Maximum Likelihood (ML) Detection Algorithm for 2x2 MIMO with QPSK Modulation

This article focuses on the 2x2 antenna configuration and modulation order 2, but let's explore these concepts in greater depth regarding their significance and functionality in communication systems.

First, the 2x2 antenna configuration refers to a Multiple-Input Multiple-Output (MIMO) system employing two transmitting and two receiving antennas. This setup enables simultaneous transmission and reception of wireless signals across multiple spatial paths, significantly enhancing signal coverage and data transmission rates. From an implementation perspective, a 2x2 MIMO system can be modeled using a channel matrix H ∈ C^(2×2), where each element h_ij represents the complex channel gain between transmit antenna j and receive antenna i. The spatial diversity achieved through this configuration helps mitigate signal interference and fading, thereby improving communication quality and reliability. In code implementation, this typically involves channel estimation algorithms and spatial multiplexing techniques.

Second, modulation order 2 commonly refers to Quadrature Phase Shift Keying (QPSK) modulation in digital signal processing. In this modulation scheme, each symbol carries 2 bits of information, effectively doubling the data transmission rate compared to BPSK. The QPSK constellation consists of four points located at 45°, 135°, 225°, and 315° phases, represented mathematically as s_k = exp(j(2π(k-1)/4 + π/4)) for k=1,2,3,4. From an algorithmic perspective, QPSK demodulation involves phase detection and decision boundaries at ±π/4 and ±3π/4. This modulation technique demonstrates superior resistance to multipath fading and noise interference compared to higher-order modulations, while maintaining reasonable implementation complexity. In practical systems, QPSK is often implemented using I/Q modulators and coherent detection receivers with carrier recovery loops.

In summary, both 2x2 antenna configurations and modulation order 2 (QPSK) are fundamental concepts in modern communication systems. Their combined implementation through ML detection algorithms significantly enhances data transmission speed, communication quality, and system reliability. The Maximum Likelihood detector for this scenario computes the Euclidean distance between received signals and all possible transmitted symbol combinations, selecting the hypothesis that minimizes ||y - Hx||², where y is the received vector and x is the candidate transmit symbol vector from the QPSK constellation.