# Uni-Cycle Genetic Algorithm as an Adaptation Engine for Wireless Channel Equalizers
## 1 Introduction  
Adaptation refers to a chain of steps needed by the filter to adjust its parameters (coefficients) in accordance with the input data so that its characteristics are optimized [1]. Adaptive equalizers create a subgroup of adaptive filters. The area of adaptive equalization has found wide usage in all forms of communication systems. In a communication system transmitting over a wireless channel, the adaptive equalizer is applied to compensate for the harmful effects of multipath transmission on the received signal quality [2]. Adaptation or learning algorithm is one of the characteristics that define the adaptive equalizer, i.e., it specifies how the coefficients are adjusted from one time instant to the next. RLS exemplifies one of the well-known adaptation algorithms used to tune adaptive equalizer coefficients. RLS algorithm possesses a fast convergence rate, which is measured by the number of adaptation cycles (iterations) necessary to accomplish a solution exhibiting satisfactorily low mean square error (MSE). A disadvantage of RLS is high computational complexity [3]. A couple of years ago, evolutionary algorithms, such as the GA, gained researchers' attention as an optimization framework in the field of wireless communication systems [4, 5]. Giving consideration to equalization, [PERSON] et al. [6] introduced an integrated learning algorithm by hybridizing the standard Least Mean Square (LMS) with the GA; the algorithm is capable of tuning both Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters. The GA-based equalizer for a wireless communication system that incorporates direct sequence ultra-wideband (DS-UWB) signal spreading has been considered in [7]. In [8], GA was used to estimate the coefficients of high-order IIR filters by applying a time-frequency fitness function. [PERSON] et al. [9] combined a so-called micro-GA (i.e., a version of GA with small population size assumed) with the Viterbi algorithm. As a result, data estimation is conducted jointly with channel estimation. However, the method does not allow channel tracking; it seems clear that the channel equalizer from [9] would require periodical injections of training sequences for re-tuning. Undoubtedly, the GA has been known for years, but that does not dismiss this method. On the contrary, we believe it is still worth being developed and improved. The GA employsa population search strategy and utilizes probabilistic transition rules. The search directions are controlled by the objective function and corresponding fitness levels. Therefore, the GA is quite good at navigating through broad search spaces and can quickly reach the globally optimal solution to the optimization problem [10]. The UCGA, considered herein, has been introduced in [11] as an adaptation engine for linear channel equalizers. In the cited work, the GA considers just one generation per one signaling interval, which seems to be enough for efficient channel tracking--a key feature of the systems transmitting over nonstationary radio channels. Accordingly, the optimal settings of the equalizer's taps continue on changing in the sequel of the change of channel conditions. The UCGA computational cost is significantly smaller than that of the regular GA. (The original GA must process hundreds of generations per one signaling interval before it can output a vector containing the optimal equalizer coefficients). From [11], it can be concluded that in the performance contest between the popular LMS-based equalizer and the considered UCGA-based equalizer, the latter is an undisputed winner. In the current research, we consider RLS as the reference equalizer algorithm instead of LMS. Additionally, we explore an alternative method of the UCGA initialization and check if the single-1 initialization, introduced hereinafter, can add any gain to the system performance. The remaining part of the paper is organized as follows: In Section 2, the system model and the tools, used in the current research, are introduced. Section 3 describes the UCGA details.