# Designing optimal wireless basestation MIMO antennae: Part 1 – Sorting out the confusion

Embedded developers building today’s wireless network spectrum infrastructure are constantly striving to provide solutions to the growing demand for higher data rates in mobile devices. Given that radio spectrum is limited and expensive, it is vital to discover a better way to utilize the same bandwidth while transmitting even more data – or in other words, to improve the spectral efficiency of the channel.

MIMO (Multiple Input Multiple Output) is one of the leading approaches for improving data rates and/or SNR (signal-to-noise ratio). By using multiple receive and transmit antennas, MIMO can exploit the diversity of the wireless channel. This is then used to increase the spectral efficiency of the channel and improve the data rates for any given channel bandwidth.

The MIMO dimension depends on the number of antennas transmitting and receiving. In a 4X4 MIMO configuration, four transmit antennas and four receive antennas are used. Under the right conditions, this enables transmitting up to four times more data on the same channel bandwidth.

On the one hand, a simple MIMO receiver is based on a linear receiver algorithm, which is easy to implement but cannot fully exploit the MIMO benefits. On the other hand, an optimal MAP (maximum a posteriori) approximation MIMO algorithm can be implemented using an iterative technique; however, this incurs high latency penalties.

A more practical non-linear MIMO receiver implementation known as ML (maximum likelihood) or MLD (maximum likelihood detector) is fundamentally based on an exhaustive constellation search. The MLD is more demanding on processing than a conventional linear receiver, but can offer significantly higher bit rates for the same channel conditions. In addition, the MLD is more robust to channels with antenna correlation.

Working with high-order MIMO dimensions (more than two receive and two transmit antennas) can result in significantly improved spectral efficiency, but this comes at a cost. The computational complexity of the MLD receiver grows exponentially with the increase of the MIMO dimension. High-order MIMO requires considerable processing power – to the point where a straightforward MLD approach is impractical, and suboptimal MLD algorithms must be used to enable user equipment (UE) implementations.

Considering these multiple challenges, this article will first review the relevant MIMO modes and technology and the advantages of choosing a suboptimal MLD receiver over a minimal mean square error (MMSE) receiver. It will also explain the complexities of the MLD implementation and how to resolve them using suboptimal ML solutions.

**Sorting out the various MIMO techniques**

MIMO techniques can be split into three main groups:

- Beam-forming is used to improve the SNR of a given channel
- Transmit and receive diversity is used to improve channel quality or robustness
- Spatial Multiplexing is used to increase data throughput for a given channel

**Beam-forming** utilizes knowledge of the channel at the transmitter to focus the power in the direction of the receiver. Details of the channel can be obtained by receiving feedback from the receiver regarding direction and attenuation properties.

By identifying the direction of the UE, the transmitter can steer a beam in that direction and thus amplify the received signal. This MIMO technique is most effective for low-SNR channels. **Figure 1 ** below describes a directional wave front achieved by timing the phase of the transmit antennas.

**Figure ?1: Tx beam forming****Transmit and receive diversity** creates redundancy by transmitting the same data on multiple antennas and combining the signals received at the destination antennas to increase the robustness for a given channel. This MIMO technique is most effective for low SNR and rich multipath (or scattering) conditions. The diversity can maximize the utilization of the channel by overcoming attenuations at antennas, and make better use of antennas that receive strong signals. Overall, the SNR obtained at each antenna is improved, and this reduces decoding errors at the receiver.

By improving the SNR, it is possible to increase the throughput by switching to a higher modulation (for example: 64QAM instead of 16QAM/QPSK) or increasing the code rate (transmitting less redundant data). However, improving the SNR of the channel has its limits. It has been shown that above a certain point, the throughput gains for each dB of SNR diminishes rapidly. This ‘knee’ point describes the highest modulation and code rate defined by the standard. In order to further increase the throughput, it is necessary to utilized more advanced transmission methods such as space-time blocking coding (**Figure 2** ).

**Figure ?2: STBC throughput peak****Spatial multiplexing** is introduced in order to push the channel throughput to the next level . Spatial multiplexing requires minimal channel conditions to work effectively. This technique takes advantage of rich multipath channels in order to differentiate between the data transmitted on each antenna – this is called a spatial layer.

Rich multipath conditions are generated by the reflections of the transmitted signals from obstacles such as buildings and vehicles in the urban environment. These reflections improve signal separation at the receiver, enabling reconstruction of the data into the layers in which the data was originally transmitted.

The number of possible spatial layers is determined by the number of transmitting and receiving antennas. For a configuration of four transmitting antennas and three receiving antennas, the channel can contain up to three spatial layers min(4Tx, 3Rx). The actual number of layers is determined by the multipath conditions denoted as channel rank.

For the configuration shown in** Figure 1** (4Tx, 3Rx) with line-of-sight conditions and no multipath reflections, the rank would be equal to one, thereby enabling only a single spatial layer of data. As these conditions improve (multipath increases) we can add more spatial layers – or in other words, multiply the rate of transmitted data on the channel.

There is no single MIMO technique that supports all channel conditions. The eNB (base station) must adapt the transmission scheme – depending on the multipath, SNR and mobility – many times per second in order to maximize the throughput for each specific UE.

**MIMO antenna correlation**

An important factor in choosing the MIMO technique is the level of antenna correlation. **Figure ?3** describes a 2X2 MIMO LTE channel (EPA 5Hz conditions) using two transmission schemes in different antenna correlation propagation conditions, either transmit and receive diversity (STBC) or spatial multiplexing (SM).

**Figure ? 3: Antenna correlation effects**As shown in **Figure 3** , for low SNR conditions STBC provides superior results. In high SNR conditions, SM provides close to twice the throughput delivered by STBC (for 2X2 MIMO). The MIMO order defines the throughput gain at high SNR values, a gain of three for 3X3 MIMO, a gain of four for 4X4 MIMO, and so on. The crossing point between the two graphs represents the SNR value at which SM starts exceeding the STBC throughput.

SM is more sensitive to antenna correlation and requires higher SNR values to surpass STBC in high correlation scenarios. Therefore, it is important to choose an SM solution with high immunity to antenna correlation.**Picking the right MIMO receiver implementation **

The UE MIMOreceiver has many possible implementations. Among them, the most commonare linear receivers, which include the zero-forcing (ZF) and minimalmean square error (MMSE) detectors. Another implementation solution is anon-linear receiver based on the maximum likelihood (ML) detector.Assuming the following mathematical baseband signal model, where

*y=Hs+ ρn*

* y * is the vector of the signals sampled at the receiver. The size of this vector corresponds to the number of receive antennas (Nr).

*is the vector of transmitted symbols from multiple antennas. The sizeof this vector corresponds to the number of transmit antennas (Nt).*

**s***is the channel impulse response matrix that describes the channelbetween each transmit antenna and each receive antenna. The dimensionsof this matrix correspond to Nr X Nt.*

**H***is the vector of independent complex valued Gaussian random variables each with variance of*

**Pn**

**ρ**.^{2}Receiverperformance is evaluated using a tool called an error probabilitycurve, which is a graph that plots the channel SNR on the X-axis and theerror rate on the Y-axis. The channel SNR is measured in dB. The errorrate is a logarithmic axis that can have several representations: biterror rate (BER), symbol error rate (SER), or packet error rate (PER).

Thepacket error rate (PER) is the number of incorrectly received datapackets divided by the total number of received packets. A packet isdeclared incorrect if at least one bit is erroneous. For codedcommunications systems, PER is measured including the FEC (forward errorcorrection) decoder.

**Figures 4 and 5** refer to BER – the number of incorrect bits divided by the total amount of transmitted bits.

**Figure 4: Diversity order**Theerror probability curve for MIMO receivers is characterized by two mainparameters: diversity order and array gain. Diversity order (DO) isdefined as the slope of error probability curve at high SNR. The greaterthe DO, the steeper the slope of the error probability curve; higher DOis preferable.

**Figure 5: Array gain****Table 1** describes the DO and AG calculations for three types of receivers using spatial multiplexing.

**Table 1: Spatial multiplexing parameters**Usingthe table above it is simple to calculate a 4X4 MIMO configuration (Nr =4, Nt = 4) transmitting with spatial multiplexing.

Thediversity order for an ML receiver will be 4, equal to the number ofreceive antennas (Nr = 4) compared to a diversity order of 1 for thelinear receivers (Nr – Nt +1 = 4 – 4 + 1 = 1). This indicates a clearadvantage of the ML receiver compared to the linear solution –especially at high SNR values.

The same calculation for arraygain will produce an array gain of 1 for the ML receiver, compared to anarray gain of ¼ for the linear solution. Once again, the ML receiverprovides superior results.

The main benefits of the ML receiversare at high SNR values. Under these conditions, the DO and AG parametersare significantly greater than the linear receivers. On the one hand,this indicates that for low SNR conditions it might be sufficient toimplement a simpler linear receiver or refrain from spatial multiplexingaltogether, and choose a more robust transmission scheme. On the otherhand, for spatial multiplexing with high throughput at adequate SNR, theML receiver is the obvious choice.

It is important to note thatthis article refers to soft-output MIMO solutions as opposed tohard-output solutions. Instead of producing definitive bit solutions of‘one’ or ‘zero’, the soft-output solution consists of a ratio betweenthe probability that a certain bit is ‘one’ and the probability that itis ‘zero’. This ratio is denoted as soft-bit or LLR (log likelihoodratio).

**Using the MIMO turbo mode**

The methods describedabove are called ‘one-shot’ as they complete the processing of theinput signal or tone after a single activation of the detector.

Anotherapproach that aims for MAP performance offers an iterative solutionthat involves a soft symbol detector and an external FEC decoder .

TheFEC decoder is a separate module in the receiver that performs forwarderror correction (FEC). By taking advantage of redundancy introducedinto the transmitted signal, the FEC decoder can detect errors in thereceived bit stream and can often correct these errors without the needfor retransmission.

A turbo-MIMO receiver structure (**Figure 6** )consists of two stages: soft-output symbol detector and FEC decoding.In the first iteration, the symbol detector produces LLR results basedonly on the received input signal. The FEC decoder will then weaken orstrengthen LLRs, in accordance with the coding constraints.

**Figure 6: Turbo MIMO receiver**Subsequently,the symbol detector reiterates taking advantage of the prior knowledgeof the LLRs supplied by the FEC decoder. These two stages iterativelyexchange information transferred from one to the other until thereceiver converges.

The symbol detector may consist of asoft-output ML detector implementation, or alternatively may use asimpler zero-forcing/MMSE detector followed by a soft-symbol de-mapper.

By performing this iterative process, the receiver can surpass the precision of the ML-decoder and obtain lower error rates.

Advantages of this receiver are:

- Very high precision results can be obtained, exceeding the ML solution and approaching maximum a posteriori (MAP) results.
- The symbol detector can be simplified to a linear solution at the expense of more iterations between the detector and the turbo decoder.
- Disadvantages of this receiver are:
- Large data transfers are required between the FEC decoder and the symbol detector; these need to be scheduled and stored in intermediate buffers.
- Latency is increased due to multiple iterations and transfers.
- Throughput is reduced.
- Additional power consumption due to multiple data transfers and iterations.

Next in **Part 2: Implementing a maximum likelihood (ML) receiver**

**Noam Dvoretzki** is a senior DSP processor architect at CEVA. His 12 years of experienceinclude architectures of the CEVA-XC DSP and hardware accelerators for4G wireless communication standards. In addition he has designed DSPs infield of computer vision and HD Audio. His expertise includes RTL andbackend design. He holds a BSc. in Computer and Electrical Engineeringfrom Ben-Gurion University.

**Zeev Kaplan** is a seniorCommunication Algorithms Engineer in the Architecture Department inCEVA. He has over 12 years of experience in communications engineeringwith expertise in algorithms and systems design. Other expertiseincludes LTE, Wi-Fi and wired home-networking (HomePNA, HomePlug, G.hn)networking standards. Zeev Kaplan has a BSc. and MSc. in ElectricalEngineering from the Technion – Israel Institute of Technology.

**References: **

P.W.Wolniansky, G.J. Foschini, G.D. Golden and R.A. Valenzuela, “V-blast:an architecture for realizing very high data rates over therich-scattering wireless channel”, Signals, Systems, and Electronics,URSI International Symposium on, vol. 1998, pp. 295-300, 1998.

B. M. Hochwald and S. ten Brink, “Achieving near-capacity on a multiple-antenna channel”.

Y.Lomnitz and D. Andelman, “Ef?cient maximum likelihood detector for MIMOsystems with small number of streams”, Electronics Letters, vol. 43,no. 22, pp. 1212–1214, 2007.

M. Siti, and M.P. Fitz, “A NovelSoft-Output Layered Orthogonal Lattice Detector for Multiple AntennaCommunications”, IEEE International Conference Communications, 2006. ICC’06.