrices with elements identically and independently distributed (i.i.d.) as CN (0, σ z ), and σ z denotes the noise power. The proposed PSAP for a given CU or VTx i is shown by where X is an arbitrary diagonal matrix satisfying XX H = I N c , and σ t denotes the pilot signal transmit power. Define D φ k diag f N c ,φ k , and we can obtain from (9) that, for which indicates that only the phase shift differences between different users have influence on the corresponding cross correlations of the proposed PSAPs. After decorrelating the received signals, the power normalized observation obtained at the BS for the channel H cb k, of the kth CU is given by (11), as shown at the bottom of the previous page, where (a) derives from (4) and (10), (b) derives from the unitary transformation property, elements in the normalized AWGN matrix Z iid k ∈ C M ×N g are distributed as CN (0, 1), and the term PI means pilot interference. Similarly, the dth VRx can obtain the corresponding observation for the dth VTx shown by (12), as shown at the bottom of the previous page.
The PI from CUs defined in (11) satisfies where (a) derives from (6), and (b) derives from the definition of the permutation matrix n N . From (13), we can see that can be obtained by implementing φ k − φ k cyclic column shift and then the first N g column truncation to the extended ADCRMH cb k , . Recalling (5), it is readily shown that elements of H cb,φ k −φ k k , are statistically uncorrelated. Thus, we have the following definition which represents the corresponding power matrix of H and can be obtained by implementing the same cyclic column shift and column truncation to the extended ADCPM¯ (11) and (12) and their corresponding power matrices satisfy similar expressions as in (13) and (14).
From (5), it can be known that elements of the AD domain channel are uncorrelated. Thus we can obtain the MMSE estimates at the BS for CU k and at the dth VRx for VTx d in an element-wise manner, which are given by (15), as shown at the bottom of the page, and the corresponding MSEs are shown in (16) and (17), as shown at the bottom of the page.
Define the sMSE of all the CUs at the BS and the sMSE of all the VTxs at the corresponding VRxs for CE as b,CE VOLUME 8, 2020 Then in the following proposition, we derive the optimal condition under which the sMSEs defined in (18) can both be minimized. Proposition 1: The sMSE b,CE can be minimized as and the corresponding optimal condition is that for ∀k = k ∈ K and ∀d ∈ V Tx , In addition, the sMSE v,CE can be minimized as and the corresponding optimal condition is that for ∀d = d ∈ V Tx and ∀k ∈ K, The physical explanation of Propsition 1 is that the PI among users can be eliminated when the non-overlapping property for the equivalent AD domain channel power spectra of different CUs and VTxs are satisfied after proper pilot phase shift allocation, and thus the optimal sMSE performance can be achieved. Note that wireless channels in many practical propagation scenarios satisfy the sparse property in the AD domain [13]- [15], which suggests that the proposed approach is feasible for V2V underlay mMIMO-OFDM. Thus, in our proposed approach, the phase shifts for different pilots are adjustable and pilots with the same pilot shift can even be allocated to different users, leading to more available pilots.

IV. CHANNEL PREDICTION WITH PSAPs
Taking into account the high mobility scenario and the fast V2V channel fading, it might be improper to directly utilize the channel estimates of the pilot segment for the transmission during the data segment. In this section, CP based on the PSAPs is investigated for the data segment in V2V underlay mMIMO-OFDM.
With the statistical property of the ADCRM given in (5) (23), as shown at the bottom of the next page. From (23) and (15), it can be easily obtained that From (24), we can immediately obtain the channel estimates in the data segment via the corresponding channel TCFs and the channel estimates of the pilot segment, which reduces the complexity of CP. Similar to (18), the sMSE of CP for a given delay is defined as in (25), as shown at the bottom of the next page. In the following proposition, we will show that the PI affects among users can still be eliminated with the pilot phase shifts properly allocated.
Proposition 2: The sMSE b,CP ( ) ∀ can be minimized as and the corresponding optimal condition is that for ∀k = k ∈ K and ∀d ∈ V Tx , In addition, the sMSE v,CP ( ) ∀ can be minimized as and the corresponding optimal condition is that for ∀d = d ∈ V Tx and ∀k ∈ K, Proof: The proof is similar to that of Propsition 1, and is omitted for brevity. Propsition 2 shows that the optimal pilot phase shift allocation condition for CE is still applicable to CP, which indicates that the optimal performance of CE and CP can be achieved simultaneously with proper pilot allocation.

V. PILOT PHASE SHIFT ALLOCATION
Note that the optimal condition (20) and (22) cannot always be satisfied in practice, especially at the same time, which means the importance of proper pilot allocation. Considering the high computational complexity of the exhaustive search, we develop an ADCPS-PA algorithm combining the two optimal conditions in this section.
We first define some functions which represent the PI degree between two arbitrary transmitters in K ∪ V Tx for channel acquisition at the BS or some VRx as follows where k, k ∈ K, d, d ∈ V Tx , m ∈ V Rx . Then we define a degree of relevance between two given transmitter sets A and B as where both A and B can contain CUs and VTxs. It is obvious that for transmitters in A and B, the value of DR (A, B) depends on the overlapping degree of their equivalent AD domain channel power spectra and lower overlapping degree leads to smaller DR (A, B). When their equivalent channel power distributions are non-overlapping, DR (A, B) = 0 and the PI between the two transmitter sets is eliminated.
With the definitions presented above, the ADCPS-PA algorithm is displayed in Algorithm 1. The output of Algorithm 1 is the pilot phase shift pattern, which is defined as The threshold γ is preset to balance the algorithm complexity and the performance of channel acquisition, where smaller γ leads to better channel acquisition performance but higher algorithm complexity. T sch denotes the user set in which users have been allocated pilot phase shifts after proper scheduling, and T un denotes the user set in which users have not been allocated pilot phase shifts.

VI. SIMULATION RESULTS
In this section, we show the simulation results and analyze the channel acquisition performance with the proposed PSAPs in V2V underlay mMIMO-OFDM transmission. Note that the approximations in (3) are tight enough with a relatively large and practically feasible number of antennas (64 to 512), b,CP ( ) Algorithm 1 AD Domain Channel Power Spectrum Based Pilot Allocation (ADCPS-PA) Algorithm For i ∈ T un , find a phase shift φ from the available phase shifts 0, 1, . . . in sequence which firstly satisfies DR {i}, T sch ≤ γ

4:
If φ cannot be obtained via step 3, then φ = arg min DR {i}, T sch 5: which has been widely adopted in previous works such as [8], [12], [16]. Assume that a ULA with half wavelength spacing antennas is considered at the BS and the VRxs, and the major parameters for the V2V underlay mMIMO-OFDM are set as follows: M = 128, N d = 64, K = D = 21, N c = 2048, N g = 144, T s = 32.6 ns, and the system bandwidth is 20 MHz.
With the above settings, the OFDM symbol length of the pilot segment for the conventional PSOP approach is given by (K + D)N g /N c = 3 [17]. Meanwhile, the pilot length for the proposed PSAP approach is set as 1 symbol. Assume that a frame consists of 7 OFDM symbols, where the first part is set to be the pilot segment and the following symbols are utilized for the uplink data segment and the downlink data segment, both occupying half of the data segment.
We consider channels with an exponential power delay profile and a Laplacian power angle spectrum in each tap [8]. Assume that uniform distributions are employed for the mean angles of arrival and the locations of all the CUs and VTxs. The large-scale fading coefficient can be obtained by β = d −α for all links, where d is the distance between the transmitter and the receiver and α denotes the path-loss propagation exponent. Set β xb i = 120 −4.37 and β xv i,d = 50 −3.76 for x ∈ {c, v}, i ∈ K ∪ V Tx , and d ∈ V Rx . Assume that the transmit power during the pilot segment and the data segment are equal, and the noise power is set as −105 dBm.
Assume that the Doppler, delay, and angle spread are same for all the CUs and VTxs. Two typical mobility scenarios are considered: urban macro (UMa) scenario (doppler is 1.4 × 10 −2 , delay spread is 1.85 µs, angle spread is 2 • , velocity is 100 km/h), and urban micro (UMi) scenario (doppler is 6.6 × 10 −3 , delay spread is 0.62 µs, angle spread is 10 • , velocity is 50 km/h). Besides, Algorithm 1 is adopted to perform pilot allocation and the threshold is set as γ = 10 −7 in the simulations.  In Fig. 2, we plot the sMSE performance in pilot segment obtained by the proposed PSAPs and the conventional PSOPs under UMa and UMi scenarios. It can be observed that for both cellular and V2V links, CE performance with the PSAPs is comparable to that obtained by the PSOP approach in both the considered scenarios, while the pilot overhead is decreased by 66.7%. Fig. 3 and Fig. 4 present the sMSE performance during data segment versus the delay between the data symbol and pilot segment with σ t = −30 dBm under UMa scenario and UMi scenario, respectively. We can see that CP achieves better performance than CE with PSAPs, especially when the delay increases. Besides, there is not much difference between the CP performance obtained via the PSAPs and the PSOPs in both scenarios, whereas pilot overhead for PSAPs is only 33.7% of that for PSOPs.
Consider an MMSE receiver for the uplink data segment and an MMSE precoder for the downlink data segment. In Fig. 5, we compare the achievable spectral efficiency with  PSAPs and PSOPs under the UMa scenario and the UMi scenario. From Fig. 5, we can see that the spectral efficiency performances are dramatically improved with PSAPs for both cellular and V2V links, compared with those obtained by the conventional PSOPs. Note that the performance boost is more significant at high transmit power where the PI is dominant and high mobility where the pilot overhead is dominant. Especially, with a transmit power of −15 dBm, the proposed PSAP approach provides about 37.7 % and 22.6 % achievable spectral efficiency increase for the cellular and V2V communications respectively over the conventional PSOP approach under the UMi scenario, whereas the performance gains are about 51.6 % and 30.3 % for the cellular and V2V links respectively under the UMa scenario with the same transmit power.

VII. CONCLUSION
In this paper, PSAPs were proposed for the channel acquisition in V2V underlay mMIMO-OFDM communication for the pilot overhead reduction and the spectral efficiency improvement. According to the channel sparse property in the AD domain, We investigated channel estimation in the pilot segment and channel prediction in the data segment with the proposed PSAPs, and derived the optimal conditions to achieve the minimum sMSEs. Then according to the optimal conditions, we developed an ADCPS-PA algorithm. Simulation results showed that significantly enhanced spectral efficiency can be obtained by the proposed PSAPs compared with the PSOPs for both CUs and V2V communication pairs.

APPENDIX A PROOF OF PROPSITION 1
Based on the definition for cb,φ k −φ k k and vb,φ d −φ k d , we can know that the elements of these matrices are all non-negative. Thus, the minimum value of b,CE can be readily obtained as shown in (32) at the top of the next page.
If the condition ¯ cb = 0 is met, after performing the same column permutation and column truncation for these matrices, it is obvious that Obviously the permutation matrix satisfies the following property Then from (14) and (34), we can see that and similarly, Thus, the condition in (33) is equivalent to Then for ∀k = k ∈ K and ∀d ∈ V Tx , (38), as shown at the top of the next page, can be obtained, leading to (39), as shown at the top of the next page. Substituting (39) to (16), we get i.e., the minimum of the sMSE b,CE is achieved.