# Distributed Transmit Beamforming without Phase Feedback

- Chen Wang
^{1}Email author, - Qinye Yin
^{1}, - Jingjing Zhang
^{1}, - Bo Hao
^{1}and - Wei Li
^{1}

**2010**:270894

https://doi.org/10.1155/2010/270894

© ChenWang et al. 2010

**Received: **30 October 2009

**Accepted: **30 March 2010

**Published: **10 May 2010

## Abstract

Phase feedback and adjustment between wireless nodes greatly reduce the power efficiency of distributed beamforming. In this paper, we propose a distributed transmit beamforming method without any phase feedback between nodes. The concept of our approach is to have the received signals retrace their ways, so that the phase offset of the forward path compensates that of the backward path; as a result, signals from different nodes in-phase combine at the destination. Therefore, the received power or the communication range is increased. In order to implement the concept of "retracement", we also propose a transceiver prototype which is based on the Direct Digital Synthesis technique. Experimental and simulation results validate the effectiveness of our approach.

## Keywords

## 1. Introduction

Although distributed beamforming promises many advantages, it faces many practical challenges too. The first challenge is the frequency synchronization between nodes [5]. The traditional SAS does not suffer from this problem because all antennas share a common local oscillator, so the signals are coherent in nature. However, in distributed beamforming system, nodes have their independent oscillators; so there are frequency offsets between them. In order to synchronize the frequency, one node (e.g., destination) broadcasts a high-power reference signal to each source node and source node adjusts its frequency of oscillator to that of [6–8]. Second, phase synchronization is also needed so that the signals are constructively combined at the destination, or they will cancel out each other. It should be noted that our phase synchronization means that signals have the same phase at the destination, not at the sources. The work in [9] divides the phase synchronization methods into closed-loop and open-loop approaches, which either synchronize the phases of nodes one by one [10] or adjust the phases of all nodes simultaneously [11, 12]. However, they all require the feed back of phase adjustment information from a certain node. The work in [13] proposes a scheme that does not require any phase precompensation. Instead, the destination node broadcasts a node selection vector to the pool of available source nodes to opportunistically select a subset of nodes whose transmitting signals combine in a quasi-in-phase manner at the destination. However, this node selection vector is also a feedback. Moreover, the energy on all the nodes cannot be fully exploited because it only selects a subset of available nodes. In one word, the feedback procedure decreases the efficiency of distributed beamforming.

This paper proposes a distributed transmit beamforming scheme which eliminates the inefficient feedback procedure. It utilizes the reciprocity of the signal propagation in space. By reversing the transmit sequence, the transmitting signals of the collaborative nodes "retrace their ways", and the phase shifts from the forward and backward path are automatically cancelled out so that they are in-phase combined at the destination. The collaborative nodes synchronize to the reference signal simultaneously and independently. The complexity of the network does not increase with the number of collaborative nodes, which fits the massively deployed WSNs.

The rest of the paper is organized as follows. Section 2 describes the system model for distributed beamforming. Then, we introduce our proposed beamforming method with discussion on the implementation aspect in Section 3. Section 4 simulates the influence of frequency and phase synchronization errors on performance. A hardware experiment is described in Section 5, which demonstrates the validity of distributed beamforming. Finally, the conclusions are given in Section 6.

## 2. Models and Main Assumptions

### 2.1. Network Structure

Nodes in the system are classified into two kinds: source node and destination node. A source node is typically characterized by low-cost, small size, resource-constrained, power limited, and so forth, while a destination node usually has more resources, adequate power supply, and higher transmission power so that all the source nodes could receive its signal. In WSNs, the wireless sensor nodes (source nodes) usually need to send their gathered messages to the data sink node; so the destination is also referred to as the sink node. Source collects data and transmits them back to the destination for further data analysis. However, a single source node constrained by node transmit power cannot directly send the information back to the destination node by single-hop. In this case, the source nodes perform distributed beamforming at the distant destination, making the signals in-phase combined there so that information is delivered by just one hop.

### 2.2. Signal Model

Distributed beamforming at the destination node is to make the transmitting signals of multiple nodes have the same phase at the destination, that is, in-phase combination.

## 3. Beamforming without Phase Feedback

### 3.1. Synchronization Time Slot

where and are channel gain and propagation delay between the source and the destination, respectively.

There are many ways for frequency and phase synchronization. Readers may refer to [14, 15], and so forth.

### 3.2. Beamforming Time Slot

So transmitted signals in-phase combine at the destination node, and the received amplitude is the summation of the amplitudes of nodes.

Compared with a single-node case, there is an enhancement of in received power.

Note that for non-LOS environment, as long as the backward propagation environment is consistent with the forward one, the above method can also result in in-phase combination at the destination. Theoretically, the scheme of the proposed method is feasible if the synchronization process can catch up with the change of wireless channels. As far as our following experiment concerns, we just carried out experiments in static environment.

### 3.3. Discussion on Design and Implementation of Source Node

## 4. Simulations

which indicates that the amplitude of the received signal is no longer the sum of signals' amplitudes. The following simulation shows the effect of frequency and phase error on beamforming performance.

### 4.1. Effect of Phase Error on Performance

It shows that transmit signals do not completely in-phase combine at the destination node, which reduces the amplitude of the received signal.

As is shown in Figure 5, the average received power increases with node number. However, it is not proportional to , because of the existence of phase error. With the phase error increasing, the average of the received power falls while its variance rises. Nevertheless, we note that the beamforming is not sensitive to phase error; when the variance of phase error is 40 degree, the received power could still reach 60% of the ideal value.

### 4.2. Effect of Frequency Error on Performance

According to Figure 6, decreases as frequency offset increases. Besides, the number of nodes also affects . When the number of sensors is small , falls rapidly as increases. does not change greatly any more with for . When the standard deviation of frequency errors among sensors is 100 Hz, is millisecond order of magnitude, which satisfies the demands of most of the communication protocols (e.g., the longest packet duration is 4.256 ms for IEEE 802.15.4).

## 5. Hardware Experiment

### 5.1. Verification of Coherent Transmission Using Independent Wireless Nodes

### 5.2. Experiment of the Proposed Method

Ideally, the maximum beamforming power of Source no. 1 and no. 2 can be 266.55 mV, while the actual measured result is 251.47 mV. The beamforming efficiency is 94.3% (equivalent beamforming gain is 5.5 dB with 6 dB for ideal situation) compared with the experiment result of beamforming efficiency 90.3% (5.1 dB beamforming gain) in [9].

## 6. Conclusion

In this paper, we present a distributed transmit beamforming method, whose most distinct characteristic is to make the signals "retrace their ways to the destination". Consequently, it avoids the complicated feedback adjustment process. In addition, the simulation shows that an increase in the number of collaborative nodes, the phase error, or the frequency synchronization error results in decrease of the beamforming efficiency. Moreover, a transceiver reference prototype based on DDS is introduced, and some hardware experiments based on this architecture have been conducted. Experiment result shows the feasibility of coherent transmission among independent wireless nodes. In the case of two nodes beamforming using the proposed method, the received signal power achieves 92% of its ideal value, which is 5.3 dB higher compared with signal node transmission.

## Declarations

### Acknowledgments

This work is supported in part by the National Natural Science Foundation of China (NSFC) under Grant no. 60772095 and the Funds for Creative Research Groups of China under Grant no. 60921003.

## Authors’ Affiliations

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