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Multi-Input Multi-Output (MIMO) techniques can be used to increase the data rate for a given bit error rate (BER) and transmission power. Due to the small form factor, energy and processing constraints of wireless sensor nodes, a cooperative Virtual MIMO as opposed to True MIMO system architecture is considered more feasible for wireless sensor network (WSN) applications. Virtual MIMO with Vertical-Bell Labs Layered Space-Time (V-BLAST) multiplexing architecture has been recently established to enhance WSN performance. In this paper, we further investigate the impact of different modulation techniques, and analyze for the first time, the performance of a cooperative Virtual MIMO system based on V-BLAST architecture with multi-carrier modulation techniques. Through analytical models and simulations using real hardware and environment settings, both communication and processing energy consumptions, BER, spectral efficiency, and total time delay of multiple cooperative nodes each with single antenna are evaluated. The results show that cooperative Virtual-MIMO with Binary Phase Shift Keying-Wavelet based Orthogonal Frequency Division Multiplexing (BPSK-WOFDM) modulation is a promising solution for future high data-rate and energy-efficient WSNs.

Due to advancement in Micro-Electro-Mechanical Systems (MEMS) technology, low power and low cost WSNs can be deployed in many real life applications, including environmental monitoring, home automation, traffic control, precision agriculture and health care [

MIMO techniques can be used to increase data rate using spatial multiplexing and bit error rate (BER) can be improved by using spatial diversity. MIMO techniques can also be used to improve signal to noise ratio (SNR) at the receiver and to mitigate co-channel interference (CCI) along with beam forming techniques [

In true/co-located MIMO architecture, multiple antennas are connected to a single transmitter/receiver node. This architecture can be used for space division multiplexing (SDM) as well as for space time coding (STC). The signal processing can be done at transmitter and/or receiver side. However, due to small form factor of wireless sensor nodes, limited energy availability, and the need to maintain a minimum distance among the antennas (to avoid fading), it can be difficult to realize the advantages of MIMO techniques for such wireless nodes [

This paper focuses on cooperative virtual MIMO systems based on V-BLAST architecture for WSNs. Specifically, it analyzes the performance of such systems under different modulation techniques, including multi-carrier modulation techniques, which to our knowledge have yet to be investigated in literature for such systems. The modulation techniques considered include Fourier based OFDM (FOFDM), WOFDM, BPSK-FOFDM, BPSK-WOFDM,

The rest of the paper is organized as follows: Section 2 gives an overview of related works on performance evaluation of MIMO systems for WSNs. Section 3 introduces background concepts on cooperative virtual MIMO, V-BLAST, and multi-carrier modulation. In Section 4, the system model of the cooperative virtual MIMO WSN is presented. This is followed by the parametric modeling of performance parameters for virtual MIMO and SISO systems in Section 5. Evaluation results are then presented and discussed in Section 6. Finally, the paper is concluded in Section 7.

In [

A V-BLAST based virtual MIMO WSN with QAM was proposed in [

With the advent of smart antennas for WSNs [

Based on existing studies, cooperative virtual MIMO with V-BLAST detection can be a promising communication architecture for WSNs. Furthermore, the choice of the modulation scheme for use with the architecture is also critical for reliable communication in WSNs. As discussed in [

Multi-carrier modulation techniques such as WOFDM is promising for enabling high data-rate WSNs and which can be implemented with low complexity [

MIMO techniques are capable of providing high system performance without additional transmission power and bandwidth. However, due to the small form factor and limited energy of sensor nodes, it is often not realistic to equip each sensor with multiple antennas to implement MIMO. Instead, a cluster of single-antenna sensor nodes can cooperate to form a virtual antenna array (VAA) to achieve virtual MIMO communication. Virtual MIMO systems are distributed in nature because multiple nodes are placed at different physical locations to cooperate with each other. With proper timing and frequency synchronization between constituent nodes of the VAA, virtual MIMO can realize the advantages of true MIMO techniques for WSNs.

V-BLAST is a spatial multiplexing technique to achieve spectral efficiency for a given bit rate and transmission power. It can boost channel capacity to improve the single-sensor data rate, or increase the number of supported sensors in the system. Its spectral efficiency ranges from 20–40 bps/Hz [_{t}_{t}

FOFDM is a multi-carrier modulation technique in which a high data rate substream is demultiplexed into lower data rate substreams to increase the duration of each substream so that inter-symbol interference (ISI) can be reduced. The orthogonal subcarriers are generated using sine/cosine bases and the orthogonality is achieved in a time window of width equal to the duration of the symbol. Therefore, FOFDM is not band limited. Each subcarrier produces side lobes that in turn create inter-carrier interference (ICI), which can be increased due to multipath channel effect that also cause an increase in ISI. Cyclic prefix (CP)/Guard Interval (GI) is added to each FOFDM symbol to avoid this problem at the cost of transmission efficiency degradation.

WOFDM is another multi-carrier modulation technique with lower computational complexity than FOFDM [^{P}_{k,p}_{(n)} ∈ {_{l}_{(}_{n}_{)}, _{h}_{(}_{n}_{)}} is the filter impulse response corresponding to _{th}_{th}_{l}_{(}_{n}_{)} and _{h}_{(}_{n}_{)} are impulse responses of the low-pass, and high-pass filters respectively, for perfect reconstruction of QMF bank. The high pass filter can be derived from the low pass filter by the relation: _{h}^{n}_{l}

The output _{k}_{th}_{k,p}_{(}_{n}_{)} ∈ {_{l}_{(}_{n}_{)}, _{h}_{(}_{n}_{)}} is the filter impulse response corresponding to _{th}_{th}_{l}_{(}_{n}_{)} and _{h}_{(}_{n}_{)} are time reversals of _{l}_{(}_{n}_{)}, and _{h}_{(}_{n}_{)}, respectively [

From

We consider a wireless communication link between _{t}_{r}

In our system model, we consider V-BLAST signal processing by DGN at the receiving side with the assumption that it can cope with more computational complexity than its DANs. Moreover, no local communication and processing are essential among the DSNs. It is assumed that _{t}_{r}_{r}_{r}_{t}_{r}_{o}_{r}_{t}_{t}_{r}

At each DSN, a serial-to-parallel converter is used to form the input for WOFDM modulator. Every _{th}^{P}_{k}_{r}_{t}_{t}_{t}^{t}^{t}Q^{t}ζ_{th} element of
_{k}^{P}

In [

The total energy consumption in RF section is due to long-haul communication (from DSNs to receiving side DANs and DGN itself) and receiver side local communication (from DANs to DGN). The total average power consumption along the signal path for long-haul can be divided into two main components: power consumption of all power amplifiers
_{b}^{L}_{t}_{r}_{l}_{f}

The power consumption in all circuit blocks for long-haul communication with _{t}_{r}_{DAC}_{mix}_{ftl}_{LO}_{LNA}_{IFA}_{ADC}_{DAC}_{ADC}

Total power consumption in all circuit blocks for long-haul communication with _{t}_{r}_{PS}_{Add}_{b}

_{b}_{t}_{r}^{L}_{bi}_{ti}_{ri}^{l}_{bi}^{l}^{L}_{ti}_{ri}_{r}_{t}

The energy efficiency (EE) can be calculated by taking the inverse of

The number of CPU cycles of a processing block is estimated by using Odyssey prediction model [_{Mod}_{x}) mode, can be calculated by multiplying the estimated number of CPU cycles of the modulation processing block with energy consumption per CPU cycle and dividing it with total number of bits. The energy consumption per bit by CPU during demodulation (_{Dmod}_{Det}_{x}) mode. With _{t}_{r}

The spectral efficiency (SE) of a MIMO system without the knowledge of the channel at the transmitter can be calculated as [_{j}^{H}

The total time delay (_{V}_{–}_{mimo}_{t}_{r}_{tr_MIM0}_{pr_MIMO}_{pc_MIMO}

_{tr_MIMO}_{i}_{n}_{r}_{pr_MIMO}^{L}^{l}

_{pc_MIMO}_{Mod}_{Dmod}_{Det}

For the SISO system, the RF (Analog) energy consumption per bit per node (E_{b_Analog_SISO}) can be calculated by replacing
_{r} = N_{t} = 1 as discussed in Section 5.1.1. The Base Band (Digital) energy consumption per bit per node (E_{b_Digital_SISO}) can be calculated by removing E_{Det} in _{r} = N_{t} = 1.

The total time delay (T_{SISO}) of the SISO system can be calculated as the sum of transmission delay (T_{tr_SISO}), propagation delay (T_{pr_SISO}), and processing delay (T_{pc_SISO}).

_{tr_SISO}_{t}_{pr_SISO}

_{pc_SISO}

Simulations were carried out to investigate BER performance _{b}_{o}

The information source of each DSN generates data at a rate of 250 kbps according to IEEE 802.15.4-2009 standard for WSNs. The typical transmission range of IEEE 802.15.4 based radio transceivers is 10–20 m, with a nominal maximum range of about 100 m in clear line-of-scenarios. Accordingly, the distance ^{L}

At each DSN, information bits are modulated into a symbol stream using 16-DQPSK, 16-QAM, 16-OQPSK, 16-FOFDM, 16-WOFDM, BPSK-16FOFDM, and BPSK-16WOFDM. As in [

^{b}

The RF (Analog) energy consumption per bit per node over a transmission distance ^{L}

In all the simulations, it is assumed _{t}_{r}_{c}_{l}_{f}^{2} = −174 dBm/Hz, _{ti}_{ri}^{l}_{DAC}_{ADC}_{fil}_{LO}_{LNA}_{IFA}_{mix}_{Add}_{PS}

The RF (Analog) energy per bit per node is calculated using

The base band energy consumption per bit per node (_{b_Digital}_{b_Digital}_{Det}_{b_Digital}

_{b_Analog}_{bTotal}_{b_Analog}_{b_Digital}_{b_Digital}^{L}_{b_Digital}_{bTotal}^{L}_{b_Analog}_{b_Digital}^{L}_{b_Digital}_{b_Analog}_{b_Analog}_{b_Total}

As discussed, the base band (digital) energy consumption and RF (analog) energy consumption is the energy consumed by the CPU, and radio transceiver, of the sensor nodes, respectively. We assume that both the CPU and radio transceiver has two active states (Transmit and Receive). For the CPU, the energy consumption in Transmit mode is the base band energy consumed by the digital modulator (hence depends on the modulation type) for processing each bit for transmission. On the other hand, the CPU or processing energy consumption in Receive mode is the base band energy consumed by the digital demodulator and V-BLAST detection algorithm.

The overall energy consumption per bit per node in Transmit mode (_{b_Total_Tx}_{b_Total_Rx}^{L}_{b_Total_Tx}_{Mod}_{b_Analog_Tx}_{b_Total_Rx}_{Dmod}_{Det}_{b_Analog_Rx}_{b_Analog_Tx}_{b_Analog_Rx}

The CPU is also assumed to have two inactive states (Idle and Sleep), which are low power modes during which different functions of the CPU are shutdown to save power. To calculate the CPU energy consumption in these modes, we used the voltage and current values for these modes given in the data sheet of MSP430F1611 (the CPU model of TelosB mote). The CPU energy consumption per second in idle and sleep mode is found to be −39.5860 dBJ, and −56.1618 dBJ, respectively.

For the radio transceiver, we assume that whenever it is not transmitting or receiving, it will be put into sleep, _{b_Analog_Rx}

The time delays involved during the communication are listed in _{tr_MIMO}_{pr_MIMO}^{L}^{L}_{Mod}_{Dmod}_{pc_MIMO}_{tr_MIMO}_{pr_MIMO}_{pc_MIMO}_{V_MIMO}_{pc_MIMO}_{SISO}_{V}_{–}_{MIMO}_{Det}_{pc_MIMO}_{b_Digital}_{pc_MINMO}_{b_Digital}^{−3} J), respectively, while for BPSK-16FOFDM, it is 0.2836 s, and −29.8167dBJ (or 1.0431 × 10^{−3} J), respectively.

The spectral efficiency can be calculated using ^{−1}, 10^{−2}, 10^{−3}, and 10^{−4}. It can be observed from ^{−3} (third data point), BPSK-16WOFDM and BPSK-16FOFDM have a spectral efficiency of 27 bit/sec/Hz at
^{−1}, 10^{−2}, 10^{−3} and 10^{−4}. From the graph, it can be observed that there is a trade-off between EE and SE, where an increase in SE due to higher

This paper analyzes the performance of a cooperative virtual MIMO system using different modulation techniques in the context of WSNs. In terms of BER performance, BPSK-16WOFDM is found to outperform other evaluated modulation techniques by up to 95% for a given
^{L}

Symmetric multistage WOFDM modulator and demodulator. (

Equivalent structure of WOFDM modulator and demodulator using noble identities. (^{P}^{P}

Real and imaginary components of BPSK-16WOFDM, 16WOFDM, BPSK-16FOFDM, and 16FOFDM.

Communication between Transmitting and Receiving side Virtual MIMO nodes.

Transmitter and receiver architecture for WOFDM (analog).

Transmitter and receiver architecture (In-Phase/Quadrature-Phase) for FOFDM, QAM, DQPSK, and OQPSK (analog).

BER performance over transmission distance ^{L}

Total energy per bit per node over transmission distance ^{L}

Energy efficiency ^{L}

Base Band (Digital) Energy Consumption.

_{Mod} |
_{Dmod} |
_{Det} |
_{b_Digital} | |
---|---|---|---|---|

16-DQPSK | −31.7203 | −32.1389 | −30.7033 | −31.2591 |

16-QAM | −31.2628 | −31.9686 | −30.7033 | −30.9803 |

16-OQPSK | −30.8951 | −31.1203 | −30.7033 | −30.4600 |

16-FOFDM | −30.0134 | −30.7192 | −30.7033 | −29.8781 |

16-WOFDM | −31.0294 | −31.7203 | −30.7033 | −30.8009 |

BPSK-16FOFDM | −29.86 | −30.587 | −30.7033 | −29.8167 |

BPSK-16WOFDM | −30.8764 | −31.2681 | −30.7033 | −30.5142 |

SISO-BPSK-16WOFDM | −30.8764 | −31.2681 | −∞ | −31.0678 |

RF (Analog) Energy Consumption and Total Energy Consumption.

_{b_Analog} |
_{b_Total}_{b_Analog}_{b_Digital} | |||||||
---|---|---|---|---|---|---|---|---|

| ||||||||

^{L} |
^{L} |
^{L} |
^{L} |
^{L} |
^{L} |
^{L} |
^{L} | |

16-DQPSK | −29.0354 | −11.4148 | −1.1630 | 6.4758 | −26.9961 | −11.3700 | −1.1587 | 6.4765 |

16-QAM | −29.5144 | −11.8938 | −1.6419 | 5.9967 | −27.1754 | −11.8405 | −1.6369 | 5.99766 |

16-OQPSK | −48.4654 | −30.6948 | −20.6230 | −12.6442 | −30.3918 | −27.5655 | −20.1940 | −12.5729 |

16-FOFDM | −44.0580 | −26.2874 | −16.2156 | −8.2368 | −29.7153 | −24.7115 | −16.0327 | −8.20722 |

16-WOFDM | −46.0988 | −28.4682 | −18.4363 | −10.4776 | −30.6746 | −26.4695 | −18.1914 | −10.4374 |

BPSK-16FOFDM | −50.7654 | −33.2648 | −22.9930 | −15.1242 | −29.7819 | −28.1969 | −22.1730 | −14.9792 |

BPSK-16WOFDM | −52.9461 | −35.2855 | −25.2637 | −17.2949 | −30.4894 | −29.2648 | −24.1293 | −17.09279 |

SISO-BPSK-16WOEDM | −30.402 | −17.285 | −7.263 | 0.705 | −27.7118 | −17.107 | −7.2449 | 1.1769 |

Energy Consumption in Transmit and Receive Modes.

_{x}) Mode |
_{x}) Mode | ||||||
---|---|---|---|---|---|---|---|

| |||||||

_{Mod}per bit per node in dBJ |
_{b_Analog_Tx}per bit per node in dBJ |
_{b_Total_Tx}per bit per node in dBJ |
_{Dmod}per bit per node in dBJ |
_{Det}per bit per node in dBJ |
_{b_Analog_Rx}per bit per node in dBJ |
_{b_Total_Rx}per bit per node in dBJ | |

16-DQPSK | −31.7203 | −36.4958 | −30.4720 | −32.1389 | −30.7033 | −58.7955 | −28.3517 |

16-QAM | −31.2628 | −38.995 | −30.5863 | −31.9686 | −30.7033 | −58.7955 | −28.2797 |

16-OQPSK | −30.8951 | −55.8558 | −30.8813 | −31.1203 | −30.7033 | −58.7955 | −27.8965 |

16-FOFDM | −30.0134 | −53.855 | −29.9955 | −30.7192 | −30.7033 | −58.7955 | −27.7009 |

16-WOFDM | −31.0294 | −56.370999 | −31.0167 | −31.7203 | −30.7033 | −60.3395 | −28.1718 |

BPSK-16FOFDM | −29.86 | −58.1958 | −29.8536 | −30.587 | −30.7033 | −58.7955 | −27.6345 |

BPSK-16WOFDM | −30.8764 | −60.741 | −30.8719 | −31.2681 | −30.7033 | −60.3395 | −27.9662 |

Time Delay.

_{tr_MIMO} |
_{pr_MIMO} |
_{pc_MIMO} |
_{V}_{−}_{MIMO} | ||||||
---|---|---|---|---|---|---|---|---|---|

| |||||||||

^{L} |
^{L} |
_{Mod} |
_{Dmod} |
_{Det} |
_{pc} |
^{L} |
^{L} | ||

16-DQPSK | 1.75 × 10^{−6} |
3.33 × 10^{−8} |
3.33 × 10^{−7} |
0.069230 | 0.06286 | 0.0875 | 0.21959 | 0.21959 | 0.21959 |

16-QAM | 1.75 × 10^{−6} |
3.33 × 10^{−8} |
3.33 × 10^{−7} |
0.076925 | 0.06537 | 0.0875 | 0.2298 | 0.2298 | 0.2298 |

16-OQPSK | 1.75 × 10^{−6} |
3.33 × 10^{−8} |
3.33 × 10^{−7} |
0.083717 | 0.07948 | 0.0875 | 0.25070 | 0.25070 | 0.25070 |

16-FOFDM | 1.75 × 10^{−6} |
3.33 × 10^{−8} |
3.33 × 10^{−7} |
0.102575 | 0.08717 | 0.0875 | 0.27725 | 0.27725 | 0.27725 |

16-WOFDM | 1.75 × 10^{−6} |
3.33 × 10^{−8} |
3.33 × 10^{−7} |
0.0800 | 0.06922 | 0.0875 | 0.236725 | 0.236727 | 0.236727 |

BPSK-16FOFDM | 1.75 × 10^{−6} |
3.33 × 10^{−8} |
3.33 × 10^{−7} |
0.10625 | 0.08987 | 0.0875 | 0.28360 | 0.28360 | 0.28360 |

BPSK-16WOFDM | 1.75 − 10^{−6} |
3.33 × 10^{−8} |
3.33 × 10^{−7} |
0.084075 | 0.07682 | 0.0875 | 0.24840 | 0.24840 | 0.24840 |

| |||||||||

SISO-BPSK-16WOFDM | _{tr_SISO} |
_{pr_SISO} |
_{pc_SISO} |
_{SISO} | |||||

| |||||||||

_{Mod} |
_{Dmod} |
_{pc_SISO} |
|||||||

| |||||||||

1 × l0^{−6} |
3.33 × ^{−8} |
3.33 × ^{−7} |
0.084075 | 0.07682 | 0.160895 | 0.160895 | 0.160895 |